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Search Results (461)

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16 pages, 2102 KiB  
Article
Semantic Segmentation Method for High-Resolution Tomato Seedling Point Clouds Based on Sparse Convolution
by Shizhao Li, Zhichao Yan, Boxiang Ma, Shaoru Guo and Hongxia Song
Agriculture 2025, 15(1), 74; https://doi.org/10.3390/agriculture15010074 (registering DOI) - 31 Dec 2024
Viewed by 166
Abstract
Semantic segmentation of three-dimensional (3D) plant point clouds at the stem-leaf level is foundational and indispensable for high-throughput tomato phenotyping systems. However, existing semantic segmentation methods often suffer from issues such as low precision and slow inference speed. To address these challenges, we [...] Read more.
Semantic segmentation of three-dimensional (3D) plant point clouds at the stem-leaf level is foundational and indispensable for high-throughput tomato phenotyping systems. However, existing semantic segmentation methods often suffer from issues such as low precision and slow inference speed. To address these challenges, we propose an innovative encoding-decoding structure, incorporating voxel sparse convolution (SpConv) and attention-based feature fusion (VSCAFF) to enhance semantic segmentation of the point clouds of high-resolution tomato seedling images. Tomato seedling point clouds from the Pheno4D dataset labeled into semantic classes of ‘leaf’, ‘stem’, and ‘soil’ are applied for the semantic segmentation. In order to reduce the number of parameters so as to further improve the inference speed, the SpConv module is designed to function through the residual concatenation of the skeleton convolution kernel and the regular convolution kernel. The feature fusion module based on the attention mechanism is designed by giving the corresponding attention weights to the voxel diffusion features and the point features in order to avoid the ambiguity of points with different semantics having the same characteristics caused by the diffusion module, in addition to suppressing noise. Finally, to solve model training class bias caused by the uneven distribution of point cloud classes, the composite loss function of Lovász-Softmax and weighted cross-entropy is introduced to supervise the model training and improve its performance. The results show that mIoU of VSCAFF is 86.96%, which outperformed the performance of PointNet, PointNet++, and DGCNN, respectively. IoU of VSCAFF achieves 99.63% in the soil class, 64.47% in the stem class, and 96.72% in the leaf class. The time delay of 35ms in inference speed is better than PointNet++ and DGCNN. The results demonstrate that VSCAFF has high performance and inference speed for semantic segmentation of high-resolution tomato point clouds, and can provide technical support for the high-throughput automatic phenotypic analysis of tomato plants. Full article
(This article belongs to the Section Digital Agriculture)
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<p>The raw tomato seedling point cloud and point cloud labeled into semantic classes of ‘leaf’, and ‘stem’, and ‘soil’.</p>
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<p>The structure of network.</p>
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<p>Encoding-decodin g architecture based on SpConv.</p>
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<p>Three kinds of convolution kernel structures.</p>
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<p>Attention-based feature fusion method.</p>
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<p>Semantic segmentation of the tomato plant point clouds. Note1: GT represents ground truth. Note2: Four seedling point clouds scanned in four discrete days represented.</p>
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15 pages, 4991 KiB  
Article
Enhanced Small Reflections Sparse-Spike Seismic Inversion with Iterative Hybrid Thresholding Algorithm
by Yue Feng, Ronghuo Dai and Zidan Fan
Mathematics 2025, 13(1), 37; https://doi.org/10.3390/math13010037 - 26 Dec 2024
Viewed by 331
Abstract
Seismic inversion is a process of imaging or predicting the spatial and physical properties of underground strata. The most commonly used one is sparse-spike seismic inversion with sparse regularization. There are many effective methods to solve sparse regularization, such as L0-norm, L1-norm, weighted [...] Read more.
Seismic inversion is a process of imaging or predicting the spatial and physical properties of underground strata. The most commonly used one is sparse-spike seismic inversion with sparse regularization. There are many effective methods to solve sparse regularization, such as L0-norm, L1-norm, weighted L1-norm, etc. This paper studies the sparse-spike inversion with L0-norm. It is usually solved by the iterative hard thresholding algorithm (IHTA) or its faster variants. However, hard thresholding algorithms often lead to a sharp increase or numerical oscillation of the residual, which will affect the inversion results. In order to deal with this issue, this paper attempts the idea of the relaxed optimal thresholding algorithm (ROTA). In the solution process, due to the particularity of the sparse constraints in this convex relaxation model, this model can be considered as a L1-norm problem when dealt with the location of non-zero elements. We use a modified iterative soft thresholding algorithm (MISTA) to solve it. Hence, it forms a new algorithm called the iterative hybrid thresholding algorithm (IHyTA), which combines IHTA and MISTA. The synthetic and real seismic data tests show that, compared with IHTA, the results of IHyTA are more accurate with the same SNR. IHyTA improves the noise resistance. Full article
(This article belongs to the Special Issue Inverse Problems and Numerical Computation in Mathematical Physics)
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<p>Synthetic seismic data. (<b>a</b>) Noise free; (<b>b</b>) Noise-contaminated synthetic seismic data with 5% Gaussian random noise; (<b>c</b>) Noise-contaminated synthetic seismic data with 20% Gaussian random noise.</p>
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<p>The true reflectivity series and inverted reflectivity series with synthetic seismic data in <a href="#mathematics-13-00037-f001" class="html-fig">Figure 1</a>b. (<b>a</b>) true; (<b>b</b>) IHTA; (<b>c</b>) IHyTA.</p>
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<p>The true impedance and inverted impedance with synthetic seismic data in <a href="#mathematics-13-00037-f001" class="html-fig">Figure 1</a>b. (<b>a</b>) true; (<b>b</b>) IHTA; (<b>c</b>) IHyTA.</p>
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<p>The true reflectivity series and inverted reflectivity series with synthetic seismic data in <a href="#mathematics-13-00037-f001" class="html-fig">Figure 1</a>c. (<b>a</b>) true; (<b>b</b>) IHTA; (<b>c</b>) IHyTA.</p>
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<p>The true impedance and inverted impedance with synthetic seismic data in <a href="#mathematics-13-00037-f001" class="html-fig">Figure 1</a>c. (<b>a</b>) true; (<b>b</b>) IHTA; (<b>c</b>) IHyTA.</p>
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<p>The real seismic data profile for Inline 598, and its corresponding inverted reflectivity series profiles and inverted impedance profiles. (<b>a</b>) real seismic data; (<b>b</b>) reflectivity series; (<b>c</b>) impedance.</p>
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<p>The real seismic data profile for Inline 598, and its corresponding inverted reflectivity series profiles and inverted impedance profiles. (<b>a</b>) real seismic data; (<b>b</b>) reflectivity series; (<b>c</b>) impedance.</p>
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<p>The real seismic data for Crossline 800, and its corresponding inverted reflectivity series profiles and inverted impedance profiles. (<b>a</b>) real seismic data; (<b>b</b>) reflectivity series; (<b>c</b>) impedance.</p>
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<p>The real seismic data for Crossline 800, and its corresponding inverted reflectivity series profiles and inverted impedance profiles. (<b>a</b>) real seismic data; (<b>b</b>) reflectivity series; (<b>c</b>) impedance.</p>
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<p>The single trace comparison between well log data and inverted impedance. The red curve is well log, the blue curve is inverted impedance.</p>
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13 pages, 695 KiB  
Review
Stroke in Athletes with Atrial Fibrillation: A Narrative Review
by Joana Certo Pereira, Maria Rita Lima, Francisco Moscoso Costa, Daniel A. Gomes, Sérgio Maltês, Gonçalo Cunha, Hélder Dores and Pedro Adragão
Diagnostics 2025, 15(1), 9; https://doi.org/10.3390/diagnostics15010009 - 25 Dec 2024
Viewed by 266
Abstract
Atrial fibrillation (AF) is the most common sustained arrhythmia, linked with a significantly heightened risk of stroke. While moderate exercise reduces AF risk, high-level endurance athletes paradoxically exhibit a higher incidence. However, their stroke risk remains uncertain due to their younger age, higher [...] Read more.
Atrial fibrillation (AF) is the most common sustained arrhythmia, linked with a significantly heightened risk of stroke. While moderate exercise reduces AF risk, high-level endurance athletes paradoxically exhibit a higher incidence. However, their stroke risk remains uncertain due to their younger age, higher cardiovascular fitness, and lower rate of comorbidities. Several key studies highlight that AF may increase the risk of stroke in endurance athletes, particularly those over 65. However, the overall risk within this population remains relatively low. Notably, older male athletes show a higher AF incidence but experience lower stroke risk than their non-athletic counterparts. Regular physical activity prior to a first stroke appears to reduce mortality, though recurrent stroke risk in athletes with AF mirrors that of non-athletes, despite an elevated AF incidence. Management of AF in athletes is complex, with limited evidence guiding anti-thrombotic strategies. In this setting, specific recommendations are sparse, particularly in sports where bleeding risk is heightened. Individualized management, emphasizing shared decision-making, is critical to balance stroke prevention with athletic performance. Rhythm control strategies, such as catheter ablation, may be a reasonable first-line treatment option for athletes, particularly in those desiring to avoid long-term medication. This review synthesizes the current literature on the incidence, predictors, and management of stroke in athletes with AF. Full article
(This article belongs to the Special Issue Diagnosis and Management of Arrhythmias)
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<p>Relationship between exercise, AF, and stroke.</p>
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17 pages, 1524 KiB  
Article
Discovering PDEs Corrections from Data Within a Hybrid Modeling Framework
by Chady Ghnatios and Francisco Chinesta
Mathematics 2025, 13(1), 5; https://doi.org/10.3390/math13010005 - 24 Dec 2024
Viewed by 290
Abstract
In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven [...] Read more.
In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven enrichment is usually represented by a regression, whose main drawbacks are (i) the difficulty of understanding the subjacent physics and (ii) the risks induced by the data-driven model extrapolation. This paper proposes a procedure enabling the extraction of a differential operator associated with the enrichment provided by the data-driven regression. For that purpose, a sparse Singular Value Decomposition, SVD, is introduced. It is then employed, first, in a full operator representation regularized optimization problem, where sparsity is promoted, leading to a linear programming problem, and then in a tensor decomposition of the operator’s identification procedure. The results show the ability of the method to identify the exact missing operators from the model. The regularized optimization problem was also able to identify the weights of the missing terms with a relative error of about 10% on average, depending on the selected use case. Full article
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<p>Solution and discrepancy of the problem defined in Equation (<a href="#FD28-mathematics-13-00005" class="html-disp-formula">28</a>). (<b>a</b>) Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> of Equation (<a href="#FD28-mathematics-13-00005" class="html-disp-formula">28</a>). (<b>b</b>) Difference between the reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> of the solution of the physics-based model <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Solution of the physics-based problem <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> and discrepancy <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> related to Problem (<a href="#FD29-mathematics-13-00005" class="html-disp-formula">29</a>). (<b>a</b>) Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) Discrepancy <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> and discrepancy <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> related to the problem (<a href="#FD30-mathematics-13-00005" class="html-disp-formula">30</a>). (<b>a</b>) Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> and discrepancy <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> related to the Problem (<a href="#FD31-mathematics-13-00005" class="html-disp-formula">31</a>). (<b>a</b>) Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math> and discrepancy <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> related to the Problem (<a href="#FD32-mathematics-13-00005" class="html-disp-formula">32</a>). (<b>a</b>) Reference solution <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Non-separated approximation of the reference solution and the discrepancy. (<b>a</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>u</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msup> <mover accent="true"> <mi>u</mi> <mo stretchy="false">^</mo> </mover> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>u</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <msup> <mover accent="true"> <mi>u</mi> <mo stretchy="false">^</mo> </mover> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>u</mi> <mi>c</mi> </msup> <mrow> <mo>(</mo> <mi mathvariant="bold">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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16 pages, 5341 KiB  
Article
A Sparse Representation-Based Reconstruction Method of Electrical Impedance Imaging for Grounding Grid
by Ke Zhu, Donghui Luo, Zhengzheng Fu, Zhihang Xue and Xianghang Bu
Energies 2024, 17(24), 6459; https://doi.org/10.3390/en17246459 - 22 Dec 2024
Viewed by 283
Abstract
As a non-invasive imaging method, electrical impedance tomography (EIT) technology has become a research focus for grounding grid corrosion diagnosis. However, the existing algorithms have not produced ideal image reconstruction results. This article proposes an electrical impedance imaging method based on sparse representation, [...] Read more.
As a non-invasive imaging method, electrical impedance tomography (EIT) technology has become a research focus for grounding grid corrosion diagnosis. However, the existing algorithms have not produced ideal image reconstruction results. This article proposes an electrical impedance imaging method based on sparse representation, which can improve the accuracy of reconstructed images obviously. First, the basic principles of EIT are outlined, and the limitations of existing reconstruction methods are analyzed. Then, an EIT reconstruction algorithm based on sparse representation is proposed to address these limitations. It constructs constraints using the sparsity of conductivity distribution under a certain sparse basis and utilizes the accelerated Fast Iterative Shrinkage Threshold Algorithm (FISTA) for iterative solutions, aiming to improve the imaging quality and reconstruction accuracy. Finally, the grounding grid model is established by COMSOL simulation software to obtain voltage data, and the reconstruction effects of the Tikhonov regularization algorithm, the total variation regularization algorithm (TV), the one-step Newton algorithm (NOSER), and the sparse reconstruction algorithm proposed in this article are compared in MATLAB. The voltage relative error is introduced to evaluate the reconstructed image. The results show that the reconstruction algorithm based on sparse representation is superior to other methods in terms of reconstruction error and image quality. The relative error of the grounding grid reconstructed image is reduced by an average of 12.54%. Full article
(This article belongs to the Special Issue Simulation and Analysis of Electrical Power Systems)
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<p>Schematic diagram of the corrosion diagnosis by EIT technology.</p>
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<p>Schematic diagram of sparse representation.</p>
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<p>Schematic diagram of adjacent excitation.</p>
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<p>Grounding grid model.</p>
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<p>Meshing grid of inverse problem.</p>
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<p>Single branch corrosion imaging.</p>
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<p>Dual-branch corrosion imaging.</p>
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<p>GCV optimization result for regularization parameter.</p>
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<p>Reconstructed images under different regularization parameters.</p>
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<p>Voltage waveforms without noise and with noise (SNR = 20 dB).</p>
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<p>Imaging with noise (SNR = 20 dB).</p>
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<p>Voltage waveforms without noise and with noise (SNR = 30 dB).</p>
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<p>Imaging with noise (SNR = 30 dB).</p>
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<p>Multi-grid corrosion settings.</p>
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<p>Multi-grid imaging comparison: 3 × 3 Grid.</p>
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<p>Multi-grid imaging comparison: 3 × 1 Grid.</p>
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<p>Comparison of voltage relative error.</p>
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22 pages, 1890 KiB  
Article
FedSparse: A Communication-Efficient Federated Learning Framework Based on Sparse Updates
by Jiachen Li, Yuchao Zhang, Yiping Li, Xiangyang Gong and Wendong Wang
Electronics 2024, 13(24), 5042; https://doi.org/10.3390/electronics13245042 - 22 Dec 2024
Viewed by 347
Abstract
Federated learning (FL) strikes a balance between privacy preservation and collaborative model training. However, the periodic transmission of model updates or parameters from each client to the federated server incurs substantial communication overhead, especially for participants with limited network bandwidth. This overhead significantly [...] Read more.
Federated learning (FL) strikes a balance between privacy preservation and collaborative model training. However, the periodic transmission of model updates or parameters from each client to the federated server incurs substantial communication overhead, especially for participants with limited network bandwidth. This overhead significantly hampers the practical applicability of FL in real-world scenarios. To address this challenge, we propose FedSparse, an innovative sparse communication framework designed to enhance communication efficiency. The core idea behind FedSparse is to introduce a communication overhead regularization term into the client’s objective function, thereby reducing the number of parameters that need to be transmitted. FedSparse incorporates a Resource Optimization Proximal (ROP) term and an Importance-based Regularization Weighting (IRW) mechanism into the client update objective function. The local update process optimizes both the empirical risk and communication overhead by applying a sparse regularization weighted by update importance. By making minimal modifications to traditional FL approaches, FedSparse effectively reduces the number of parameters transmitted, thereby decreasing the communication overhead. We evaluate the effectiveness of FedSparse through experiments on various datasets under non-independent and identically distributed (non-IID) conditions, demonstrating its flexibility in resource-constrained environments. On the MNIST, Fashion-MNIST, and CIFAR datasets, FedSparse reduces the communication overhead by 24%, 17%, and 5%, respectively, compared to the baseline algorithm, while maintaining similar model performance. Additionally, on simulated non-IID datasets, FedSparse achieves a 6% to 8% reduction in communication resource consumption. By adjusting the sparsity intensity hyperparameter, we demonstrate that FedSparse can be tailored to different FL applications with varying communication resource constraints. Finally, ablation studies highlight the individual contributions of the ROP and IRW modules to the overall improvement in communication efficiency. Full article
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<p>The framework of federated learning.</p>
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<p>Comparison of the convergence processes of the model across three datasets.</p>
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<p>A comparison of the average communication sparsity rates and the sparsity rate variations during the convergence process across the MNIST, Fashion, and CIFAR datasets.</p>
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<p>Comparison of convergence performance under different non-IID settings.</p>
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<p>Comparison of communication sparsity rates under different non-IID settings.</p>
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<p>Model convergence performance under different sparsity intensity (SI) settings.</p>
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<p>Model accuracy across convergence process at different SI settings.</p>
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<p>The variation of sparsity rates during the convergence process under different SI settings.</p>
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<p>Average communication sparsity rate under different SI settings.</p>
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<p>On the Fashion-MNIST and MNIST datasets, we conduct ablation studies to evaluate the impact of ROP and the additional introduction of the IRW module on the convergence performance and communication sparsity rates. Figure (<b>a</b>) illustrates the convergence performance of the different methods, while (<b>b</b>,<b>c</b>) show the communication sparsity rates during the convergence process and the average communication sparsity rates for each method, respectively.</p>
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24 pages, 46652 KiB  
Article
Hyperspectral Reconstruction Method Based on Global Gradient Information and Local Low-Rank Priors
by Chipeng Cao, Jie Li, Pan Wang, Weiqiang Jin, Runrun Zou and Chun Qi
Remote Sens. 2024, 16(24), 4759; https://doi.org/10.3390/rs16244759 - 20 Dec 2024
Viewed by 326
Abstract
Hyperspectral compressed imaging is a novel imaging detection technology based on compressed sensing theory that can quickly acquire spectral information of terrestrial objects in a single exposure. It combines reconstruction algorithms to recover hyperspectral data from low-dimensional measurement images. However, hyperspectral images from [...] Read more.
Hyperspectral compressed imaging is a novel imaging detection technology based on compressed sensing theory that can quickly acquire spectral information of terrestrial objects in a single exposure. It combines reconstruction algorithms to recover hyperspectral data from low-dimensional measurement images. However, hyperspectral images from different scenes often exhibit high-frequency data sparsity and existing deep reconstruction algorithms struggle to establish accurate mapping models, leading to issues with detail loss in the reconstruction results. To address this issue, we propose a hyperspectral reconstruction method based on global gradient information and local low-rank priors. First, to improve the prior model’s efficiency in utilizing information of different frequencies, we design a gradient sampling strategy and training framework based on decision trees, leveraging changes in the loss function gradient information to enhance the model’s predictive capability for data of varying frequencies. Second, utilizing the local low-rank prior characteristics of the representative coefficient matrix, we develop a sparse sensing denoising module to effectively improve the local smoothness of point predictions. Finally, by establishing a regularization term for the reconstruction process based on the semantic similarity between the denoised results and prior spectral data, we ensure spatial consistency and spectral fidelity in the reconstruction results. Experimental results indicate that the proposed method achieves better detail recovery across different scenes, demonstrates improved generalization performance for reconstructing information of various frequencies, and yields higher reconstruction quality. Full article
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<p>Structural composition of the DCCHI system and data structure of SD-CASSI detector sampling.</p>
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<p>Reconstruction algorithm framework.</p>
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<p>RGB images from the KAIST, Harvard, and hyperspectral remote sensing datasets.</p>
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<p>Selected spectral curves of the pixel point with coordinates (180, 70), showing a visual comparison of different methods in the spectral dimension and comparing the pseudocolor images and local spatial detail information under different wavelengths.</p>
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<p>Selected spectral curves of the pixel point with coordinates (150, 100), showing a visual comparison of different methods in the spectral dimension and comparing the pseudocolor images and local spatial detail information of different wavelengths.</p>
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<p>Comparison of the spectral consistency of reconstruction results with different methods on the PaviaU hyperspectral remote sensing datast at sample point coordinates (180, 110), along with a comparison of the spatial detail information of the reconstruction results at different wavelengths.</p>
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<p>Comparison of the spectral consistency of reconstruction results with different methods on the PaviaC hyperspectral remote sensing dataset at sample point coordinates (190, 50), along with a comparison of the spatial detail information of the reconstruction results at different wavelengths.</p>
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<p>Comparison of spectral reconstruction results for different crops.</p>
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<p>Impact of hyperparameter settings on reconstruction quality.</p>
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<p>Comparison of pseudocolor images generated from the predictions of different prior models for the Harvard Scene 04 hyperspectral data at the 5th, 12th, and 25th bands, along with the spectral differences of the predictions at different wavelengths.</p>
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<p>Comparison of pseudocolor images generated from the predictions of different prior models for the PaviaU hyperspectral remote sensing data at the 3rd, 13th, and 26th bands, along with the spectral differences of the predictions at different wavelengths.</p>
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<p>Variation in reconstruction quality with increasing iteration count under the same solving framework for different regularization constraint methods.</p>
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17 pages, 348 KiB  
Article
Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy
by Aaron Lanterman
Stats 2024, 7(4), 1496-1512; https://doi.org/10.3390/stats7040088 - 17 Dec 2024
Viewed by 611
Abstract
Image formation in radio astronomy is often posed as a problem of constructing a nonnegative function from sparse samples of its Fourier transform. We explore an alternative approach that reformulates the problem in terms of estimating the entries of a diagonal covariance matrix [...] Read more.
Image formation in radio astronomy is often posed as a problem of constructing a nonnegative function from sparse samples of its Fourier transform. We explore an alternative approach that reformulates the problem in terms of estimating the entries of a diagonal covariance matrix from Gaussian data. Maximum-likelihood estimates of the covariance cannot be readily computed analytically; hence, we investigate an iterative algorithm originally proposed by Snyder, O’Sullivan, and Miller in the context of radar imaging. The resulting maximum-likelihood estimates tend to be unacceptably rough due to the ill-posed nature of the maximum-likelihood estimation of functions from limited data, so some kind of regularization is needed. We explore penalized likelihoods based on entropy functionals, a roughness penalty proposed by Silverman, and an information-theoretic formulation of Good’s roughness penalty crafted by O’Sullivan. We also investigate algorithm variations that perform a generic smoothing step at each iteration. The results illustrate that tuning parameters allow for a tradeoff between the noise and blurriness of the reconstruction. Full article
(This article belongs to the Section Computational Statistics)
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<p>Fourier sampling pattern associated with the simulated scenario.</p>
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<p>Top row: two 32 × 32 ideal intensity functions used in the simulations. Bottom row: traditional “dirty maps” formed from simulated data. Images in this paper are displayed using MATLAB’s “hot” colormap.</p>
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<p>Results of the unconstrained EM algorithm for two different data sets (shown in different rows). From left to right, the columns show results at 100, 200, and 1000 iterations.</p>
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<p>Results of the unconstrained EM algorithm for two different data sets (shown in different rows). From left to right, the columns show results at 100, 200, and 1000 iterations.</p>
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<p>Results of 1000 iterations of the EM algorithm using Good’s roughness penalty with <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mo>(</mo> <mi>N</mi> <mi>M</mi> <mo>)</mo> <mo>=</mo> <mn>0.002</mn> </mrow> </semantics></math> (left column) and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mo>(</mo> <mi>N</mi> <mi>M</mi> <mo>)</mo> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math> (right column).</p>
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<p>Results of 1000 iterations of the EM algorithm using Silverman’s roughness penalty with <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mo>(</mo> <mi>N</mi> <mi>M</mi> <mo>)</mo> <mo>=</mo> <mn>0.002</mn> </mrow> </semantics></math> (left column) and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mo>(</mo> <mi>N</mi> <mi>M</mi> <mo>)</mo> <mo>=</mo> <mn>0.005</mn> </mrow> </semantics></math> (right column).</p>
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<p>Results of 1000 iterations of an EMS algorithm using the linear smoothing step defined by (<a href="#FD27-stats-07-00088" class="html-disp-formula">27</a>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> (left column) and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.003</mn> </mrow> </semantics></math> (right column).</p>
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<p>The left column shows the results of 1000 iterations of the EMS algorithm using a nearest-neighbor median filter as the smoothing step. The right column shows the results of median filtering 1000 iterations with the unconstrained EM algorithm.</p>
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<p>The left column shows the results of 1000 iterations of the EMS algorithm using a nearest-neighbor median filter as the smoothing step. The right column shows the results of median filtering 1000 iterations with the unconstrained EM algorithm.</p>
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30 pages, 63876 KiB  
Article
A Low-Cost 3D Mapping System for Indoor Scenes Based on 2D LiDAR and Monocular Cameras
by Xiaojun Li, Xinrui Li, Guiting Hu, Qi Niu and Luping Xu
Remote Sens. 2024, 16(24), 4712; https://doi.org/10.3390/rs16244712 - 17 Dec 2024
Viewed by 651
Abstract
The cost of indoor mapping methods based on three-dimensional (3D) LiDAR can be relatively high, and they lack environmental color information, thereby limiting their application scenarios. This study presents an innovative, low-cost, omnidirectional 3D color LiDAR mapping system for indoor environments. The system [...] Read more.
The cost of indoor mapping methods based on three-dimensional (3D) LiDAR can be relatively high, and they lack environmental color information, thereby limiting their application scenarios. This study presents an innovative, low-cost, omnidirectional 3D color LiDAR mapping system for indoor environments. The system consists of two two-dimensional (2D) LiDARs, six monocular cameras, and a servo motor. The point clouds are fused with imagery using a pixel-spatial dual-constrained depth gradient adaptive regularization (PS-DGAR) algorithm to produce dense 3D color point clouds. During fusion, the point cloud is reconstructed inversely based on the predicted pixel depth values, compensating for areas of sparse spatial features. For indoor scene reconstruction, a globally consistent alignment algorithm based on particle filter and iterative closest point (PF-ICP) is proposed, which incorporates adjacent frame registration and global pose optimization to reduce mapping errors. Experimental results demonstrate that the proposed density enhancement method achieves an average error of 1.5 cm, significantly improving the density and geometric integrity of sparse point clouds. The registration algorithm achieves a root mean square error (RMSE) of 0.0217 and a runtime of less than 4 s, both of which outperform traditional iterative closest point (ICP) variants. Furthermore, the proposed low-cost omnidirectional 3D color LiDAR mapping system demonstrates superior measurement accuracy in indoor environments. Full article
(This article belongs to the Special Issue New Perspectives on 3D Point Cloud (Third Edition))
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<p>The structure of the proposed low-cost 3D indoor mapping system.</p>
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<p>Process of associating 3D point clouds with 2D image pixels. From right to left, (i) rigid body transformation from the world coordinate system to the camera coordinate system, (ii) perspective projection from the camera coordinate system to the image plane, (iii) mapping from the image plane to the pixel coordinate system.</p>
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<p>Neighborhood search and depth prediction diagram. The example of a failed prediction is represented by a triangle symbol and highlighted with a red dashed box at the top, while the example of a successful prediction is represented by a star symbol and highlighted with a red dashed box on the far right. At the bottom, the conditions for algorithm convergence and the corresponding output are shown. The arrows represent the prediction steps.</p>
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<p>Globally uniform alignment schematic diagram. The main components include key LiDAR frames (in blue), device poses (in orange) and several state nodes corresponding to the sensor fusion results. The system uses particle filtering (green lines) to update the system state and uses ICP (red dashed lines) to perform registration between adjacent frames. The diagram also highlights the fusion process between LiDAR and device observations to achieve global pose alignment.</p>
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<p>Experimental system design drawing. (<b>a</b>) Structure of a low-cost 3D point cloud acquisition device. (<b>b</b>) Diagram of camera detection range and installation configuration. (<b>c</b>) Overall design diagram of the acquisition system integrated into the UGV.</p>
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<p>Experimental scene layout and partial display. The upper figure is a 2D schematic of the experimental scene, while the lower images show real-world photos from certain nodes along with the measured dimensions of related objects.</p>
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<p>Sampling density analysis of the low-cost 3D point cloud acquisition system, showing the sampling density distribution along the X-axis, Y-axis, and Z-axis from top to bottom.</p>
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<p>The depth prediction result maps generated by the PS-DGAR algorithm and the SuperPixel segmentation-based prediction algorithm at different scan distances, as well as the enhanced 3D point cloud imaging result maps based on these depth maps.</p>
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<p>The point cloud registration results for adjacent frames under different initial transformations are illustrated as follows, from top to bottom: initial transformation, G−ICP, R−ICP, M−ICP, FGR, and the proposed PF−ICP method. Specifically, (<b>a</b>) an initial transformation involving only translation along the x-axis without any rotation (<math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mn>3.0</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0.0</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.0</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, roll <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math>, pitch <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math>, yaw <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math>). (<b>b</b>) An initial transformation with translation along the x-axis and slight rotation about the three axes (<math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mn>3.144</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0.001</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.0</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, roll <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>002</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, pitch <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>.</mo> <msup> <mn>004</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, yaw <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>001</mn> <mo>°</mo> </msup> </mrow> </semantics></math>). (<b>c</b>) An initial transformation involving translation along the y-axis and significant rotation (<math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mn>0.004</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>2.4</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mo>−</mo> <mn>0.001</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, roll <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>001</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, pitch <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>001</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, yaw <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>90</mn> <mo>°</mo> </msup> </mrow> </semantics></math>).</p>
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<p>Result of globally consistent indoor colored map reconstruction. Subfigures (<b>a</b>–<b>f</b>) show the mapping results and real scenes of randomly selected indoor scene nodes.</p>
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<p>Three-dimensional imaging results of indoor complex environments.</p>
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33 pages, 30049 KiB  
Article
Blind Infrared Remote-Sensing Image Deblurring Algorithm via Edge Composite-Gradient Feature Prior and Detail Maintenance
by Xiaohang Zhao, Mingxuan Li, Ting Nie, Chengshan Han and Liang Huang
Remote Sens. 2024, 16(24), 4697; https://doi.org/10.3390/rs16244697 - 16 Dec 2024
Viewed by 411
Abstract
The problem of blind image deblurring remains a challenging inverse problem, due to the ill-posed nature of estimating unknown blur kernels and latent images within the Maximum A Posteriori (MAP) framework. To address this challenge, traditional methods often rely on sparse regularization priors [...] Read more.
The problem of blind image deblurring remains a challenging inverse problem, due to the ill-posed nature of estimating unknown blur kernels and latent images within the Maximum A Posteriori (MAP) framework. To address this challenge, traditional methods often rely on sparse regularization priors to mitigate the uncertainty inherent in the problem. In this paper, we propose a novel blind deblurring model based on the MAP framework that leverages Composite-Gradient Feature (CGF) variations in edge regions after image blurring. This prior term is specifically designed to exploit the high sparsity of sharp edge regions in clear images, thereby effectively alleviating the ill-posedness of the problem. Unlike existing methods that focus on local gradient information, our approach focuses on the aggregation of edge regions, enabling better detection of both sharp and smoothed edges in blurred images. In the blur kernel estimation process, we enhance the accuracy of the kernel by assigning effective edge information from the blurred image to the smoothed intermediate latent image, preserving critical structural details lost during the blurring process. To further improve the edge-preserving restoration, we introduce an adaptive regularizer that outperforms traditional total variation regularization by better maintaining edge integrity in both clear and blurred images. The proposed variational model is efficiently implemented using alternating iterative techniques. Extensive numerical experiments and comparisons with state-of-the-art methods demonstrate the superior performance of our approach, highlighting its effectiveness and real-world applicability in diverse image-restoration tasks. Full article
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<p>Degraded image characterization: (<b>a</b>) original image; (<b>b</b>) degraded image; (<b>c</b>) clear-image edge-area gradients; (<b>d</b>) blurred-image edge-area gradients; (<b>f</b>) gradient-direction difference matrix of clear images; (<b>g</b>) gradient-direction difference matrix of blurred images; (<b>i</b>) clear image <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">E</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </semantics></math> preserves the edge region; (<b>j</b>) blurred image <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">E</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </semantics></math> preserves the edge region; (<b>k</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2016;" close="&#x2016;" separators="|"> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">S</mi> </mrow> <mrow> <mi mathvariant="bold-italic">I</mi> </mrow> </msub> <mo>−</mo> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </mfenced> </mrow> </semantics></math> of clear image; (<b>l</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2016;" close="&#x2016;" separators="|"> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">S</mi> </mrow> <mrow> <mi mathvariant="bold-italic">I</mi> </mrow> </msub> <mo>−</mo> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </mfenced> </mrow> </semantics></math> of blurred image; (<b>e</b>) comparison of <span class="html-italic">L</span>1 norm of edge gradients between clear and blurred images; (<b>h</b>) comparison of <span class="html-italic">L</span>1 norm of gradient-direction difference matrix between clear and blurred images.</p>
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<p>Degraded image characterization: (<b>a</b>) original image; (<b>b</b>) degraded image; (<b>c</b>) clear-image edge-area gradients; (<b>d</b>) blurred-image edge-area gradients; (<b>f</b>) gradient-direction difference matrix of clear images; (<b>g</b>) gradient-direction difference matrix of blurred images; (<b>i</b>) clear image <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">E</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </semantics></math> preserves the edge region; (<b>j</b>) blurred image <math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">E</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </semantics></math> preserves the edge region; (<b>k</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2016;" close="&#x2016;" separators="|"> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">S</mi> </mrow> <mrow> <mi mathvariant="bold-italic">I</mi> </mrow> </msub> <mo>−</mo> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </mfenced> </mrow> </semantics></math> of clear image; (<b>l</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2016;" close="&#x2016;" separators="|"> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">S</mi> </mrow> <mrow> <mi mathvariant="bold-italic">I</mi> </mrow> </msub> <mo>−</mo> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> <mo>(</mo> <mi mathvariant="bold-italic">I</mi> <mo>)</mo> </mrow> </mfenced> </mrow> </semantics></math> of blurred image; (<b>e</b>) comparison of <span class="html-italic">L</span>1 norm of edge gradients between clear and blurred images; (<b>h</b>) comparison of <span class="html-italic">L</span>1 norm of gradient-direction difference matrix between clear and blurred images.</p>
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<p>Composition of the prior term and main flowchart of the algorithm.</p>
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<p><math display="inline"><semantics> <mrow> <mi mathvariant="bold-italic">E</mi> <mfenced separators="|"> <mrow> <mi>I</mi> </mrow> </mfenced> </mrow> </semantics></math> Mechanism for selecting edge-area gradient pixels.</p>
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<p>The visual differences in edge region selection of C<span class="html-italic">GF</span>(<span class="html-italic"><b>I</b> </span>): (<b>a</b>) the grayscale differences before and after image blurring; (<b>b</b>) the differences in <b><span class="html-italic">E</span> </b>(<span class="html-italic">I</span>) selection for edge regions before and after image blurring; (<b>c</b>) the <span class="html-italic">∇</span>(<span class="html-italic"><b>I</b> </span>) differences before and after image blurring; (<b>d</b>) the <span class="html-italic">φ</span>(<b><span class="html-italic">H</span> </b>(<b><span class="html-italic">I</span> </b>)(<span class="html-italic">s</span>)) differences before and after image blurring.</p>
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<p>Comparison before and after intermediate latent-image detail compensation: (<b>a</b>) before detail compensation; (<b>b</b>) after detail compensation.</p>
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<p>Recovery results of images from image A: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Recovery results of images from image B: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
Full article ">Figure 7 Cont.
<p>Recovery results of images from image B: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Recovery results of images from image C: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Recovery results of images from image D: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Recovery results of images from image E: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Recovery results of images from image F: (<b>a</b>) blurred image (<b>b</b>) TRIP; (<b>c</b>) FMIR; (<b>d</b>) CSRDIR (<b>e</b>) PMG; (<b>f</b>) extreme; (<b>g</b>) PMP; (<b>h</b>) HCTIR; (<b>i</b>) DCP; (<b>j</b>) proposed.</p>
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<p>Evaluation metrics for various methods: (<b>a</b>) PSNR; (<b>b</b>) SSIM; (<b>c</b>) VIF; (<b>d</b>) NIQE; (<b>e</b>) DE; (<b>f</b>) EME.</p>
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<p>Evaluation metrics for various methods: (<b>a</b>) PSNR; (<b>b</b>) SSIM; (<b>c</b>) VIF; (<b>d</b>) NIQE; (<b>e</b>) DE; (<b>f</b>) EME.</p>
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<p>Evaluation metrics for various methods: (<b>a</b>) PSNR; (<b>b</b>) SSIM; (<b>c</b>) VIF; (<b>d</b>) NIQE; (<b>e</b>) DE; (<b>f</b>) EME.</p>
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<p>Quantitative evaluation of <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>G</mi> <mi>F</mi> </mrow> </semantics></math> prior and the other priors on the dataset: (<b>a</b>) contrast between our method with and without <math display="inline"><semantics> <mrow> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> </mrow> </semantics></math>; (<b>b</b>) contrast of our method with other methods with the only distinction being the use of different prior terms.</p>
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<p>Intermediate latent-image results of our method and the other methods on the dataset: (<b>a</b>) intermediate latent-image results of PMG; (<b>b</b>) intermediate latent-image results of extreme channels; (<b>c</b>) intermediate latent-image results of dark channels; (<b>d</b>) intermediate latent-image results of PMP; (<b>e</b>) intermediate latent- image results of HCTIR; (<b>f</b>) intermediate latent-image results of ours.</p>
Full article ">Figure 14 Cont.
<p>Intermediate latent-image results of our method and the other methods on the dataset: (<b>a</b>) intermediate latent-image results of PMG; (<b>b</b>) intermediate latent-image results of extreme channels; (<b>c</b>) intermediate latent-image results of dark channels; (<b>d</b>) intermediate latent-image results of PMP; (<b>e</b>) intermediate latent- image results of HCTIR; (<b>f</b>) intermediate latent-image results of ours.</p>
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<p>Quantitative evaluation of our method and the other methods on the dataset: (<b>a</b>) comparison of our method with and without <math display="inline"><semantics> <mrow> <mi mathvariant="normal">C</mi> <mi>G</mi> <mi>F</mi> </mrow> </semantics></math>; (<b>b</b>) comparison of our method with the other methods.</p>
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<p>Relationship between PSNR and the parameter patch size <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mi>q</mi> </mrow> </msub> <mo>.</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the recovery results of our method with the other methods: (<b>a</b>) blurred image; (<b>b</b>) dark-channel + traditional TV deconvolution; (<b>c</b>) dark-channel + edge-preservation deconvolution; (<b>d</b>) ours.</p>
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<p>Comparison of the recovery results of our method with the other methods: (<b>a</b>) blurred image; (<b>b</b>) extreme channel + traditional TV deconvolution; (<b>c</b>) extreme channel + edge-preservation deconvolution; (<b>d</b>) ours.</p>
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<p>Comparison of the recovery results of our method with the other methods: (<b>a</b>) blurred image; (<b>b</b>) PMP + traditional TV deconvolution; (<b>c</b>) PMP + edge-preservation deconvolution; (<b>d</b>) ours.</p>
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<p>Sensitivity analysis of three main parameters <math display="inline"><semantics> <mrow> <mi>τ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> in our model on the dataset: (<b>a</b>) the parameter sensitivity of <math display="inline"><semantics> <mrow> <mi>τ</mi> </mrow> </semantics></math>; (<b>b</b>) the parameter sensitivity of <math display="inline"><semantics> <mrow> <mi>γ</mi> </mrow> </semantics></math>; (<b>c</b>) the parameter sensitivity of <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>.</p>
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<p>Gaussian noise-robustness testing results: (<b>a</b>) original image; (<b>b</b>) degenerate fuzzy kernel; (<b>c</b>) fuzzy kernel; (<b>d</b>) evaluation index of each method; (<b>e</b>) noisy images with different noise density levels.</p>
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<p>Salt-and-pepper noise-robustness testing results: (<b>a</b>) original image; (<b>b</b>) degenerate fuzzy kernel; (<b>c</b>) fuzzy kernel; (<b>d</b>) evaluation index of each method; (<b>e</b>) noisy images with different noise density levels.</p>
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22 pages, 1503 KiB  
Article
Deep Neural Networks for Estimating Regularization Parameter in Sparse Time–Frequency Reconstruction
by Vedran Jurdana
Technologies 2024, 12(12), 251; https://doi.org/10.3390/technologies12120251 - 1 Dec 2024
Viewed by 1185
Abstract
Time–frequency distributions (TFDs) are crucial for analyzing non-stationary signals. Compressive sensing (CS) in the ambiguity domain offers an approach for TFD reconstruction with high performance, but selecting the optimal regularization parameter for various signals remains challenging. Traditional methods for parameter selection, including manual [...] Read more.
Time–frequency distributions (TFDs) are crucial for analyzing non-stationary signals. Compressive sensing (CS) in the ambiguity domain offers an approach for TFD reconstruction with high performance, but selecting the optimal regularization parameter for various signals remains challenging. Traditional methods for parameter selection, including manual and experimental approaches, as well as existing optimization procedures, can be imprecise and time-consuming. This study introduces a novel approach using deep neural networks (DNNs) to predict regularization parameters based on Wigner–Ville distributions (WVDs). The proposed DNN is trained on a comprehensive dataset of synthetic signals featuring multiple linear and quadratic frequency-modulated components, with variations in component amplitudes and random positions, ensuring wide applicability and robustness. By utilizing DNNs, end-users need only provide the signal’s WVD, eliminating the need for manual parameter selection and lengthy optimization procedures. Comparisons between the reconstructed TFDs using the proposed DNN-based approach and existing optimization methods highlight significant improvements in both reconstruction performance and execution time. The effectiveness of this methodology is validated on noisy synthetic and real-world signals, emphasizing the potential of DNNs to automate regularization parameter determination for CS-based TFD reconstruction in diverse signal environments. Full article
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<p>Considering synthetic signal with two crossing components: (<b>a</b>) TFD; (<b>b</b>) ideal (<math display="inline"><semantics> <msub> <mover accent="true"> <mi>M</mi> <mo stretchy="false">^</mo> </mover> <mi>t</mi> </msub> </semantics></math>) versus estimated local number of components rounded to the nearest integer (<math display="inline"><semantics> <mrow> <mo>⌊</mo> <msub> <mi>M</mi> <mi>t</mi> </msub> <mo>⌉</mo> </mrow> </semantics></math>). Considering synthetic signal with two components exhibiting different amplitudes: (<b>c</b>) TFD; (<b>d</b>) ideal (<math display="inline"><semantics> <msub> <mover accent="true"> <mi>M</mi> <mo stretchy="false">^</mo> </mover> <mi>t</mi> </msub> </semantics></math>) versus estimated local number of components rounded to the nearest integer (<math display="inline"><semantics> <mrow> <mo>⌊</mo> <msub> <mi>M</mi> <mi>t</mi> </msub> <mo>⌉</mo> </mrow> </semantics></math>).</p>
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<p>Block diagram of the proposed approach.</p>
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<p>Synthetic signal examples for DNN training: (<b>a</b>) WVD, three QFM components in noise; (<b>b</b>) WVD, three LFM components; (<b>c</b>) ideal TFD, three QFM components in noise; (<b>d</b>) ideal TFD, three LFM components; (<b>e</b>) YALL1 (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>opt</mi> </msub> <mo>=</mo> <mn>3.10</mn> </mrow> </semantics></math>), three QFM components in noise; (<b>f</b>) YALL1 (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>opt</mi> </msub> <mo>=</mo> <mn>1.60</mn> </mrow> </semantics></math>), three LFM components.</p>
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<p>WVDs of the considered synthetic and real-world signals: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi mathvariant="normal">G</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>EEG</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>(<b>Top</b>) Scatter plot of predicted versus optimal regularization parameters obtained using: (<b>a</b>) MOPSO-LRE [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>]; (<b>b</b>) proposed DNN. (<b>Bottom</b>) Probability densities for the discrepancy <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>−</mo> <msub> <mi>λ</mi> <mi>opt</mi> </msub> </mrow> </semantics></math> obtained using: (<b>c</b>) MOPSO-LRE [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>]; (<b>d</b>) the proposed DNN. Calculated for 1000 examples from the validation set.</p>
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<p>Reconstructed TFDs of the considered synthetic and real-world gravitational signals obtained using YALL1: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>], <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>6.5730</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>], <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.770</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>], <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.660</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, DNN, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>2.3758</mn> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, DNN, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>5.2562</mn> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi mathvariant="normal">S</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, DNN, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>3.2020</mn> </mrow> </semantics></math>.</p>
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<p>Reconstructed TFDs of the considered real-world gravitational and EEG signals obtained using YALL1: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi mathvariant="normal">G</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>], <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>4.4620</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>EEG</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, [<a href="#B18-technologies-12-00251" class="html-bibr">18</a>], <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.121</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi mathvariant="normal">G</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, DNN, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>1.4731</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>EEG</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, DNN, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
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10 pages, 479 KiB  
Article
The Capped Separable Difference of Two Norms for Signal Recovery
by Zhiyong Zhou and Gui Wang
Mathematics 2024, 12(23), 3717; https://doi.org/10.3390/math12233717 - 27 Nov 2024
Viewed by 339
Abstract
This paper introduces a novel capped separable difference of two norms (CSDTN) method for sparse signal recovery, which generalizes the well-known minimax concave penalty (MCP) method. The CSDTN method incorporates two shape parameters and one scale parameter, with their appropriate selection being crucial [...] Read more.
This paper introduces a novel capped separable difference of two norms (CSDTN) method for sparse signal recovery, which generalizes the well-known minimax concave penalty (MCP) method. The CSDTN method incorporates two shape parameters and one scale parameter, with their appropriate selection being crucial for ensuring robustness and achieving superior reconstruction performance. We provide a detailed theoretical analysis of the method and propose an efficient iteratively reweighted 1 (IRL1)-based algorithm for solving the corresponding optimization problem. Extensive numerical experiments, including electrocardiogram (ECG) and synthetic signal recovery tasks, demonstrate the effectiveness of the proposed CSDTN method. Our method outperforms existing methods in terms of recovery accuracy and robustness. These results highlight the potential of CSDTN in various signal-processing applications. Full article
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<p>The plots for the regularization functions of CSDTN method with the scale parameter <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, respectively. We set <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo>{</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.9</mn> <mo>,</mo> <mn>1</mn> <mo>}</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>1.1</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> </mrow> </semantics></math>. All the functions are scaled to attain the point <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> for a better comparison.</p>
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<p>Comparison of reconstruction performance for ECG signal.</p>
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<p>A comparison of reconstruction performance for Gaussian random matrix and oversampled DCT random matrices with <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>∈</mo> <mo>{</mo> <mn>2</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>}</mo> </mrow> </semantics></math> for the noiseless case.</p>
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<p>MSE of sparse recovery from noisy Gaussian random measurements.</p>
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16 pages, 4090 KiB  
Article
Enhancing Chinese Dialogue Generation with Word–Phrase Fusion Embedding and Sparse SoftMax Optimization
by Shenrong Lv, Siyu Lu, Ruiyang Wang, Lirong Yin, Zhengtong Yin, Salman A. AlQahtani, Jiawei Tian and Wenfeng Zheng
Systems 2024, 12(12), 516; https://doi.org/10.3390/systems12120516 - 24 Nov 2024
Viewed by 542
Abstract
Chinese dialogue generation faces multiple challenges, such as semantic understanding, information matching, and response fluency. Generative dialogue systems for Chinese conversation are somehow difficult to construct because of the flexible word order, the great impact of word replacement on semantics, and the complex [...] Read more.
Chinese dialogue generation faces multiple challenges, such as semantic understanding, information matching, and response fluency. Generative dialogue systems for Chinese conversation are somehow difficult to construct because of the flexible word order, the great impact of word replacement on semantics, and the complex implicit context. Existing methods still have limitations in addressing these issues. To tackle these problems, this paper proposes an improved Chinese dialogue generation model based on transformer architecture. The model uses a multi-layer transformer decoder as the backbone and introduces two key techniques, namely incorporating pre-trained language model word embeddings and optimizing the sparse Softmax loss function. For word-embedding fusion, we concatenate the word vectors from the pre-trained model with character-based embeddings to enhance the semantic information of word representations. The sparse Softmax optimization effectively mitigates the overfitting issue by introducing a sparsity regularization term. Experimental results on the Chinese short text conversation (STC) dataset demonstrate that our proposed model significantly outperforms the baseline models on automatic evaluation metrics, such as BLEU and Distinct, with an average improvement of 3.5 percentage points. Human evaluations also validate the superiority of our model in generating fluent and relevant responses. This work provides new insights and solutions for building more intelligent and human-like Chinese dialogue systems. Full article
(This article belongs to the Section Artificial Intelligence and Digital Systems Engineering)
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<p>Transformer-based generative dialogue system.</p>
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<p>Workflow of embedding of word–phrase fusion.</p>
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<p>An example of embedding of word–phrase fusion.</p>
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<p>Evaluation results. (<b>a</b>) Evaluation results based on recall rate; (<b>b</b>) evaluation results of greedy matching and embedding average.</p>
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<p>Evaluation results of different parameters k under char word dialog model.</p>
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<p>Attention-matching heatmap examples. (<b>a</b>) Attention-matching heatmap based on tokenization; (<b>b</b>) attention-matching heatmap based on character–word fusion embedding.</p>
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32 pages, 6565 KiB  
Article
Sparse Feature-Weighted Double Laplacian Rank Constraint Non-Negative Matrix Factorization for Image Clustering
by Hu Ma, Ziping Ma, Huirong Li and Jingyu Wang
Mathematics 2024, 12(23), 3656; https://doi.org/10.3390/math12233656 - 22 Nov 2024
Viewed by 422
Abstract
As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide [...] Read more.
As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide the decomposition process, using fixed data graphs and feature graphs to capture relationships between data points and features. However, these fixed graphs may limit the model’s expressiveness. Additionally, many NMF variants face challenges when dealing with complex data distributions and are vulnerable to noise and outliers. To overcome these challenges, we propose a novel method called sparse feature-weighted double Laplacian rank constraint non-negative matrix factorization (SFLRNMF), along with its extended version, SFLRNMTF. These methods adaptively construct more accurate data similarity and feature similarity graphs, while imposing rank constraints on the Laplacian matrices of these graphs. This rank constraint ensures that the resulting matrix ranks reflect the true number of clusters, thereby improving clustering performance. Moreover, we introduce a feature weighting matrix into the original data matrix to reduce the influence of irrelevant features and apply an L2,1/2 norm sparsity constraint in the basis matrix to encourage sparse representations. An orthogonal constraint is also enforced on the coefficient matrix to ensure interpretability of the dimensionality reduction results. In the extended model (SFLRNMTF), we introduce a double orthogonal constraint on the basis matrix and coefficient matrix to enhance the uniqueness and interpretability of the decomposition, thereby facilitating clearer clustering results for both rows and columns. However, enforcing double orthogonal constraints can reduce approximation accuracy, especially with low-rank matrices, as it restricts the model’s flexibility. To address this limitation, we introduce an additional factor matrix R, which acts as an adaptive component that balances the trade-off between constraint enforcement and approximation accuracy. This adjustment allows the model to achieve greater representational flexibility, improving reconstruction accuracy while preserving the interpretability and clustering clarity provided by the double orthogonality constraints. Consequently, the SFLRNMTF approach becomes more robust in capturing data patterns and achieving high-quality clustering results in complex datasets. We also propose an efficient alternating iterative update algorithm to optimize the proposed model and provide a theoretical analysis of its performance. Clustering results on four benchmark datasets demonstrate that our method outperforms competing approaches. Full article
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<p>Construction of optimal graph.</p>
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<p>Clustering ACC on the dataset JAFFE.</p>
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<p>Clustering NMI on the dataset JAFFE.</p>
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<p>Clustering ACC on the dataset COIL20.</p>
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<p>Clustering NMI on the dataset COIL20.</p>
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<p>Clustering ACC on the dataset UMIST.</p>
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<p>Clustering NMI on the dataset UMIST.</p>
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<p>Clustering ACC on the dataset YaleB.</p>
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<p>Clustering NMI on the dataset YaleB.</p>
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<p>Two-dimensional representations of UMIST dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of UMIST dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of COIL20 dataset using t-SNE on the results of different methods.</p>
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<p>Two-dimensional representations of COIL20 dataset using t-SNE on the results of different methods.</p>
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<p>The ACC and NMI of SFLRNMF with different <span class="html-italic">α</span> and <span class="html-italic">β</span> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMF with different <span class="html-italic">α</span> and θ on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>θ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>The ACC and NMI of SFLRNMTF with different <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> on JAFFE.</p>
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<p>Convergence curves of the SFLRNMF algorithm on four datasets.</p>
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<p>Convergence curves of the SFLRNMTF algorithm on four datasets.</p>
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19 pages, 7944 KiB  
Article
Method for Reconstructing Velocity Field Images of the Internal Structures of Bridges Based on Group Sparsity
by Jian Li, Jin Li, Chenli Guo, Hongtao Wu, Chuankun Li, Rui Liu and Lujun Wei
Electronics 2024, 13(22), 4574; https://doi.org/10.3390/electronics13224574 - 20 Nov 2024
Viewed by 453
Abstract
Non-destructive testing (NDT) enables the determination of internal defects and flaws in concrete structures without damaging them, making it a common application in current bridge concrete inspections. However, due to the complexity of the internal structure of this type of concrete, limitations regarding [...] Read more.
Non-destructive testing (NDT) enables the determination of internal defects and flaws in concrete structures without damaging them, making it a common application in current bridge concrete inspections. However, due to the complexity of the internal structure of this type of concrete, limitations regarding measurement point placement, and the extensive detection area, accurate defect detection cannot be guaranteed. This paper proposes a method that combines the Simultaneous Algebraic Reconstruction Technique with Group Sparsity Regularization (SART-GSR) to achieve tomographic imaging of bridge concrete under sparse measurement conditions. Firstly, a mathematical model is established based on the principles of the tomographic imaging of bridge concrete; secondly, the SART algorithm is used to solve for its velocity values; thirdly, on the basis of the SART results, GSR is applied for optimized solution processing; finally, simulation experiments are conducted to verify the reconstruction effects of the SART-GSR algorithm compared with those of the SART and ART algorithms. The results show that the SART-GSR algorithm reduced the relative error to 1.5% and the root mean square error to 89.76 m/s compared to the SART and ART algorithms. This improvement in accuracy makes it valuable for the tomographic imaging of bridge concrete and provides a reference for defect detection in bridge concrete. Full article
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<p>Sketch of the travel-time tomography model.</p>
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<p>Adaptive group sparsity image reconstruction.</p>
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<p>Construction of similar block groups.</p>
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<p>Flowchart of the SART-GSR algorithm.</p>
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<p>Medium model conditions.</p>
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<p>Media simulation ray paths.</p>
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<p>Medium model condition 1 algorithm reconstruction effect diagram.</p>
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<p>Medium model condition 2 algorithm reconstruction effect diagram.</p>
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<p>Medium model condition 3 algorithm reconstruction effect diagram.</p>
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<p>Field Experiment Medium simulation ray paths.</p>
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<p>Partial Layout Diagram of Sensors in the Field Experiment.</p>
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<p>Diagram of the entire layout of the sensors in the field experiment.</p>
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<p>Diagram of the algorithm reconstruction effect in the field experiment.</p>
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<p>Relative error of velocity in each grid.</p>
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<p>Comparison chart concerning the root mean square errors of the different algorithms.</p>
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