Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain
<p>(<b>a</b>) The test image “Barbara”. The boundary of a 64 × 64 image patch is shown; (<b>b</b>) a magnified image patch; (<b>c</b>) the singular value curves corresponding to the image patch degraded by different levels of Additive White Gaussian Noise (AWGN).</p> "> Figure 2
<p>Noise level estimation in the singular value decomposition (SVD) domain.</p> "> Figure 3
<p>The average <span class="html-italic">P</span>(<span class="html-italic">M</span>) values across a range of noise levels and the associated results of the least square fitting.</p> "> Figure 4
<p>The test images: (<b>a</b>) Car, (<b>b</b>) Lena, (<b>c</b>) Town, (<b>d</b>) Couple, (<b>e</b>) Einstein, (<b>f</b>) Girlface, (<b>g</b>) Goldhill, (<b>h</b>) Pirate, (<b>i</b>) Blonde woman, (<b>j</b>) Barbara, (<b>k</b>) Boat, and (<b>l</b>) Crowd.</p> "> Figure 5
<p>A comparative analysis of the noise level estimation algorithms in terms of (<b>a</b>) the mean square error across noise levels and (<b>b</b>) the average error across noise levels.</p> "> Figure 6
<p>The MSE levels for different block-based noise level estimation algorithms in the SVD domain and for different test images: (<b>a</b>) Car, (<b>b</b>) Lena, (<b>c</b>) Town, (<b>d</b>) Couple, (<b>e</b>) Einstein, (<b>f</b>) Girlface, (<b>g</b>) Goldhill, (<b>h</b>) Pirate, (<b>i</b>) Blonde woman, (<b>j</b>) Barbara, (<b>k</b>) Boat, and (<b>l</b>) Crowd.</p> "> Figure 7
<p>The distribution of noise level estimates corresponding to different image patches. All patches in a fully tessellated image are considered. The images: (<b>a</b>) Lena, (<b>b</b>) Town, (<b>c</b>) Couple, (<b>d</b>) Einstein, and (<b>e</b>) Girlface.</p> "> Figure 8
<p>The distribution of noise level estimates for the entire image corresponding to 30 independent trials for each image. For each estimate, 40% of the randomly selected image patches are considered. The images: (<b>a</b>) Lena, (<b>b</b>) Town, (<b>c</b>) Couple, (<b>d</b>) Einstein, and (<b>e</b>) Girlface.</p> "> Figure 9
<p>The test images from the highly textural dataset: (<b>a</b>) bumpy_0129, (<b>b</b>) bumpy_0148, (<b>c</b>) marbled_0128, and (<b>d</b>) marbled_0132.</p> "> Figure 10
<p>The MSE levels for different block-based noise level estimation algorithms in the SVD domain and for different test images: (<b>a</b>) bumpy_0129, (<b>b</b>) bumpy_0148, (<b>c</b>) marbled_0128, and (<b>d</b>) marbled_0132.</p> ">
Abstract
:1. Introduction
2. Noise Level Estimation in the SVD Domain
2.1. Image-Based Noise Level Estimation in the SVD Domain
2.2. Block-Based Noise Level Estimation in the SVD Domain
2.3. Adaptive Block-Based Noise Level Estimation in the SVD Domain
3. Proposed ANN-Based Algorithm for Noise Level Estimation in the SVD Domain
3.1. Overview of the Proposed ANN-Based Noise Level Estimation Algorithm in the SVD Domain
- Tessellate an input image A into r × r blocks.
- Randomly select 40% of the available blocks.
- Apply the singular value decomposition on each block to obtain the associated sequence of singular values , where i = 1, 2, …, r.
- Add the AWGN of a known standard deviation, e.g., , to the selected set of image blocks to obtain a new set of image blocks that are now associated with the image B.
- Apply the singular value decomposition on each block corresponding to image B to obtain the associated sequence of singular values , where i = 1, 2, …, r.
- From each selected block, extract the feature vector to form the artificial neural network input as
- A noise level estimate is obtained for each of the K selected image blocks using the artificial neural network that has been trained to perform the noise level estimation in the SVD domain across a range of noise levels.
- Evaluate the noise level estimate for the entire image as the average value of K independent noise level estimates, where each independent estimate is associated with one distinct block.
3.2. Applying Artifical Neural Network for the Noise Level Estimation in the SVD domain
4. Results and Discussion
4.1. Mean Square Error and Average Noise Level Estimation Error
4.2. Estimator Variability
4.3. Highly Textural Images
4.4. Image Denoising
4.5. Computational Time
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Block Size | Noise Level, σ | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | |
32 × 32 | 34.098 | 51.081 | 68.437 | 85.237 | 102.381 | 119.100 | 137.077 | 153.730 | 168.914 | 188.073 |
48 × 48 | 41.999 | 62.778 | 84.013 | 104.561 | 125.994 | 146.364 | 167.638 | 188.123 | 209.965 | 230.173 |
64 × 64 | 48.545 | 72.760 | 97.179 | 121.180 | 145.495 | 169.147 | 193.799 | 217.674 | 242.477 | 266.374 |
96 × 96 | 59.674 | 89.173 | 118.963 | 148.577 | 178.454 | 208.266 | 237.717 | 266.795 | 297.003 | 327.294 |
128 × 128 | 68.784 | 103.148 | 137.403 | 171.966 | 206.436 | 240.356 | 274.850 | 308.780 | 343.950 | 378.292 |
Initial Noise Level | = 2 | |||
---|---|---|---|---|
Noise Estimation Method | SVD 32 | ASVD 64 | ANN 96 | |
Lena | Noise estimate | = 2.37 | = 2.77 | = 3.02 |
Denoised image MSE | 3.20 | 3.42 | 3.62 | |
Town | Noise estimate | = 2.58 | = 2.77 | = 3.26 |
Denoised image MSE | 3.26 | 3.33 | 3.66 | |
Couple | Noise estimate | = 2.64 | = 2.92 | = 3.48 |
Denoised image MSE | 3.73 | 3.94 | 4.56 | |
Einstein | Noise estimate | = 2.57 | = 3.07 | = 3.71 |
Denoised image MSE | 3.43 | 3.73 | 4.51 | |
Girlface | Noise estimate | = 2.08 | = 2.39 | = 2.70 |
Denoised image MSE | 2.73 | 2.76 | 2.87 |
Algorithm | SVD | SVD | ANN | SVD | ANN | SVD | ANN | SVD | ANN | SVD | ANN |
---|---|---|---|---|---|---|---|---|---|---|---|
Block size | Image | 32 × 32 | 32 × 32 | 48 × 48 | 48 × 48 | 64 × 64 | 64 × 64 | 96 × 96 | 96 × 96 | 128 × 128 | 128 × 128 |
Time (s) | 0.0811 | 0.0590 | 0.8906 | 0.0413 | 0.4146 | 0.0396 | 0.2417 | 0.0435 | 0.1549 | 0.0403 | 0.1073 |
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Turajlic, E.; Begović, A.; Škaljo, N. Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain. Electronics 2019, 8, 163. https://doi.org/10.3390/electronics8020163
Turajlic E, Begović A, Škaljo N. Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain. Electronics. 2019; 8(2):163. https://doi.org/10.3390/electronics8020163
Chicago/Turabian StyleTurajlic, Emir, Alen Begović, and Namir Škaljo. 2019. "Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain" Electronics 8, no. 2: 163. https://doi.org/10.3390/electronics8020163
APA StyleTurajlic, E., Begović, A., & Škaljo, N. (2019). Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain. Electronics, 8(2), 163. https://doi.org/10.3390/electronics8020163