Open AccessArticle

Reconstruction of High-Resolution Solar Spectral Irradiance Based on Residual Channel Attention Networks

School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

Key Laboratory of Optical Calibration and Characterization, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China

Author to whom correspondence should be addressed.

Remote Sens. 2024, 16(24), 4698; https://doi.org/10.3390/rs16244698

Submission received: 4 November 2024 / Revised: 6 December 2024 / Accepted: 11 December 2024 / Published: 17 December 2024

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Abstract

The accurate measurement of high-resolution solar spectral irradiance (SSI) and its variations at the top of the atmosphere is crucial for solar physics, the Earth’s climate, and the in-orbit calibration of optical satellites. However, existing space-based solar spectral irradiance instruments achieve high-precision SSI measurements at the cost of spectral resolution, which falls short of meeting the requirements for identifying fine solar spectral features. Therefore, this paper proposes a new method for reconstructing high-resolution solar spectral irradiance based on a residual channel attention network. This method considers the stability of SSI spectral features and employs residual channel attention blocks to enhance the expression ability of key features, achieving the high-accuracy reconstruction of spectral features. Additionally, to address the issue of excessively large output features from the residual channel attention blocks, a scaling coefficient adjustment network block is introduced to achieve the high-accuracy reconstruction of spectral absolute values. Finally, the proposed method is validated using the measured SSI dataset from SCIAMACHY on Envisat-1 and the simulated dataset from TSIS-1 SIM. The validation results show that, compared to existing scaling coefficient adjustment algorithms, the proposed method achieves single-spectrum super-resolution reconstruction without relying on external data, with a Mean Absolute Percentage Error (MAPE) of 0.0302% for the reconstructed spectra based on the dataset. The proposed method achieves higher-resolution reconstruction results while ensuring the accuracy of SSI.

Keywords:

high-resolution; solar spectral irradiance; convolutional neural network; residual network; channel attention; spectral super-resolution reconstruction

1. Introduction

The Sun is the primary energy source for the Earth’s climate system, yet the quantitative assessment of the impact of solar variability on climate change remains incomplete. The influence of solar forcing, combined with additional natural variability, is complex in both magnitude and phase [1]. Separating these natural effects from anthropogenic ones is crucial for understanding the attribution of human-induced variability in Earth’s surface temperature [2]. The absorption of radiation by the atmosphere, oceans, and land depends on wavelength, and in the atmosphere, it is sensitive to some high-resolution spectral details. For this reason, long-term measurements of solar spectral irradiance (SSI) with a spectral resolution better than 0.1 nm are considered increasingly important for fully elucidating the link between the Sun and climate, relative to total solar irradiance (TSI) [3]. Accurate and long-term SSI measurements are thus important direct inputs for advancing the scientific understanding of wavelength-specific processes affecting atmospheric response and climate variability.

Solar spectral irradiance is also commonly used for the radiometric calibration of satellite sensors and for converting satellite radiometric measurements into reflectance values, a critical step in many optical remote sensing applications [4]. Furthermore, the Sun is often used as a stable and well-characterized light source for precision space-based instruments to correct for instrument degradation due to harsh space environments and variations among various instruments, thereby ensuring data reliability and consistency across various missions. Therefore, the absolute accuracy of solar spectra plays a vital role in the global space-based calibration system. However, there are significant differences in both measurement accuracy and spectral resolution among existing reference solar spectral irradiance datasets. Studies by Rajendra Bhatt, Fuqin Li, and others have shown that due to significant differences (up to 15% at some wavelengths) among the many SSI spectra currently used in satellite ground processing systems, the derived channel radiance can vary by more than 3% when different SSI datasets are used [5].

To date, although solar spectral irradiance observation missions covering various resolutions, absolute accuracies, and spectral coverage have been conducted, a complete, high-resolution, absolutely calibrated solar spectral irradiance dataset has not been reported from observations due to the difficulties of conducting high-resolution solar spectral irradiance measurements from space and the inability to accurately correct for atmospheric absorption in ground-based SSI measurements. To improve the absolute measurement accuracy of SSI, several research institutions at home and abroad have initiated space-based radiometric benchmark missions. These include the TRUTHS program of the European Space Agency (ESA) [6], the CLARREO Pathfinder program of the National Aeronautics and Space Administration (NASA) [7], and the LIBRA program of the China Meteorological Administration (CMA) [8].

However, due to the inherent trade-off between spectral resolution and measurement accuracy in spectrometer measurement mechanisms, existing space-based observation plans satisfy measurement accuracy requirements by sacrificing spectral resolution, resulting in the limited spectral resolution of SSI measurable by current space-based instruments [9]. In summary, traditional observations have struggled to meet the demand for refined and high-precision solar spectra in fields such as solar physics, atmospheric physics, and climate physics.

To overcome hardware limitations, researchers have proposed software-based methods to obtain high-precision, high-spectral-resolution solar spectral irradiance. Among them, the spectral ratio method, which combines high-precision, low-resolution space-based solar spectra with low-precision, high-resolution ground-based solar spectra, has become a common method for obtaining high-resolution solar spectral irradiance. This method was initially proposed by Dobber et al. [10], who constructed a new high-resolution solar reference spectrum in the 250 to 550 nm spectral range and used it to calibrate the Dutch–Finnish Ozone Monitoring Instrument (OMI). Based on this, Coddington et al. proposed an improved spectral ratio method that adjusts ground-measured high-resolution solar spectral data to the SI-traceable irradiance scale of the Total and Spectral Solar Irradiance Sensor-1 Spectral Irradiance Monitor (TSIS-1 SIM) instrument hosted by NASA on the International Space Station, producing a new reference spectrum known as the TSIS-1 Hybrid Solar Reference Spectrum (TSIS-1 HSRS) [11]. However, it still has limitations, requiring simultaneous, co-located measurements of high-precision, low-resolution space-based solar spectra and low-precision, high-resolution ground-based solar spectra, as well as the atmospheric absorption correction of ground-measured data to eliminate atmospheric absorption effects, making it difficult to meet the needs of interdecadal climate change research.

Compared to the ratio-based adjustment method that relies on fusion, the method of directly reconstructing high-resolution spectra from a single low-resolution spectrum without relying on external data has received increasing attention. This process is known as spectral super-resolution or spectral upsampling. Since most spectral information is lost in low-resolution spectra, spectral super-resolution is a severely ill-posed inverse problem, and its underlying solution is not unique. To solve this ill-posed problem, early work formulated the spectral super-resolution problem as an optimization problem constrained by prior knowledge (such as nonlocal similarity, sparsity, and low rank). Various methods based on spectral degradation models and artificial priors have been proposed to solve the spectral reconstruction problem, such as inverse filtering, Wiener filtering, Van Cittert iteration, and Jansson iteration [12]. However, the performance of these methods is greatly limited by artificial prior information and the accuracy of measured spectra, severely limiting the accuracy of spectral super-resolution results.

In recent years, deep learning methods have demonstrated good performance in spectral super-resolution, automatically learning spectral feature information from additional training data [13].

Therefore, this paper introduces deep learning into high-resolution solar spectral reconstruction and proposes a new high-resolution solar spectral irradiance reconstruction method based on a deep residual channel attention network.

The method first constructs a spectral resolution degradation model based on the spectral measurement model and formulates spectral super-resolution as a spectral prior regularization optimization problem combined with Bayesian maximum posterior estimation. Then, based on the above optimization problem, we design a spectral resolution reconstruction network architecture that employs residual channel attention blocks to enhance the expressive ability of key features for the high-accuracy reconstruction of spectral features. Additionally, considering the issue of excessively large output features from the residual channel attention blocks, we introduce a scaling coefficient adjustment network block to achieve the high-accuracy reconstruction of spectral absolute values. Finally, the feasibility of the proposed method is validated using the measured SSI dataset from Envisat-1 SCIAMACHY and the simulated dataset from TSIS-1 SIM.

2. Datasets and Methods

2.1. Datasets

2.1.1. Envisat-1 SCIAMACHY

The SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) solar reference spectrum spans a range of 0.24 to 2.4 μm [14]. Based on the Envisat satellite, the SCIAMACHY instrument aims to measure the radiance backscattered from Earth to study trace gas species in the atmosphere. To normalize the radiance backscattered from Earth, the detector measures incident solar radiation daily. The instrument comprises a scanning mirror system, a telescope, and a spectrometer, controlled by thermal and electronic subsystems. The scanning mirror system consists of an elevation scanning mechanism (ESM) and an azimuth scanning mechanism (ASM), allowing for various observation geometries (nadir, limb, solar, and lunar occultations, as well as direct solar and lunar measurements). The spectrometer disperses the solar radiance or irradiance into eight spectral bands (channels) covering UV-VIS-NIR-SWIR. It is a double monochromator consisting of a pre-dispersive prism and a grating. Each spectral channel has its own grating and detector. SCIAMACHY uses the in-flight measurements of atomic spectral lines from an internal spectral line source (SLS), a Pt/Cr-Ne hollow cathode lamp for spectral calibration, NIST-calibrated FEL lamps with an external spectral diffuser for radiometric calibration, and an internal white light source (WLS) for in-flight degradation correction. Additionally, stray light correction and polarization correction are applied to account for the instrument’s polarization sensitivity. The resolution and uncertainty of the data used can be found in Table 1. SCIAMACHY data can be accessed at https://www.iup.uni-bremen.de/UVSAT/data/solartimeseries/ (accessed on 10 September 2024).

2.1.2. TSIS-1 SIM

The Spectral Irradiance Monitor (SIM) on the Total and Spectral Solar Irradiance Sensor (TSIS-1) is a prism spectrometer designed to measure solar spectral irradiance across the 0.2 to 2.4 μm spectral range with a spectral resolution ranging from approximately 0.25 to 42 nm. TSIS-1 SIM shares the same name as the traditional SORCE SIM instrument but includes several key upgrades. Compared to the traditional SORCE SIM, TSIS-1 SIM eliminates the relay mirror structure, adds channels for in-orbit calibration, and exhibits improved noise performance, enhanced stability, and higher absolute calibration accuracy. The entire system’s spectral irradiance is verified and absolutely calibrated using the Spectral Irradiance and Radiance Responsivity Calibrations with Uniform Sources (SIRCUS) facility developed by the National Institute of Standards and Technology (NIST) [15], reducing pre-launch relative uncertainty by 0.24% (>460 nm) to 0.41% (<460 nm). Observations from redundant and independent instrument channels exposed to the Sun with different duty cycles are utilized to monitor and correct for instrument degradation, maintaining the stability of in-orbit calibration. Compared to previous solar irradiance reference spectra, the uncertainty in radiometric accuracy for TSIS-1 SIM has been reduced by an order of magnitude. TSIS-1 SIM data can be accessed at https://lasp.colorado.edu/home/tsis/data/ssi-data/ (accessed on 10 September 2024).

2.1.3. Generation of Training Datasets

We selected spectral data from Channel 3 (wavelength range: 405.1–591.7 nm) of the SCIAMACHY instrument onboard the Envisat-1 satellite. A total of 3000 spectra from March 2003 to March 2012 were collected. Subsequently, all Envisat-1 SCIAMACHY data were convolved with the Line Shape Function (LSF) of the SIM instrument to resample them into spectral data with the same spectral resolution as TSIS-1 SIM, forming the training dataset. The LSF for TSIS-1 SIM can be obtained from https://lasp.colorado.edu/tsis/data/ssi-data/#tsis_sim_lsf (accessed on 10 September 2024), covering a wavelength range of 200 to 2400 nm with a sampling interval of 0.1 nm. Figure 1 (left) illustrates the high-resolution solar spectral irradiance from Envisat-1 SCIAMACHY at 0.1 nm resolution and the solar spectral irradiance data convolved to the resolution of TSIS-1 SIM. Figure 1 (right) shows the line shape function (LSF) of TSIS-1 SIM at 443 nm, which has a triangular shape.

2.2. Methods

2.2.1. The Spectral Degradation Model

The spectral degradation model describes the intrinsic relationship between the measured spectrum and the incident spectrum. Assuming within the wavelength range from λ_min to λ_max, a solar spectral irradiance instrument measures the continuous solar spectrum at N wavebands with central wavelengths [λ₁, …, λ_N] to obtain a discrete signal (E = [E₁, …, E_N]) and calculates the measured spectral irradiance E(λ). The measured spectral irradiance E(λ) can be expressed as

E_{i} = \int_{λ_{m i n}}^{λ_{m a x}} E (λ) R (λ_{i}) d λ, \forall_{i} \in {1, \dots, N},

(1)

where E_i is the spectral irradiance measured at the i-th wavelength point, E(λ) is the spectral irradiance at the entrance pupil of the solar spectral irradiance instrument, and R(λ_i) is the spectral response function at the i-th wavelength channel.

If we assume that the number of measurement bands of a high-resolution solar spectral irradiance instrument is very large, that the band resolution is extremely high, and that the bands are adjacent (λ_i+₁ − λ_i → 0, i∈{1, ⋯, M−1}), then the spectral response function of each wavelength point can be approximated by a delta function (the spectral response function of the i-th wavelength point is δ(λ − λ_i)). Thus, the measured spectral irradiance

E_{i}^{h}

can be approximated as

E_{i}^{h} \approx \int_{λ_{m i n}}^{λ_{m a x}} E (λ) δ (λ_{i}) d λ, \forall_{i} \in {1, \dots, M},

(2)

Equations (1) and (2) can be discretized as

E_{i} = \sum_{i = 1}^{N} E (λ_{i}) R (λ - λ_{i}),

(3)

E_{i}^{h} \approx \sum_{i = 1}^{M} E (λ_{i}) δ (λ - λ_{i}) = E (λ_{i}),

(4)

Combining Equations (3) and (4), we obtain

E_{i} \approx \sum_{i = 1}^{N} E_{i}^{h} R (λ - λ_{i}),

(5)

Equation (5) can be expressed in matrix form as

E_{N} = E_{M}^{h} R_{M \times N},

(6)

where R_{M × N} is the spectral response function matrix of the actual solar spectral irradiance instrument. Equation (6) provides the theoretical basis for reconstructing the high-resolution solar spectral irradiance

E_{M}^{h}

from the actually measured low-resolution solar spectral irradiance E_N. However, the number of elements M in the desired high-resolution solar spectral irradiance

E_{M}^{h}

is always much larger than the number of elements N in the measured low-resolution solar spectral irradiance E_N, making the problem difficult to solve; Equation (6) does not have a stable solution mathematically. Fortunately, solar radiation exhibits significant spectral characteristics, and we can learn these characteristics by constructing a convolutional neural network to solve the ill-posed problem of reconstructing

E_{M}^{h}

from E_N.

2.2.2. The Spectral Super-Resolution Optimization Model

The spectral super-resolution problem can be formulated as inferring the high-resolution spectrum

E_{M}^{h}

from the given low-resolution spectrum E_N based on model (6). We utilize Bayesian estimation to infer

E_{M}^{h}

based on the posterior probability. Utilizing the MAP framework, the spectral super-resolution problem is written as

E_{M}^{h} = \underset{E_{M}^{h}}{a r g m a x} p (E_{M}^{h} | E_{N}),

(7)

According to Bayes’ theorem, Equation (7) can be expressed as

E_{M}^{h} = \underset{E_{M}^{h}}{a r g m a x} p (E_{M}^{h} | E_{N}) = \underset{E_{M}^{h}}{a r g m a x} \frac{p (E_{N} | E_{M}^{h}) p (E_{M}^{h})}{p (E_{N})} = \underset{E_{M}^{h}}{a r g m i n} [- l o g {p (E_{N} | E_{M}^{h})} - l o g {p (E_{M}^{h})}],

(8)

where P(E_N) is independent of

E_{M}^{h}

, so it can be ignored. In Equation (8), the log-likelihood term

- l o g {p (E_{N} | E_{M}^{h})}

is the spectral degradation model between

E_{M}^{h}

and E_N. For the spectral super-resolution problem,

- l o g {p (E_{N} | E_{M}^{h})}

is equivalent to

- l o g {p (E_{N} | E_{M}^{h})} = \frac{1}{2 σ^{2}} E_{M}^{h} R_{M \times N} - E_{N},

(9)

where σ² is the variance of the Gaussian white noise in the spectral degradation model. The

- l o g {p (E_{M}^{h})}

term in Equation (8) is the prior information in high spectral resolution, also known as the regularization term, which aids in recovering the unknown spectrum

E_{M}^{h}

- l o g {p (E_{M}^{h})}

can be written as

- l o g {p (E_{M}^{h})} = w ϕ (E_{M}^{h}),

(10)

where

ϕ (E_{M}^{h})

is the spectral regularization function, and

w

controls the weight of the regularization term. Combining (8), (9), and (10), we formulate the spectral super-resolution as solving the following spectral prior regularization optimization problem:

\underset{E_{M}^{h}}{m i n} [‖ E_{M}^{h} R_{M \times N} - E_{N} ‖_{F}^{2} + w ϕ (E_{M}^{h})],

(11)

2.2.3. Network Architecture

In the previous section, we formulated the spectral super-resolution problem as an optimization problem aiming to minimize a target function. To leverage the powerful learning capabilities of convolutional neural networks (CNNs), we construct the proposed neural network based on problem (11). As shown in Figure 2, the network consists of one fully connected layer, two convolutional nonlinear layers, and a series of residual layers.

Solar spectra exhibit strong spectral features, which play a crucial role in spectral super-resolution reconstruction. Compared to traditional artificial priors such as sparse priors and spectral smoothness priors, CNNs with convolutional layers and nonlinear mappings have been proven to be more effective in learning spectral feature priors. Therefore, instead of adopting artificial priors, we propose using a CNN, referred to as the Spectral Feature Learning (SFL) module, to address the spectral-to-spectral feature mapping problem. High-resolution solar spectra typically have significant correlations between spectral bands, and spectral vectors often reside in low-dimensional subspaces. Therefore, it is essential to exploit the similarities between different spectral bands. In this paper, we use a channel attention (CA) scheme to capture the correlations between different spectral bands. Thus, the SFL module employs convolutional layers, Parametric Rectified Linear Unit (PReLU) activation functions, and an adaptive CA layer to learn the spectral features of high-resolution solar spectra, as shown in Figure 3. The use of PReLU as the activation function ensures both the nonlinear mapping of the CNN and the ability for gradients to flow through the entire network. The CA module is used to capture the features between spectral bands.

From the perspective of an encoder–decoder network, the measurement process can be likened to projecting high-resolution spectral signals onto a nonlinear subspace encoding. The network proposed in this paper, therefore, acts as a decoder, projecting the low-resolution spectral signals encoded in this nonlinear subspace back onto the original high-dimensional space. By training the network on a dataset of measured spectral irradiance, we can find the optimal super-resolution network. Once the network is trained, it can be used to project low-resolution spectral irradiance data onto high-resolution spectra through the super-resolution network.

2.2.4. Loss Function

After obtaining the reconstructed spectrum, we continue to train the network using the following loss function formula:

L_{1} (E, \hat{E}) = {‖ E - \hat{E} ‖}_{1},

(12)

where E is the reconstructed spectral irradiance, and

\hat{E}

is the SCIAMACHY spectral irradiance. The L1 loss function, also known as the Mean Absolute Error (MAE), is chosen here because it tends to produce sharper results by minimizing the absolute differences between the predicted and target values. This is particularly useful in spectral reconstruction tasks where preserving fine details and sharp transitions is crucial. By minimizing the L1 loss, the network learns to generate reconstructed spectra that are closer to the true SCIAMACHY spectral irradiance in terms of absolute error, thus improving the overall quality of the spectral reconstruction.

3. Components of the Network Architecture

Our network architecture integrates residual connections, convolutional layers, nonlinear activation functions, and channel attention mechanisms. These components collaborate to achieve the efficient learning and representation of spectral features.

3.1. Convolutional Layers

Convolutional layers are a crucial type of layer structure in CNNs [16]. The basic idea is to extract local features from the input image through convolutional operations and use these features for subsequent processing and analysis. Convolutional operations typically employ a filter or kernel to scan the input image and generate corresponding feature maps. Convolutional layers are used to extract local features from spectra. By stacking multiple convolutional layers, the network architecture can gradually construct more abstract and high-level feature representations. These features are essential for capturing complex relationships among spectral bands. By adjusting the number and parameters of convolutional layers, we have found that they are crucial for extracting local features in spectra and constructing high-level feature representations. Increasing the number of convolutional layers can generally improve model performance but also increase computational complexity.

3.2. Residual Connections

Residual networks, also known as ResNets [17], are a type of deep neural network architecture designed to address the issues of vanishing gradients and training difficulties. The core idea is to build the network using residual blocks and add inputs directly to the layer outputs through skip connections. Residual connections allow the network to directly pass information from previous layers to subsequent layers, which helps alleviate the problem of vanishing gradients in deep networks and facilitates cross-layer propagation and the fusion of features. In the network architecture, residual connections ensure that even in deeper layers, the features of the input spectrum can be effectively retained and utilized. Experimental results show that residual connections play a crucial role in accelerating model training and improving model performance. They allow the network to learn spectral features more deeply while avoiding issues such as vanishing gradients and overfitting.

If we remove the skip connections from the network structure without altering other components, as shown in Figure 4, we find that the training time increases significantly, and the resulting performance deteriorates considerably.

3.3. Nonlinear Activation Function

An activation function is a functional relationship between the output of a neuron in one layer and the input of a neuron in the next layer in a multilayer neural network [18]. This function is known as the activation function. The purpose of introducing activation functions is to increase the nonlinear fitting capability of neural networks. The PReLU (Parametric Rectified Linear Unit) activation function introduces nonlinear mapping capability to the network structure. It allows the model to learn complex feature transformations while maintaining simplicity and efficiency in computation.

If the PReLU activation function is removed from the network structure without altering other components, the output of each layer in this scenario will be a linear function of the input from the previous layer. It is easy to verify that regardless of how many layers the neural network has, the output will be a linear combination of the inputs, equivalent to having no hidden layers. The network model will not function accordingly, and the resulting outcomes will be meaningless.

3.4. Channel Attention

In the fields of deep learning and computer vision, channel attention is a mechanism that focuses on allocating importance to feature map channels in convolutional neural networks (CNNs). Its primary goal is to emphasize the channels that contribute most to the task and suppress irrelevant or redundant channels, thereby enhancing model performance. The core idea of the channel attention mechanism is to weight the features of different channels to emphasize those that are more important for the current task while suppressing those that are relatively less important. This approach allows the model to dynamically adjust its focus on different feature maps, improving overall performance.

A common method for implementing channel attention is the use of “Squeeze-and-Excitation” (SE) blocks [19]. SE blocks consist of two main operations: squeeze and excitation. The squeeze operation aims to compress dimensions to globally describe the features of each channel. Typically, this is achieved by performing global average pooling on the feature map of each channel, resulting in a vector equal in length to the number of channels, which contains global information for each channel. Following the squeeze operation, the excitation operation uses a simple fully connected layer (or a 1 × 1 convolutional layer) to learn the weights (or attention weights) for each channel. These weights are used to adjust the importance of each channel in the original feature map. Often, this step introduces a nonlinear activation function (such as ReLU or Sigmoid) to allow the model to learn complex inter-channel relationships. Finally, by multiplying these learned weights with the original feature map, the SE block can rescale the features of each channel, enhancing those useful for the task and suppressing those that are not important.

As shown in Figure 5, in our model, our objective is to enhance the spectral peak-to-trough features by utilizing the scaling mechanism in channel attention, thereby improving the model’s performance.

If we remove the channel attention component from the network structure without altering other components, the network structure would be equivalent to ResNets. As shown in Figure 6, we found that the performance slightly decreases, and the reconstruction effect at the spectral peaks and troughs is inferior to the results obtained with our designed model.

4. Results

4.1. Model Training

Using the 3000 sets of spectral data generated in the previous section, 70% of the spectral data were selected as the training dataset, while the remaining 30% were used as the validation set. The training and testing environment for the network consisted of an Intel i7-12650H 2.30 GHz processor and an NVIDIA RTX 4060 graphics card. During the training of the neural network, Adam [20] was used as the optimizer with a learning rate of 9.41 × 10⁻⁵. The batch size was set to 6, the number of features F was 16, the filter size K was 3, the stride was 1, the number of SFL blocks L was 2, and, addressing the issue of excessively large output features from the residual channel attention block, a scaling factor was introduced to adjust the network block, with a ratio of 1:0.5 for the scaling factors in the two SFL blocks. Early stopping and validation were implemented after every 1000 Adam iterations. The relationship between the number of validations and the training/validation errors is shown in Figure 7. From the figure, it can be observed that as the number of Adam iterations increases, the training loss function value gradually approaches 0, indicating that the loss function adopted in this paper can effectively optimize the model parameters.

4.2. Evaluation Metrics

To comprehensively evaluate the effectiveness of our method, we have selected five evaluation metrics to assess the spectra reconstructed using our approach. These metrics include the Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Spectral Angle Mapper (SAM) [21], Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index (SSIM) [22]. The expression for RMSE is

R M S E = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(E_{s u n} (i) - E_{s u n, s u p e r} (i))}^{2}},

(13)

The expression for RMSE is

M A P E = \frac{1}{N} \sum_{i = 1}^{N} | \frac{E_{s u n} (i) - E_{s u n, s u p e r} (i)}{E_{s u n} (i)} | \times 100 %,

(14)

where

E_{s u n}

is the SCIAMACHY spectral irradiance and

E_{s u n, s u p e r}

is the reconstructed spectral irradiance. The expression for PSNR is

P S N R = 10 * {l o g}_{10} (\frac{M A X^{2}}{M S E}),

(15)

where MAX is the maximum value of the SCIAMACHY spectral irradiance, and MSE is the Mean Squared Error between the SCIAMACHY spectral irradiance and the reconstructed spectral irradiance. The expression for SSIM is

S S I M (x, y) = \frac{(2 u_{x} u_{y} + C_{1}) (2 σ_{x y} + C_{2})}{(u_{x}^{2} + u_{y}^{2} + C_{1}) (σ_{x}^{2} + σ_{y}^{2} + C_{2})},

(16)

where x and y are the reference spectral irradiance and the reconstructed spectral irradiance, respectively;

u_{x}

and

u_{y}

are the mean values of the two spectral irradiances;

σ_{x}^{2}

and

σ_{y}^{2}

are the variances of the two spectral irradiances;

σ_{x y}

is the covariance of the two spectral irradiances; and C1 and C2 are constants used to avoid situations where the denominator is zero.

4.3. Analysis and Validation

The solar spectral irradiance measurements in the visible wavelength range (405.1–591.7 nm) from TSIS-1 SIM (inset in Figure 8) were input into the trained network presented in this paper for reconstruction, yielding a reconstructed solar spectral irradiance with a resolution of 0.1 nm. The reconstruction results are shown in Figure 8. From Figure 8, it can be observed that the 0.1 nm solar spectral irradiance reconstructed using the method proposed in this paper basically coincides with the 0.1 nm solar spectral irradiance curve from official measurements.

To demonstrate the effectiveness of our method in this study, we conducted several experiments on the dataset and compared our method with several other approaches, including the Janssen iteration method [12], a bandwidth correction method based on the Richardson–Lucy algorithm [23], and the residual networks.

As demonstrated in Table 2, traditional iterative deconvolution algorithms, including the Janssen iteration method and bandwidth correction methods, encounter challenges when processing spectra with complex features. Specifically, due to the reliance on manual prior knowledge for setting hyperparameters in the iterative deconvolution physical model and the difficulty in determining iterative stopping conditions, significant discrepancies arise between error values at low-resolution scales and those at actual high-resolution scales, especially when high-resolution spectral features are abundant (such as in solar spectra). Relying on error values at low-resolution scales to select the optimal reconstruction results can lead to substantial errors. This, in turn, may cause inaccuracies in the reconstructed spectrum, further contributing to the high RMSE values observed.

Table 2 provides an overview of the average quality metrics for our method and the other methods. It is evident that our method consistently claims the lead in all performance indicators. Specifically, in terms of the PSNR metric, our method outperforms the second-ranked method by 0.4 dB, indicating its stronger noise suppression capability. Additionally, we maintain a leading position in the SSIM metric, demonstrating that the spectra generated by our method have superior perceptual quality. In the field of spectral recovery, our SAM score significantly surpasses the second-ranked method, resulting in minimal spectral distortion. Among the aforementioned metrics, although our method yields similar results to the residual networks, we can observe from Figure 6 that our method achieves significantly better relative deviations at the peaks, with the reconstructed spectra being closer to the measured spectra.

The quality of the reconstructed spectrum, as finally calculated, is shown in Table 2. The MAPE value obtained by our method is 0.0302%, which is comparable to the uncertainty level provided by SCIAMACHY, indicating the feasibility of our spectral reconstruction method. In addition, the average time taken for reconstructing a single spectrum using our method (based on all data) is only 0.9421 s, making it a rapid reconstruction approach that meets the real-time requirements of spectral reconstruction.

5. Conclusions

In this study, we propose a solar spectral super-resolution reconstruction method based on a spectral degradation model combined with deep learning, considering the complete physical process of solar spectral irradiance measurement. Specifically, this method considers the inverse process of solar spectral irradiance measurement and formulates the spectral super-resolution problem as a spectral prior regularization optimization problem. This problem involves complex prior modeling of the solar spectrum, which is addressed through a network module composed of convolutional layers, Parametric Rectified Linear Units (PReLUs), and an Adaptive Channel Attention (CA) layer. The CA layer is utilized to enhance the performance of spectral feature prior learning in Convolutional Neural Networks (CNNs). Experiments on both synthetic and real datasets demonstrate the superiority of this method. The training dataset was generated using Envisat-1 SCIAMACHY data combined with the TSIS-1 SIM instrument line shape function, and the model was trained accordingly. Finally, the model’s effectiveness was validated using the TSIS-1 SIM measurements of solar spectral irradiance. The validation results show that the obtained super-resolution results are close to the official SCIAMACHY results, but the reconstruction time is only 0.9421 s while the model simultaneously avoids the dependence on ground-measured high-resolution solar spectral irradiance datasets required by existing spectral ratio reconstruction methods. This study indicates that convolutional neural networks (CNNs) can effectively learn the characteristics of solar spectral irradiance and its measurement instruments, which is conducive to accelerating the reconstruction speed of solar spectral irradiance and expanding the application range of high-precision space-based observations of solar spectral irradiance.

Author Contributions

Conceptualization, P.Z.; methodology, P.Z.; software, P.Z.; validation, P.Z.; formal analysis, P.Z.; investigation, J.W.; resources, J.W.; data curation, P.Z.; writing—original draft preparation, P.Z. and J.W.; writing—review and editing, J.W., J.L. and Q.K.; visualization, P.Z.; supervision, J.W., J.L. and Q.K.; project administration, J.W. and J.L.; funding acquisition, J.W. and Q.K. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the National Key Research and Development Program of China (No. 2022YFB3902901) and in part by the National Natural Science Foundation of China (No. 42105121).

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Shapiro, A.I.; Schmutz, W.; Rozanov, E.; Schoell, M.; Nyeki, S. A new approach to long-term reconstruction of the solar irradiance leads to large historical solar forcing. Astron. Astrophys. 2011, 529, A69. [Google Scholar] [CrossRef]
Thuillier, G.; Melo, S.M.L.; Lean, J.; Krivova, N.A.; Bolduc, C.; Fomichev, V.I. Analysis of different solar spectral irradiance reconstructions and their impact on solar heating rates. Sol. Phys. 2014, 289, 1115–1142. [Google Scholar] [CrossRef]
Meehl, G.A.; Washington, W.A.M.; Arblaster, M.; Dai, A. Solar and greenhouse gas forcing and climate response in the twentieth century. J. Clim. 2003, 16, 426–444. [Google Scholar] [CrossRef]
Eltbaakh, Y.A.; Ruslan, M.H.; Alghoul, M.A.; Othman, M.Y.; Sopian, K.; Fadhel, M.I. Measurement of total and spectral solar irradiance: Overview of existing research-sciencedirect. Renew. Sustain. Energy Rev. 2011, 15, 1403–1426. [Google Scholar] [CrossRef]
Li, F.; Jupp, D.L.B.; Markham, B.L.; Lau, I.C.; Ong, C.; Byrne, G.; Thankappan, M.; Oliver, S.; Malthus, T.; Fearns, P. Choice of Solar Spectral Irradiance Model for Current and Future Remote Sensing Satellite Missions. Remote Sens. 2023, 15, 3391. [Google Scholar] [CrossRef]
Green, P.D.; Fox, N.P.; Lobb, D.; Friend, J. The Traceable Radiometry Underpinning Terrestrial and Helio Studies (TRUTHS) mission. In Sensors, Systems, and Next-Generation Satellites XIX, Proceedings of the SPIE Remote Sensing, Toulouse, France, 21–24 September 2015; SPIE: Bellingham, WA, USA, 2015; Volume 9639, pp. 367–376. [Google Scholar]
Tobin, D.; Holz, R.; Nagle, F.; Revercomb, H. Characterization of the climate absolute radiance and refractivity observatory (CLARREO) ability to serve as an infrared satellite intercalibration reference. J. Geophys. Res. Atmos. 2016, 121, 4258–4271. [Google Scholar] [CrossRef]
Zhang, P.; Lu, N.; Li, C.; Ding, L.; Schmetz, J. Development of the Chinese space-based radiometric benchmark mission LIBRA. Remote Sens. 2020, 12, 2179. [Google Scholar] [CrossRef]
Fontenla, J.M.; Harder, J.; Livingston, W.; Snow, M.; Woods, T. High-resolution solar spectral irradiance from extreme ultraviolet to far infrared. J. Geophys. Res. Atmos. 2011, 116. [Google Scholar] [CrossRef]
Dobber, M.; Voors, R.; Dirksen, R.; Kleipool, Q.; Levelt, P. The high-resolution solar reference spectrum between 250 and 550 nm and its application to measurements with the ozone monitoring instrument. Sol. Phys. 2008, 249, 281–291. [Google Scholar] [CrossRef]
Coddington, O.M.; Richard, E.C.; Harber, D.; Pilewskie, P.; Woods, T.N.; Chance, K.; Liu, X.; Sun, K. The TSIS-1 hybrid solar reference spectrum. Geophys. Res. Lett. 2021, 48, e2020GL091709. [Google Scholar] [CrossRef] [PubMed]
Jansson, P.A. Deconvolution of Images and Spectra; Academic Press, Inc.: Cambridge, MA, USA, 1996. [Google Scholar]
He, J.; Yuan, Q.; Li, J.; Xiao, Y.; Liu, D.; Shen, H.; Zhang, L. Spectral super-resolution meets deep learning: Achievements and challenges. Inf. Fusion 2023, 97, 101812. [Google Scholar] [CrossRef]
Hilbig, T.; Weber, M.; Bramstedt, K.; Burrows, J.P.; Krijger, J.M. The new sciamachy reference solar spectral irradiance and its validation. Sol. Phys. 2018, 293, 121. [Google Scholar] [CrossRef]
Richard, E.; Harber, D.; Coddington, O.; Drake, G.; Woods, T. SI-traceable spectral irradiance radiometric characterization and absolute calibration of the TSIS-1 Spectral Irradiance Monitor (SIM). Remote Sens. 2020, 12, 1818. [Google Scholar] [CrossRef]
Simonyan, K.; Zisserman, A. Very deep convolutional networks for large-scale image recognition. arXiv 2014, arXiv:1409.1556. [Google Scholar]
He, K.; Zhang, X.; Ren, S.; Sun, J. Deep residual learning for image recognition. In Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA, 27–30 June 2016; IEEE: Piscataway, NJ, USA, 2016. [Google Scholar]
He, K.; Zhang, X.; Ren, S.; Sun, J. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV), Santiago, Chile, 7–13 December 2015. [Google Scholar]
Hu, J.; Shen, L.; Sun, G.; Albanie, S. Squeeze-and-excitation networks. In Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA, 18–23 June 2018; p. 99. [Google Scholar]
Kingma, D.; Ba, J. Adam: A method for stochastic optimization. arXiv 2014, arXiv:1412.6980. [Google Scholar]
Yuhas, R.H.; Goetz, A.F.; Boardman, J.W. Discrimination among semi-arid landscape endmembers using the spectral angle mapper (SAM) algorithm. In JPL, Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, CA, USA, 1–5 June 1992; NASA Jet Propulsion Laboratory (JPL): La Cañada Flintridge, CA, USA, 1992; Volume 1. [Google Scholar]
Wang, Z.; Bovik, A.C.; Sheikh, H.R.; Simoncelli, E.P. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 2004, 13, 600–612. [Google Scholar] [CrossRef]
Gardner, J.L. Spectral deconvolution applications for colorimetry. Color Res. Appl. 2014, 39, 430–435. [Google Scholar] [CrossRef]

Figure 1. (a) SCIAMACHY spectra and convolutional solar spectra; (b) The response function at 443 nm of TSIS-1 SIM.

Figure 2. The network architecture of our work.

Figure 3. Detailed description of the SFL module.

Figure 4. Comparison of relative deviations of reconstruction results between our model and the model after removing the residual skip connection.

Figure 5. A squeeze-and-excitation block.

Figure 6. Comparison of relative deviations of reconstruction results between our model and ResNets.

Figure 7. Training error.

Figure 8. The 0.1 nm resolution reconstruction of solar spectral irradiance.

Table 1. List of solar spectra used in this study.

Data Product	Spectral Resolution	Uncertainty (%)
TSIS-1 SIM	0.25–42 nm	0.24–0.41
SCIAMACHY Channel 3	0.44 nm	1.5

Table 2. Data reconstruction quality.

Title	RMSE	MAPE	SAM	PSNR	SSIM
Janssen iteration	79.5620	3.1580	0.0421	28.9094	0.1641
Bandwidth correction	76.8611	3.0373	0.0406	29.2094	0.1937
ResNets	0.7820	0.0314	0.0009	69.0617	0.9989
Our model	0.7451	0.0302	0.0001	69.4816	0.9994

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MDPI and ACS Style

Zhang, P.; Weng, J.; Kang, Q.; Li, J. Reconstruction of High-Resolution Solar Spectral Irradiance Based on Residual Channel Attention Networks. Remote Sens. 2024, 16, 4698. https://doi.org/10.3390/rs16244698

AMA Style

Zhang P, Weng J, Kang Q, Li J. Reconstruction of High-Resolution Solar Spectral Irradiance Based on Residual Channel Attention Networks. Remote Sensing. 2024; 16(24):4698. https://doi.org/10.3390/rs16244698

Chicago/Turabian Style

Zhang, Peng, Jianwen Weng, Qing Kang, and Jianjun Li. 2024. "Reconstruction of High-Resolution Solar Spectral Irradiance Based on Residual Channel Attention Networks" Remote Sensing 16, no. 24: 4698. https://doi.org/10.3390/rs16244698

APA Style

Zhang, P., Weng, J., Kang, Q., & Li, J. (2024). Reconstruction of High-Resolution Solar Spectral Irradiance Based on Residual Channel Attention Networks. Remote Sensing, 16(24), 4698. https://doi.org/10.3390/rs16244698

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