Snapshot spectral compressive imaging method based on l1 norm and low rank technique
By combining L1 norm and low-rank techniques with deep learning, the problems of high cost and slow reconstruction speed of traditional hyperspectral imaging systems are solved, achieving efficient spectral image reconstruction and better imaging quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUNAN UNIV
- Filing Date
- 2023-12-01
- Publication Date
- 2026-07-10
AI Technical Summary
Traditional hyperspectral imaging methods require multiple sensors, resulting in expensive imaging systems and long data acquisition times. Existing snapshot-based compressed spectral imaging algorithms struggle to simultaneously improve reconstruction quality and generalization performance.
A snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques is adopted. Deep learning is used to design a deep low-rank prior, L1 norm is used to measure fidelity, and iterative optimization is performed by combining the alternating direction method of multipliers to reconstruct hyperspectral images.
It achieves efficient spectral image reconstruction, improves reconstruction quality and computational efficiency, and achieves higher fidelity and imaging quality.
Smart Images
Figure CN117635744B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of hyperspectral image reconstruction technology, and in particular relates to a snapshot-type spectral compression imaging method based on L1 norm and low-rank techniques. Background Technology
[0002] In image information, spectral information provides a more comprehensive and in-depth way to interpret objects, scenes, and phenomena within an image. Spectral information not only expands our understanding of the dimensions of an image but also enables us to gain a deeper understanding of the properties of light sources, matter, and the environment. This additional information is crucial for multiple fields, including object identification and classification, material composition analysis, environmental monitoring, medical imaging, and remote sensing.
[0003] Traditional hyperspectral imaging typically requires multiple sensors or filters to capture images at different wavelengths, resulting in expensive imaging systems and large datasets. However, coded aperture snapshot spectral imaging systems simplify and increase efficiency by acquiring spectral information on a single detector. Furthermore, snapshot compressed spectral imaging algorithms based on this system can recover complete spectral information from limited projection data, significantly reducing data acquisition time and storage costs. This technology not only accelerates the hyperspectral imaging process but also provides broader opportunities across various applications, offering a powerful tool for both scientific research and practical use.
[0004] Snapshot-based compressed spectral imaging algorithms primarily aim to accurately reconstruct hyperspectral images from compressed data. To achieve this goal, researchers have employed various methods, including sparse representation, dictionary learning, and deep learning techniques. Traditional optimization methods often suffer from slow iteration speeds and mediocre reconstruction quality. Deep learning-based methods show promise in improving performance, but often struggle to simultaneously achieve excellent reconstruction and generalization performance. Summary of the Invention
[0005] To address the above technical problems, this invention provides a snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques.
[0006] The technical solution adopted by this invention to solve its technical problem is:
[0007] A snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques, the method comprising the following steps:
[0008] S100: This study investigates the data fidelity and regularization terms in hyperspectral image reconstruction, models noise, and uses the L1 norm to measure the fidelity of the reconstructed hyperspectral image.
[0009] S200: Based on deep learning, a plug-and-play deep low-rank prior is designed as a regularization term. The designed deep low-rank prior is manifested by designing two neural networks to generate two matrices representing the low-rank features of hyperspectral images, inputting random Gaussian noise, and training the two networks in a self-supervised manner.
[0010] S300: Combining a fidelity term with L1 norm and a regularization term with deep low-rank prior as a hyperspectral image reconstruction optimization algorithm, and combining the hyperspectral image reconstruction optimization algorithm based on the multiplier alternating direction method to perform transformation and iterative solution. When the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
[0011] Preferably, S100 includes:
[0012] S110: Treat hyperspectral image reconstruction as a maximum a posteriori estimation problem, and decompose it into two terms: data fidelity term and regularization term;
[0013] S120: Model the noise to simulate the distribution of unknown and unpredictable noise n in a real SCI system;
[0014] S130: Using the L1 norm to measure data fidelity in hyperspectral image reconstruction problems.
[0015] Preferably, S110 specifically comprises:
[0016] According to Bayes' theorem:
[0017]
[0018] Where y is the measured image of the coded aperture snapshot spectral imaging system, x is the target hyperspectral image, p(x|y) is the posterior term, p(y) is the known evidence term, p(y|x) is the likelihood term, and p(x) is the prior term;
[0019] Taking the logarithm of both sides, the desired hyperspectral image can be obtained by solving a maximization problem:
[0020]
[0021] in, For a target hyperspectral image, the likelihood term p(y|x) measures the difference between x and y and is regarded as the data fidelity term, while the prior term p(x) serves as a regularization term, encoding prior knowledge about the structure of the hyperspectral image.
[0022] Preferably, S120 specifically comprises:
[0023] The noise is modeled as:
[0024]
[0025] Where i represents the number of noise terms, ranging from 1 to M, and p represents the measured value y. i Compared to the expected value (Hx) i Percentage of mismatches, e i The range is from 0 to 1, representing an unknown noise level;
[0026] S130 specifically refers to:
[0027] The likelihood term p(y|x) is modeled as follows:
[0028]
[0029] In the formula, ||·||0 represents the L0 norm, and H is the sensing matrix used to spatially encode x;
[0030] The L0 norm is non-convex and non-differentiable, which introduces difficulties and instabilities to optimization methods, particularly in the range [-1,1]. M On [-1, 1], the L1 norm is the convex hull of the L0 norm, i.e., it lies within the range [-1, 1]. M The L1 norm can recover the original L0 problem. Therefore, the L1 norm data fidelity term is used to measure the difference between y and Hx, and the SCI problem is then formulated as follows:
[0031]
[0032] Where ||·||1 represents the L1 norm, ||y-Hx||1 represents the L1 data fidelity term, g(x) is the regularization term, and λ is the weight parameter.
[0033] Preferably, S200 includes:
[0034] The mathematical expression for representing the lower rank of X as two matrices U and V is as follows:
[0035] X≈L=UV
[0036] In the formula, X represents the vectorized form of the hyperspectral image, and L is the low-rank representation of X;
[0037] U and V are generated using two deep generation networks, denoted as f. U (·) and f V (·):
[0038]
[0039] in Denotes a standard Gaussian distribution, E U and E V It is Gaussian noise;
[0040] The optimization objective is to find f at the nth training epoch. U (·) and f V The optimal parameters of (·) and The formula for the optimization problem is:
[0041]
[0042] Among them ||·|| p This represents the p-norm.
[0043] Preferably, the first deep generative network f U (·) includes a first encoder and a first decoder. Both the first encoder and the first decoder include three convolutional blocks. Each convolutional block in the first encoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the first decoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, a rectified linear unit activation layer, and a two-dimensional upsampling layer. The number of channels in each convolutional layer is set to 36, and skip connections are used to connect the deep features of the convolutional blocks in the first encoder with the shallow features of the convolutional blocks in the first decoder.
[0044] The second deep generative network f V (·) includes a second encoder and a second decoder. Both the second encoder and the second decoder include three convolutional blocks. Each convolutional block in the second encoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the second decoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, a rectified linear unit activation layer, and a one-dimensional upsampling layer. The number of channels in each convolutional layer is set to 6, and skip connections are used to connect the deep features of the convolutional blocks in the second encoder with the shallow features of the convolutional blocks in the second decoder.
[0045] Preferably, S300 includes:
[0046] S310: Combining deep low-rank priors as regularization terms with L1 norm fidelity terms, we obtain a hyperspectral image reconstruction optimization algorithm.
[0047] S320: Introduce auxiliary variables and then use the alternating direction method of multipliers to transform the hyperspectral image reconstruction optimization algorithm to obtain three sub-problems;
[0048] S330: The three subproblems are solved iteratively using a denoising method based on minimizing the total variation (TV), Chamboll's projection algorithm, and the dual ascent method.
[0049] S340: After the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
[0050] Preferably, S310 includes:
[0051]
[0052] subject to x=DLR(E U E V )
[0053] DLR(·) represents a deep low-rank network.
[0054] Preferably, S320 includes:
[0055] Introducing an auxiliary variable l, the hyperspectral image reconstruction optimization algorithm obtained in S310 is rewritten as follows:
[0056]
[0057] subject tol=DLR(E U E V )&x=l
[0058] Its augmented Lagrangian function is:
[0059]
[0060] Among them, L ρ (·) is the Lagrangian function with respect to the equilibrium factor ρ, b is the Lagrange multiplier, and the scaling augmented Lagrangian function is:
[0061]
[0062] Where u = b / ρ represents the scaled dual variable;
[0063] Within the framework of the alternating direction method for multipliers, this can be broken down into three sub-problems:
[0064]
[0065] Preferably, S330 includes:
[0066] For a subproblem of x, given l and u, and assuming If x is noisy, then the x subproblem can be viewed as a generalized denoising problem. Using a denoising method based on minimizing the total variation (TV), let g(x) be the TV norm ||x||. TV :
[0067]
[0068] Therefore, the subproblem x is represented as:
[0069]
[0070] This subproblem x is solved using Chambolle's projection algorithm, and the solution to x in the k-th iteration is:
[0071]
[0072] In the formula, ω is a nonlinear dual variable obtained using the nonlinear projection method:
[0073]
[0074] In the formula n ω This represents the number of iterations to solve for ω. Here, τ is the gradient operator, τ is the denoising factor, and divω represents the discrete divergence of ω.
[0075] (divω) i =ω i -ω i-1
[0076] For the subproblem of l, we first introduce the auxiliary variable θ:
[0077]
[0078] subject to θ=y-Hl
[0079] To solve the subproblem l using deep low-rank networks, the objective function of the deep low-rank network is defined as follows:
[0080]
[0081] in Given x k+1 and u k ,l k+1 The solution is the final output of the deep low-rank network:
[0082]
[0083] Given x k+1 and l k+1 The subproblems of u are solved by the dual ascent method:
[0084] u k+1 =u k +(x k+1 -l k+1 ).
[0085] The aforementioned snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques first investigates the data fidelity and regularization terms in hyperspectral image reconstruction. It identifies the data fidelity term as a key factor affecting the performance of spectral compression imaging and uses the L1 norm to measure the fidelity of the reconstructed hyperspectral image. Next, a plug-and-play deep low-rank prior is designed as a regularization term to effectively capture the spectral low-rank features of the hyperspectral image. Finally, the fidelity term with the L1 norm and the regularization term with the deep low-rank prior are combined as an optimization problem for hyperspectral image reconstruction, and an iterative optimization algorithm based on the alternating direction of multipliers is developed to solve it. This approach achieves accurate reconstruction results and high computational efficiency, demonstrating significant advantages in hyperspectral image reconstruction applications, enabling higher fidelity and better imaging quality. Attached Figure Description
[0086] Figure 1 This is a flowchart of a snapshot-type spectral compression imaging method based on L1 norm and low-rank techniques in one embodiment of the present invention;
[0087] Figure 2 This is a structural diagram of the first deep generative network in one embodiment of the present invention;
[0088] Figure 3 This is a structural diagram of the second deep generative network in one embodiment of the present invention;
[0089] Figure 4 This diagram illustrates the optimization process of a snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques in one embodiment of the present invention. Detailed Implementation
[0090] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.
[0091] In one embodiment, such as Figure 1 As shown, a snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques includes the following steps:
[0092] S100: This study investigates the data fidelity and regularization terms in hyperspectral image reconstruction, models noise, and uses the L1 norm to measure the fidelity of the reconstructed hyperspectral image.
[0093] In one embodiment, S100 includes:
[0094] S110: Treat hyperspectral image reconstruction as a maximum a posteriori estimation problem, and decompose it into two terms: data fidelity term and regularization term;
[0095] S120: Model the noise to simulate the distribution of unknown and unpredictable noise n in a real SCI system;
[0096] S130: Using the L1 norm to measure data fidelity in hyperspectral image reconstruction problems.
[0097] Specifically, the hyperspectral image reconstruction problem can be viewed as a maximum a posteriori estimation problem. Given a measurement y in a coded aperture snapshot spectral imaging system, the optimal target x is determined by maximizing the conditional posterior probability. Most existing methods use the L2 norm to represent the data fidelity term, which assumes that the noise follows a standard Gaussian distribution. However, the distribution of noise in real SCI systems is unknown and unpredictable. Therefore, relying solely on the L2 norm as the data fidelity term may lead to poor performance. This invention addresses this limitation by explicitly modeling the noise.
[0098] In one embodiment, S110 specifically includes:
[0099] According to Bayes' theorem:
[0100]
[0101] Where y is the measured image of the coded aperture snapshot spectral imaging system, x is the target hyperspectral image, p(x|y) is the posterior term, p(y) is the known evidence term, p(y|x) is the likelihood term, and p(x) is the prior term;
[0102] Taking the logarithm of both sides, the desired hyperspectral image can be obtained by solving a maximization problem:
[0103]
[0104] in, For a target hyperspectral image, the likelihood term p(y|x) measures the difference between x and y and is regarded as the data fidelity term, while the prior term p(x) serves as a regularization term, encoding prior knowledge about the structure of the hyperspectral image.
[0105] In one embodiment, S120 specifically includes:
[0106] The noise is modeled as:
[0107]
[0108] Where i represents the number of noise terms, ranging from 1 to M, and p represents the measured value y. i Compared to the expected value (Hx) i Percentage of mismatches, e i The range is from 0 to 1, representing an unknown noise level.
[0109] Specifically, true y can be observed i The probability is given by (1-p).
[0110] S130 specifically refers to:
[0111] The likelihood term p(y|x) is modeled as follows:
[0112]
[0113] In the formula, ||·||0 represents the L0 norm, and H is the sensing matrix used to spatially encode x;
[0114] The L0 norm is non-convex and non-differentiable, which introduces difficulties and instabilities to optimization methods, particularly in the range [-1,1]. M On [-1, 1], the L1 norm is the convex hull of the L0 norm, i.e., it lies within the range [-1, 1]. M The L1 norm can recover the original L0 problem. Therefore, the L1 norm data fidelity term is used to measure the difference between y and Hx, and the SCI problem is then formulated as follows:
[0115]
[0116] Where ||·||1 represents the L1 norm, ||y-Hx||1 represents the L1 data fidelity term, g(x) is the regularization term, and λ is the weight parameter.
[0117] S200: Based on deep learning, a plug-and-play deep low-rank prior is designed as a regularization term. The designed deep low-rank prior is represented by two neural networks that generate two matrices representing the low-rank features of hyperspectral images. Random Gaussian noise is input, and the two networks are trained in a self-supervised manner.
[0118] Specifically, an untrained, priority-based low-rank neural network model was designed to capture the spectral correlation of potential hyperspectral images. Furthermore, to compensate for the long computation time of self-supervised networks, this invention designs a lightweight neural network and utilizes a warm-start optimization mechanism, significantly accelerating the computation speed.
[0119] In one embodiment, S200 includes:
[0120] The mathematical expression for representing the lower rank of X as two matrices U and V is as follows:
[0121] X≈L=UV
[0122] In the formula, X represents the vectorized form of the hyperspectral image, and L is the low-rank representation of X;
[0123] U and V are generated using two deep generation networks, denoted as f. U (·) and f V (·):
[0124]
[0125] in Denotes a standard Gaussian distribution, E U and E V It is Gaussian noise;
[0126] The optimization objective is to find f at the nth training epoch. U (·) and f V The optimal parameters of (·) and The formula for the optimization problem is:
[0127]
[0128] Among them ||·|| p This represents the p-norm.
[0129] In one embodiment, such as Figure 2 As shown, the first deep generative network f U (·) includes a first encoder and a first decoder. Both the first encoder and the first decoder include three convolutional blocks. Each convolutional block in the first encoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the first decoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, a rectified linear unit activation layer, and a two-dimensional upsampling layer. The number of channels in each convolutional layer is set to 36, and skip connections are used to connect the deep features of the convolutional blocks in the first encoder with the shallow features of the convolutional blocks in the first decoder.
[0130] like Figure 3 As shown, the second deep generative network f V (·) includes a second encoder and a second decoder. Both the second encoder and the second decoder include three convolutional blocks. Each convolutional block in the second encoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the second decoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, a rectified linear unit activation layer, and a one-dimensional upsampling layer. The number of channels in each convolutional layer is set to 6, and skip connections are used to connect the deep features of the convolutional blocks in the second encoder with the shallow features of the convolutional blocks in the second decoder.
[0131] Specifically, the Adam optimizer is used for joint training. and Save and reuse and This hot-start optimization mechanism accelerates computation without affecting reconstruction quality, serving as the initial weights for subsequent iterations.
[0132] S300: Combining a fidelity term with L1 norm and a regularization term with deep low-rank prior as a hyperspectral image reconstruction optimization algorithm, and combining the hyperspectral image reconstruction optimization algorithm based on the multiplier alternating direction method to perform transformation and iterative solution. When the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
[0133] Specifically, a hyperspectral image reconstruction optimization algorithm with L1 norm and DLR prior is proposed, and an iterative optimization algorithm based on the alternating direction method of multipliers is proposed for this optimization problem. Specifically, auxiliary variables are first introduced, treating it as a constrained optimization problem. An augmented Lagrangian function is constructed, dividing it into several subproblems, which are then solved. The solutions to the subproblems iterate with each other until a preset maximum number of iterations is reached to obtain the final solution, which is the target hyperspectral image.
[0134] In one embodiment, S300 includes:
[0135] S310: Combining deep low-rank priors as regularization terms with L1 norm fidelity terms, we obtain a hyperspectral image reconstruction optimization algorithm.
[0136] S320: Introduce auxiliary variables and then use the alternating direction method of multipliers to transform the hyperspectral image reconstruction optimization algorithm to obtain three sub-problems;
[0137] S330: The three subproblems are solved iteratively using a denoising method based on minimizing the total variation (TV), Chamboll's projection algorithm, and the dual ascent method.
[0138] S340: After the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
[0139] In one embodiment, S310 includes:
[0140]
[0141] subject tox=DLR(E U E V )
[0142] Where DLR(·) represents a deep low-rank network.
[0143] In one embodiment, S320 includes:
[0144] Introducing an auxiliary variable l, the hyperspectral image reconstruction optimization algorithm obtained in S310 is rewritten as follows:
[0145]
[0146] subject tol=DLR(E U E V )&x=l
[0147] Its augmented Lagrangian function is:
[0148]
[0149] Among them, L ρ (·) is the Lagrangian function with respect to the equilibrium factor ρ, b is the Lagrange multiplier, and the scaling augmented Lagrangian function is:
[0150]
[0151] Where u = b / ρ represents the scaled dual variable;
[0152] Within the framework of the alternating direction method for multipliers, this can be broken down into three sub-problems:
[0153]
[0154] In one embodiment, S330 includes:
[0155] For a subproblem of x, given l and u, and assuming If x is noisy, then the x subproblem can be viewed as a generalized denoising problem. Using a denoising method based on minimizing the total variation (TV), let g(x) be the TV norm ||x||. TV :
[0156]
[0157] Therefore, the subproblem x is represented as:
[0158]
[0159] This subproblem x is solved using Chambolle's projection algorithm, and the solution to x in the k-th iteration is:
[0160]
[0161] In the formula, ω is a nonlinear dual variable obtained using the nonlinear projection method:
[0162]
[0163] In the formula n ω This represents the number of iterations to solve for ω. Here, τ is the gradient operator, τ is the denoising factor, and divω represents the discrete divergence of ω.
[0164] (divω)i =ω i -pω i-1
[0165] For the subproblem of l, we first introduce the auxiliary variable θ:
[0166]
[0167] subject to θ=y-Hl
[0168] To solve the subproblem l using deep low-rank networks, the objective function of the deep low-rank network is defined as follows:
[0169]
[0170] in Given x k+1 and u k ,l k+1 The solution is the final output of the deep low-rank network:
[0171]
[0172] Given x k+1 and l k+1 The subproblems of u are solved by the dual ascent method:
[0173] u k+1 =u k +(x k+1 -l k+1 ).
[0174] The optimization process diagram of the snapshot spectral compression imaging method based on L1 norm and low-rank techniques is shown in the figure. Figure 4 As shown. First, input u 0 and l 0 x can be obtained from formula (1) 1 Then through the neural network f U / f V Then, l is obtained from formula (2). 1 Finally, u is obtained from formula (3). 1 This completes the first iteration. Then, iterating in this order until the pre-set maximum number of iterations is reached, at which point the iteration stops, and the optimal value x is output.
[0175] The effectiveness of this invention was experimentally verified on the CAVE dataset. Each scene in the CAVE dataset is 512×512×28 in size, with a spatial dimension of 512×512 and 28 spectral bands. The physical mask shape is set to 512×512, and the training epochs are 600. Image reconstruction performance is evaluated using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). PSNR measures the quality of image reconstruction; a higher PSNR value generally indicates a lower reconstruction error, meaning the image is closer to the original image. SSIM is a more comprehensive evaluation method that considers multiple aspects of the image, such as brightness, contrast, and structure. The SSIM value ranges from -1 to 1; a higher SSIM value indicates that the image's structure, brightness, and contrast are more similar to the original image, meaning the image quality is higher.
[0176] Table 1 shows the reconstruction results of eight CAVE test scenarios on four different state-of-the-art methods and the algorithm proposed in this invention. Experimental results show that the algorithm proposed in this invention exhibits superior performance in almost all scenarios, achieving an average PSNR of 37.11 dB and an average SSIM of 0.957. Compared with the existing state-of-the-art method DeSCI, the algorithm proposed in this invention represents a substantial improvement, with average PSNR and average SSIM increased by 7.53 dB and 0.067 dB, respectively. In summary, the algorithm proposed in this invention has significant advantages in hyperspectral image reconstruction applications, achieving higher fidelity and better imaging quality.
[0177] Table 1
[0178]
[0179]
[0180] The snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make several improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.
Claims
1. A snapshot-based spectral compression imaging method based on L1 norm and low-rank techniques, characterized in that, The method includes the following steps: S100: This study investigates the data fidelity and regularization terms in hyperspectral image reconstruction, models noise, and uses the L1 norm to measure the fidelity of the reconstructed hyperspectral image. S200: Based on deep learning, a plug-and-play deep low-rank prior is designed as a regularization term. The designed deep low-rank prior is manifested by designing two neural networks to generate two matrices representing the low-rank features of hyperspectral images, inputting random Gaussian noise, and training the two networks in a self-supervised manner. S300: Combining a fidelity term with L1 norm and a regularization term with deep low-rank prior as a hyperspectral image reconstruction optimization algorithm, and combining the hyperspectral image reconstruction optimization algorithm based on the multiplier alternating direction method to perform transformation and iterative solution. When the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
2. The method according to claim 1, characterized in that, S100 includes: S110: Treat hyperspectral image reconstruction as a maximum a posteriori estimation problem, and decompose it into two terms: data fidelity term and regularization term; S120: Model the noise to simulate the distribution of unknown and unpredictable noise n in a real SCI system; S130: Using the L1 norm to measure data fidelity in hyperspectral image reconstruction problems.
3. The method according to claim 2, characterized in that, S110 specifically refers to: According to Bayes' theorem: Where y is the measured image of the coded aperture snapshot spectral imaging system, x is the target hyperspectral image, p(x|y) is the posterior term, p(y) is the known evidence term, p(y|x) is the likelihood term, and p(x) is the prior term; Taking the logarithm of both sides, the desired hyperspectral image can be obtained by solving a maximization problem: in, For a target hyperspectral image, the likelihood term p(y|x) measures the difference between x and y and is regarded as the data fidelity term, while the prior term p(x) serves as a regularization term, encoding prior knowledge about the structure of the hyperspectral image.
4. The method according to claim 3, characterized in that, S120 specifically refers to: The noise is modeled as: Where i represents the number of noise terms, ranging from 1 to M, and p represents the measured value y. i Compared to the expected value (Hx) i Percentage of mismatches, e i The range is from 0 to 1, representing an unknown noise level; S130 specifically refers to: The likelihood term p(y|x) is modeled as follows: In the formula, ||·||0 represents the L0 norm, and H is the sensing matrix used to spatially encode x; The L0 norm is non-convex and non-differentiable, which introduces difficulties and instabilities to optimization methods, particularly in the range [-1,1]. M On [-1, 1], the L1 norm is the convex hull of the L0 norm, i.e., it lies within the range [-1, 1]. M The L1 norm can recover the original L0 problem. Therefore, the L1 norm data fidelity term is used to measure the difference between y and Hx, and the SCI problem is then formulated as follows: Where ||·||1 represents the L1 norm, ||y-Hx||1 represents the L1 data fidelity term, g(x) is the regularization term, and λ is the weight parameter.
5. The method according to claim 1, characterized in that, S200 includes: The mathematical expression for representing the lower rank of X as two matrices U and V is as follows: X≈L=UV In the formula, X represents the vectorized form of the hyperspectral image, and L is the low-rank representation of X; U and V are generated using two deep generation networks, denoted as F. U (·) and f V (·): Where N(0|1) represents a standard Gaussian distribution, E U and E V It is Gaussian noise; The optimization objective is to find f at the nth training epoch. U (·) and f V Optimal parameters of (·) and The formula for the optimization problem is: Among them ||·|| p This represents the p-norm.
6. The method according to claim 5, characterized in that, The first deep generative network f U (·) includes a first encoder and a first decoder. Both the first encoder and the first decoder include three convolutional blocks. Each convolutional block in the first encoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the first decoder includes a two-dimensional convolutional layer, a two-dimensional batch normalization layer, a rectified linear unit activation layer, and a two-dimensional upsampling layer. The number of channels in each convolutional layer is set to 36, and skip connections are used to connect the deep features of the convolutional blocks in the first encoder with the shallow features of the convolutional blocks in the first decoder. The second deep generative network f V (·) includes a second encoder and a second decoder. Both the second encoder and the second decoder include three convolutional blocks. Each convolutional block in the second encoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, and a rectified linear unit activation layer. Each convolutional block in the second decoder includes a one-dimensional convolutional layer, a one-dimensional batch normalization layer, a rectified linear unit activation layer, and a one-dimensional upsampling layer. The number of channels in each convolutional layer is set to 6, and skip connections are used to connect the deep features of the convolutional blocks in the second encoder with the shallow features of the convolutional blocks in the second decoder.
7. The method according to claim 1, characterized in that, The S300 includes: S310: Combining deep low-rank priors as regularization terms with L1 norm fidelity terms, we obtain a hyperspectral image reconstruction optimization algorithm. S320: Introduce auxiliary variables and then use the alternating direction method of multipliers to transform the hyperspectral image reconstruction optimization algorithm to obtain three sub-problems; S330: The three subproblems are solved iteratively using a denoising method based on minimizing the total variation (TV), Chamboll's projection algorithm, and the dual ascent method. S340: After the number of iterations reaches the preset maximum number of iterations, the target hyperspectral image is obtained.
8. The method according to claim 7, characterized in that, S310 includes: subject to x=DLR(E U ,E V ) DLR(·) represents a deep low-rank network.
9. The method according to claim 8, characterized in that, The S320 includes: Introducing an auxiliary variable l, the hyperspectral image reconstruction optimization algorithm obtained in S310 is rewritten as follows: subject tol=DLR(E U ,E V )&x=l Its augmented Lagrangian function is: Among them, L ρ (·) is the Lagrangian function with respect to the equilibrium factor ρ, b is the Lagrange multiplier, and the scaling augmented Lagrangian function is: Where u = b / ρ represents the scaled dual variable; Within the framework of the alternating direction method for multipliers, this can be broken down into three sub-problems: 。 10. The method according to claim 9, characterized in that, The S330 includes: For a subproblem of x, given l and u, and assuming If x is noisy, then the x subproblem can be viewed as a generalized denoising problem. Using a denoising method based on minimizing the total variation (TV), let g(x) be the TV norm ||x||. TV : Therefore, the subproblem x is represented as: This subproblem x is solved using Chambolle's projection algorithm, and the solution to x in the k-th iteration is: In the formula, p is a nonlinear dual variable obtained using the nonlinear projection method: In the formula n ω This represents the number of iterations to solve for ω. Here, τ is the gradient operator, τ is the denoising factor, and divω represents the discrete divergence of ω. (divō) i =ω i -oh i-1 For the subproblem of l, we first introduce the auxiliary variable θ: subject to θ=y-Hl To solve the subproblem l using deep low-rank networks, the objective function of the deep low-rank network is defined as follows: in Given x k+1 and u k ,l k+1 The solution is the final output of the deep low-rank network: Given x k+1 and l k+1 The subproblems of u are solved by the dual ascent method: u k+1 u k +(x k+1 -l k+1 )。