A hyperspectral image denoising method based on low-rank sparse coding model
By constructing a hyperspectral image denoising method based on low-rank sparse coding model, it uses iterative shrinkage soft threshold and singular value threshold algorithm to convert it into a deep neural network LRSC-Net, which solves the problem of poor interpretability of network parameters in hyperspectral image denoising, improves the denoising quality, and is suitable for multi-field applications.
Patent Information
- Application Number
- CN202310434774.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-21
- Publication Date
- 2025-08-19
- Estimated Expiration
- 2043-04-21
AI Technical Summary
The existing hyperspectral image denoising methods have problems such as poor interpretability of network parameters and insufficient denoising performance.
An image denoising method based on the low-rank sparse encoding model is constructed, and iteratively solves iteratively by iteratively shrinking soft threshold algorithm and singular value threshold algorithm, and converting it into a deep neural network LRSC-Net, and image denoising is used to use the low-rank prior information of the low-rank sparse encoding model.
It realizes hyperspectral image denoising with certain interpretability, improves the denoising quality, and is suitable for applications in agriculture, medical diagnosis, satellite remote sensing and meteorological forecasting.
Smart Images
Figure CN116452455B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the fields of computer vision and image processing, and in particular relates to a hyperspectral image denoising method based on a low-rank sparse coding model. Background Art
[0002] Hyperspectral images are three-dimensional images formed by collecting spatial images of an object at different wavelengths. Their pixel values reflect the spectral reflectance characteristics of the object. However, during the imaging process, hyperspectral images are often affected by factors such as the physical and technical limitations of the imaging equipment and external environmental noise, resulting in noise interference in the captured images, which reduces the visual quality. Compared with traditional color and grayscale images, hyperspectral images have a larger number of bands and can more accurately reflect the optical characteristics of the object. They are widely used in agricultural fields such as crop monitoring and management, medical diagnosis, satellite remote sensing, and weather forecasting. Therefore, hyperspectral image denoising has important practical applications.
[0003] Image denoising has always been a hot research topic in the field of image processing and is also an important step in computer vision preprocessing. Existing hyperspectral image denoising methods can be roughly divided into three categories: transform domain-based methods; spatial domain-based methods; and deep learning-based methods. Transform domain-based methods primarily achieve noise separation through wavelet transforms, principal component analysis, Fourier transforms, etc., but their denoising performance depends on the choice of transform function. Spatial domain-based methods seek denoising methods by constructing multidimensional spatial spectral denoising models and can be further divided into filter-based and regularization-based algorithms. Deep learning-based methods primarily train deep neural networks through end-to-end strategies to map noisy images to clean images. Such methods can achieve significant performance improvements. However, existing deep neural networks are often manually designed, and the interpretability of network parameters is poor. Summary of the Invention
[0004] To solve the above technical problems, the present invention provides a hyperspectral image denoising method based on a low-rank sparse coding model. By considering the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding is constructed, so that the network constructed by the present invention has a certain degree of interpretability while ensuring the denoising quality of the image.
[0005] A hyperspectral image denoising method based on a low-rank sparse coding model comprises the following steps:
[0006] Step 1: Based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed.
[0007] Step 2, using iterative shrinkage soft threshold algorithm and singular value threshold algorithm to iteratively solve the constructed low-rank sparse coding image denoising model;
[0008] Step 3: The optimized solution of the low-rank sparse coding image denoising model is converted into the corresponding deep neural network LRSC-Net through algorithm expansion;
[0009] Step 4: Add different levels of noise to the training data set and perform training to obtain a trained network model;
[0010] Step 5: Input the test dataset into the trained network model to obtain the denoised image and use the peak signal-to-noise ratio to evaluate the quality of the denoised image.
[0011] Furthermore, in step 1, the specific operations include the following steps:
[0012] Step 1.1, the sparse coding model represents the input signal y as a dictionary D∈R n×m Zhongyuanzi The sparse linear model, where the sparse coefficient a∈R m The l1 norm minimum optimization problem is used to obtain:
[0013]
[0014] in, represents the l1 norm, λ is the regularization parameter;
[0015] Step 1.2, for the noisy hyperspectral image Y∈R M×N×C In this paper, the overall image data is divided into blocks and each image block containing a spectral band is treated as a third-order tensor with two spatial modes and one spectral mode, where P represents all image blocks. Then, based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed.
[0016]
[0017] Among them, ||DA|| * represents the nuclear norm, A represents the sparse coefficient, and {λ1,λ2} are regularization parameters.
[0018] Furthermore, in step 2, the specific process of iterative solution is:
[0019] By introducing the auxiliary variable H=DA and constructing the Lagrangian function, the LRSC image denoising model formula (2) can be solved by the following optimization problem:
[0020]
[0021] Among them, {λ1,λ2,λ3} are regularization parameters; the optimization problem (3) is solved alternately by A-subproblems and H-subproblems until the preset number of iterations is completed to obtain the final result.
[0022] Furthermore, the A-subproblem under the t-th outer layer alternating iteration: fix the H-subproblem under the t-1-th outer layer alternating iteration to optimize the solution H t-1 , the inner iterative optimization subproblem of the k+1th A is
[0023]
[0024] Further merging the terms, problem (4) is simplified to
[0025]
[0026] in, Therefore, problem (5) has the following optimal solution
[0027]
[0028] Where L is the Laplace constant, T is the transpose symbol, and A t,k represents the kth (k=1, 2, ..., K)th inner layer iteration value under the tth outer layer alternating iteration; S λ / L is a soft threshold operator, defined as:
[0029] S θ (α)=sign(α)·max(0,|α|-θ) (7)
[0030] Here, θ represents λ / L, which is the regularization parameter in the l1-norm optimization problem divided by the Laplace constant, and α represents the variable.
[0031] Furthermore, the H-subproblem under the t-th outer alternating iteration: fix A t,k+1 , the optimization subproblem about the t-th H is
[0032]
[0033] Thus, problem (8) has the following optimal solution
[0034]
[0035] Among them, DA K =UΣV T represents singular value decomposition, U represents DA t,K The left singular value matrix of , Σ represents DA t,K The singular value matrix of DA t,K The right singular value matrix of λIt is a singular value threshold operation that eliminates small singular values through the threshold λ4 and forces it to be low-rank.
[0036] Furthermore, the specific process in step 3 is:
[0037] By introducing variables Convert formula (6) into:
[0038]
[0039] in, represents the convolution operation, Represents deconvolution operation, # represents three-dimensional convolution, and S λ / L As an activation function;
[0040] Then, each alternating iteration of formula (10) and formula (9) is expanded into a deep neural network. Specifically, each layer of LRSC-Net corresponds to each iteration in the algorithm, and the network's reasoning steps are consistent with the iterative optimization steps. The proposed network parameters have the same mathematical definitions as the parameters in the optimization model, so the proposed network parameters are all interpretable.
[0041] Furthermore, the specific operations of step 4 are as follows:
[0042] In step 4.1, the 31 grayscale images of each scene in the original data training set are treated as a three-dimensional tensor of size 512×512×31, and then cut into 32×32 pieces. After normalization, these cut data are divided into training and test sets in a ratio of 6:4.
[0043] Step 4.2, parameter initialization, including hyperspectral image Y, randomly initialized dictionary D, regularization parameters {λ1,λ2,λ3} and threshold λ4;
[0044] In step 4.3, the training image with added noise is input into the network model for training, thereby obtaining a trained denoising network model.
[0045] Furthermore, in step 5, the peak signal-to-noise ratio is calculated as:
[0046]
[0047] Among them, Q represents the maximum grayscale value in the image; is the mean square error between the original image and the denoised image, m and n represent the width and height of the image, I and K represent the original image and the denoised image; the larger the PSNR value, the smaller the distortion, the less noise, and the better the image restoration result.
[0048] The beneficial effects achieved by the present invention are:
[0049] (1) By considering the low-rank prior information in hyperspectral images, an image denoising model based on low-rank sparse coding is constructed, which makes the constructed network interpretable.
[0050] (2) The constructed image denoising deep neural network LRSC-Net can ensure the denoising quality of the image and achieve a significant performance improvement;
[0051] (3) Hyperspectral images have a wide range of application scenarios. This method can improve the denoising effect of hyperspectral images and is more conducive to their application in crop monitoring and management in the agricultural field, medical diagnosis, satellite remote sensing, and weather forecasting. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] Figure 1 is a flow chart of a method in an embodiment of the present invention.
[0053] Figure 2 It is a network structure diagram in an embodiment of the present invention. DETAILED DESCRIPTION
[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.
[0055] The present invention is a hyperspectral image denoising algorithm based on a low-rank sparse coding model. By considering the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding is constructed and solved using an alternating iterative optimization algorithm. Then, the iterative optimization solution is converted into LRSC-Net using the algorithm expansion technology. The corresponding network diagram is shown in the figure below. Figure 2 shown.
[0056] A hyperspectral image denoising algorithm based on low-rank sparse coding model, such as Figure 1 As shown, the following steps are included:
[0057] Step 1: Based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed.
[0058] In step 1, the sparse coding model represents the input signal y as a dictionary D∈R n×m Zhongyuanzi The sparse linear model, where the sparse coefficient a∈R m It can be obtained through the l1 norm minimum optimization problem:
[0059]
[0060] in, represents the l1 norm, and λ is the regularization parameter.
[0061] For noisy hyperspectral image Y∈R M×N×C In [1], the overall image data is processed into blocks, and each image block containing a spectral band is treated as a third-order tensor with two spatial modes and one spectral mode, where P represents all image blocks. Then, based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed.
[0062]
[0063] Among them, ||DA|| * represents the nuclear norm, A represents the sparse coefficient, and {λ1,λ2} are regularization parameters.
[0064] Step 2: Use the iterative shrinkage soft threshold algorithm and the singular value threshold algorithm to iteratively solve the constructed low-rank sparse coding image denoising model.
[0065] The specific process of iterative solution in step 2 is:
[0066] By introducing the auxiliary variable H=DA and constructing the Lagrangian function, the LRSC image denoising model formula (2) can be solved by the following optimization problem:
[0067]
[0068] Where {λ1,λ2,λ3} are regularization parameters. The optimization problem (3) can be solved alternately by the following A-subproblem and H-subproblem.
[0069] The A-subproblem under the t-th outer layer alternating iteration: fix the H-subproblem under the t-1-th outer layer alternating iteration to optimize the solution H t-1 , the optimization sub-problem for the inner iteration of the k+1th A is:
[0070]
[0071] Further merging the terms, problem (4) is simplified to:
[0072]
[0073] in, Therefore, problem (5) has the following optimal solution:
[0074]
[0075] Where L is the Laplace constant, T is the transpose symbol, and A t,k S represents the kth (k=1, 2, ..., K)th inner layer iteration value under the tth outer layer alternating iteration. λ / L is a soft threshold operator, defined as:
[0076] S θ (α)=sign(α)·max(0,|α|-θ) (7)
[0077] H-subproblem under the t-th outer alternating iteration: Fixed A k+1 , the optimization sub-problem about the t-th H is:
[0078]
[0079] Thus, problem (8) has the following optimal solution:
[0080]
[0081] Among them, DA t,K =UΣV T represents singular value decomposition, U represents DA t,K The left singular value matrix of , Σ represents DA t,K The singular value matrix of DA t,K The right singular value matrix of Λ λ It is a singular value threshold operation that eliminates small singular values through the threshold λ4 and forces it to be low-rank.
[0082] The final result is obtained by alternately iteratively calculating the A-subproblem and the H-subproblem until the termination condition is met.
[0083] Step 3: Use algorithm expansion technology to convert the optimized solution of the low-rank sparse coding image denoising model into the corresponding deep neural network (LRSC-Net).
[0084] In step 3, the optimized solution of the LRSC image denoising model is converted into a deep neural network LRSC-Net. Each layer of the deep neural network corresponds to each iteration of the overall formula. The entire network consists of several LS-Blocks, each of which consists of two modules. The tth LS-Block consists of A t -Module, H t -Module composition, each module is described in detail as follows.
[0085] 1)A t -Module: The main purpose of this module is to solve the A-subproblem. Its function is to use the algorithm expansion technology to iteratively optimize the solution and expand it into a deep neural sub-network. Assume that the number of times the module algorithm is expanded is set to K. Then A t -The module is constructed by K layers of networks, each layer of which can be constructed by introducing variables Convert formula (6) into:
[0086]
[0087] Among them, # represents three-dimensional convolution, and It is implemented through convolution and continuously optimized during network training. λ / L Acts as an activation function.
[0088] 2)H t -Module: The main purpose of this module is to solve the H-subproblem. Its function is to use the algorithm expansion technology to expand its iterative optimization solution into H t -deep neural sub-network of modules.
[0089] Then, each alternating iteration of Equation (10) and Equation (9) is expanded into a deep neural network. Specifically, each layer of LRSC-Net corresponds to each iteration in the algorithm, and the network's inference steps are consistent with the iterative optimization steps. The proposed network parameters have the same mathematical definitions as the parameters in the optimization model, thus making them interpretable.
[0090] Step 4: Add different levels of noise to the training data set and perform training to obtain a trained network model.
[0091] Step 4 specifically includes: constructing a data set, initializing parameters, training the network, and reconstructing the image.
[0092] Dataset Construction: This paper treats the 31 grayscale images of each scene in the original training set as a three-dimensional tensor of size 512×512×31. The images are then sliced into 32×32 slices with a step size of 31 pixels. After normalization, the sliced data is divided into training and test sets in a 6:4 ratio. The normalized data range is [0, 1].
[0093] Parameter initialization: Input hyperspectral image Y, randomly initialize dictionary D, regularization parameters {λ1,λ2,λ3} and threshold λ4.
[0094] Training the network: Gaussian noise with noise levels of 25, 50, and 75 was added to simulate noisy images. The noisy training images were input into the network for training, thereby obtaining a trained denoising network model and saving it. During the training phase, the Adam optimizer was used, and the number of samples captured in one training session and the number of training rounds were set to 8 and 200 respectively. The initial learning rate was set to 6×10 -4 , and the learning rate decays by 0.35 times every 50 epochs.
[0095] Reconstructed image: According to Reconstruct denoised image
[0096] Step 5: Input the test dataset into the trained network model to obtain the denoised image and use the peak signal-to-noise ratio to evaluate the quality of the denoised image.
[0097] The formula for calculating the peak signal-to-noise ratio is:
[0098]
[0099] Among them, Q represents the maximum grayscale value in the image. is the mean square error between the original image and the denoised image, m and n represent the image width and height, and I and K represent the original clean image and the denoised image. A larger PSNR value indicates less distortion, less noise, and better image restoration results.
[0100] The experiment trained the network using the selected CAVE dataset, input the test set into the trained network model to obtain the denoised image, and used the peak signal-to-noise ratio to objectively evaluate the quality of the denoised image.
[0101] To more objectively verify and evaluate the denoising effect of the proposed LRSC-Net, the PSNR results of different methods on the selected CAVE test set are shown in Table 1 below, with the best results marked in bold. The comparison methods include LRTV, LRMR, CSCNet, and LLRGTV. It can be seen that the proposed LRSC-Net achieves the best results at noise levels of 25 and 50, and only 0.47 dB lower than the CSCNet method at a noise level of 75, placing it in a second-best position.
[0102] Table 1 PSNR results of different methods on the selected CAVE test set
[0103]
[0104] This paper discloses a hyperspectral image denoising method based on a low-rank sparse coding model. By considering the low-rank prior information in hyperspectral images, a low-rank sparse coding-based image denoising model is constructed. This makes the constructed network interpretable while ensuring the image denoising quality. The experimental results above also demonstrate the effectiveness of the model.
[0105] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed in the present invention should be included in the protection scope recorded in the claims.
Claims
1. A hyperspectral image denoising method based on a low-rank sparse coding model, characterized by: The steps include: Step 1: Based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed. In step 1, the specific operations include the following steps: Step 1.1, the sparse coding model represents the input signal y as a dictionary D∈R n×m Zhongyuanzi The sparse linear model, where the sparse coefficient a∈R m pass The norm minimization problem is used to obtain: in, express norm, λ is the regularization parameter; Step 1.2, for the noisy hyperspectral image Y∈R M×N×C In this paper, the overall image data is divided into blocks and each image block containing a spectral band is treated as a third-order tensor with two spatial modes and one spectral mode, where P represents all image blocks. Then, based on the low-rank prior information in the hyperspectral image, an image denoising model based on low-rank sparse coding (LRSC) is constructed. Among them, ||DA|| * represents the nuclear norm, A represents the sparse coefficient, and {λ1,λ2} is the regularization parameter; Step 2, using iterative shrinkage soft threshold algorithm and singular value threshold algorithm to iteratively solve the constructed low-rank sparse coding image denoising model; Step 3: The optimized solution of the low-rank sparse coding image denoising model is converted into the corresponding deep neural network LRSC-Net through algorithm expansion; Step 4: Add different levels of noise to the training data set and perform training to obtain a trained network model; Step 5: Input the test dataset into the trained network model to obtain the denoised image, and use the peak signal-to-noise ratio to evaluate the quality of the denoised image.
2. The hyperspectral image denoising method based on a low-rank sparse coding model according to claim 1, characterized in that: In step 2, the specific process of iterative solution is: By introducing the auxiliary variable H=DA and constructing the Lagrangian function, the LRSC image denoising model formula (2) is solved by the following optimization problem: Among them, {λ1,λ2,λ3} are regularization parameters; the optimization problem (3) is solved alternately by A-subproblems and H-subproblems until the preset number of iterations is completed to obtain the final result.
3. The method for denoising hyperspectral images based on a low-rank sparse coding model according to claim 2, wherein: The A-subproblem under the t-th outer layer alternating iteration: fix the H-subproblem under the t-1-th outer layer alternating iteration to optimize the solution H t-1 , the inner iterative optimization subproblem of the k+1th A is Further merging the terms, problem (4) is simplified to in, Therefore, problem (5) has the following optimal solution Where L is the Laplace constant, T is the transpose symbol, and A t,k represents the kth (k=1, 2, ..., K)th inner layer iteration value under the tth outer layer alternating iteration; S λ / L is a soft threshold operator, defined as: S θ (a)sign(a)·max(0,|α|-θ) (7) Here, θ represents λ / L, which is the regularization parameter in the l1-norm optimization problem divided by the Laplace constant, and α represents the variable.
4. The method for denoising hyperspectral images based on a low-rank sparse coding model according to claim 3, wherein: H-subproblem under the t-th outer alternating iteration: Fixed A t,k+1 , the optimization sub-problem about the t-th H is: Thus, problem (8) has the following optimal solution: Among them, DA t,K =UΣV T represents singular value decomposition, U represents DA t,K The left singular value matrix of , Σ represents DA t,K The singular value matrix of DA t,K The right singular value matrix of ; It is a singular value threshold operation that eliminates small singular values through the threshold λ4 and forces it to be low-rank.
5. The method for denoising hyperspectral images based on a low-rank sparse coding model according to claim 4, characterized in that: The specific process in step 3 is: By introducing variables Convert formula (6) into: in, represents the convolution operation, Represents deconvolution operation, # represents three-dimensional convolution, and S λ / L As an activation function; Then, each alternating iteration of formula (10) and formula (9) is expanded into a deep neural network; each layer of LRSC-Net corresponds to each iteration in the algorithm, and the network's reasoning steps are consistent with the iterative optimization steps; the network parameters have the same mathematical definitions as the parameters in the optimization model, so the network parameters are interpretable.
6. The method for denoising hyperspectral images based on a low-rank sparse coding model according to claim 5, characterized in that: The specific operations of step 4 are as follows: In step 4.1, the 31 grayscale images of each scene in the original data training set are treated as a three-dimensional tensor of size 512×512×31, and then cut into 32×32 pieces. After normalization, these cut data are divided into training and test sets in a ratio of 6:
4. Step 4.2, parameter initialization, including hyperspectral image Y, randomly initialized dictionary D, regularization parameters {λ1,λ2,λ3} and threshold λ4; In step 4.3, the training image with added noise is input into the network model for training, thereby obtaining a trained denoising network model.
7. The method for denoising hyperspectral images based on a low-rank sparse coding model according to claim 6, characterized in that: In step 5, the peak signal-to-noise ratio is calculated as: Among them, Q represents the maximum grayscale value in the image; is the mean square error between the original image and the denoised image, m and n represent the width and height of the image, I and K represent the original image and the denoised image; the larger the PSNR value, the smaller the distortion, the less noise, and the better the image restoration result.