A hyperspectral image denoising method based on tensor high-order singular value decomposition

Abstract

This invention relates to a hyperspectral image denoising method based on tensor-based higher-order singular value decomposition (HDVDe), belonging to the field of hyperspectral image processing technology. To overcome the problems in existing technologies, this invention provides a hyperspectral image denoising method based on HDVDe, comprising: dividing the hyperspectral image tensor into blocks and merging similar blocks into clusters; establishing a hyperspectral image denoising optimization model based on the nonlocal self-similarity and global correlation in the spectral domain of the hyperspectral image; solving the hyperspectral image denoising optimization model using the ADM algorithm; and restoring a noise-free hyperspectral image by combining noise-free image blocks. This invention effectively improves the problem of imbalanced tensor expansion matrices by separating the nonlocal self-similarity domain information, spectral domain information, and spatial domain information of the hyperspectral image to apply low-rank constraints in the spectral domain, thus greatly utilizing the global and local correlations in the spectral domain of the hyperspectral image.

Description

Technical Field

[0001] This invention relates to a hyperspectral image denoising method based on tensor-based high-order singular value decomposition, belonging to the field of hyperspectral image processing technology. Background Technology

[0002] The development of multispectral and hyperspectral imaging technologies applied in real-world scenarios has created a demand for multispectral and hyperspectral image processing. However, due to limitations in imaging techniques and the influence of natural factors, the imaging process is susceptible to noise contamination. Therefore, research on noise suppression for multispectral and hyperspectral images is essential for further image processing.

[0003] The research process of noise suppression for multispectral and hyperspectral images has gone through the matrix method stage (high-dimensional transformation to two dimensions, application of two-dimensional methods, which sever the connection between the image spectral domain) and the high-order tensor method stage (including the BM3D family, tensor decomposition method LRTD, etc.).

[0004] The key challenges in denoising multispectral and hyperspectral images are algorithm efficiency and effectiveness. The increase in image size and spectral domain leads to significant computational overhead, while some computationally efficient algorithms still have room for improvement in detail restoration. Therefore, finding algorithms that balance denoising capability with the preservation of image detail has become an important research direction.

[0005] Currently, traditional image denoising algorithms can be broadly classified into three categories: matrix-based denoising methods, methods derived from the BM3D algorithm, and tensor-based methods.

[0006] Matrix-based methods: Classic hyperspectral image denoising algorithms treat spectral data as two-dimensional data in different bands or matrix-based data along different modes, and then process it using classic denoising algorithms. This approach severs the connection between the spatial domain and the spectral dimension, resulting in the loss of a large amount of relevant information and affecting the denoising effect.

[0007] Based on the BM3D method: The BM3D family of algorithms primarily processes images in the transform domain. Currently, the BM3D algorithm family boasts significant advantages in image denoising compared to traditional and neural network methods. The biggest disadvantage of BM3D is its long runtime, which is unacceptable for efficiency requirements in some applications.

[0008] Tensor-based methods: The main difference between matrix methods and tensor methods lies in whether or not tensors are expanded modularly. Compared to matrix methods, tensor methods have the advantage of better preserving structural information. However, unbalance traps are an unresolved problem in mainstream tensor decomposition. Unbalance traps in tensor representations, specifically when calculating the Tucker rank, can lead to a significant disproportion between the aspect ratios of the expanded matrix and the actual length, potentially rendering the low-rank constraint on the tensor meaningless. Summary of the Invention

[0009] To overcome the problems in the prior art, the present invention provides a hyperspectral image denoising method based on tensor-based high-order singular value decomposition.

[0010] The technical solution provided by this invention to solve the above-mentioned technical problems is: a hyperspectral image denoising method based on tensor-based high-order singular value decomposition, comprising the following steps:

[0011] Step S1: Divide the hyperspectral image tensor into blocks and cluster similar blocks;

[0012] Step S2: Establish a hyperspectral image denoising optimization model based on the nonlocal self-similarity and global correlation in the spectral domain of the hyperspectral image;

[0013] Step S3: Use the ADM algorithm to solve the hyperspectral image denoising optimization model to obtain a noise-free image patch combination;

[0014] Step S4: Obtain a noise-free hyperspectral image by combining noise-free image blocks.

[0015] A further technical solution is that the specific steps of step S1 are as follows: input a tensor, divide the tensor into blocks according to a P*P spatial size, find K+1 similar blocks for each block within a w*w window, and generate several tensors.

[0016] A further technical solution is that the tensor The dimension is B×P 2 ×(K+1), where B represents the spectral domain dimension.

[0017] A further technical solution is that the hyperspectral image denoising optimization model in step S2 is:

[0018]

[0019] In the formula: express The l1-norm of the first-order difference of mode-3 (spectral domain); express The weighted nuclear norm of the matrix expanded along the mode-2 (non-local self-similar region); This indicates that the dimension is B*P. 2 ×(K+1) Recombined into P 2 A B×(K+1) matrix; Represents a grouping tensor; Represents noise-free image variables; This indicates a hyperspectral image contaminated with noise. Let i represent the i-th nonlocal self-similar tensor block.

[0020] A further technical solution is that the specific steps of step S3 are as follows:

[0021] Step S31: Introduce auxiliary variables The original problem is decomposed into parts about the Lagrange multipliers. and Subproblems;

[0022]

[0023]

[0024]

[0025] Step S32: Introduce auxiliary variables The decomposition is further performed using the Lagrange multiplier method to facilitate the subsequent application of ADMM;

[0026]

[0027]

[0028] Step S33: Solve each subproblem using ADMM iteration.

[0029] A further technical solution is that the specific steps of step S33 are as follows:

[0030] Step S331, Initialization:

[0031] Step S332: Solve using a combination of tensor Tucker decomposition and the WNNM algorithm to obtain... The low-rank estimate;

[0032] Step S333: Calculate the result of the (l+1)th iteration using the result of the l-th iteration.

[0033]

[0034] Step S334: Utilize the results of the lth iteration and renew

[0035]

[0036] Step S335: Utilize the results of the lth iteration and renew

[0037]

[0038] Step S336: Update the Lagrange multipliers and

[0039]

[0040]

[0041] Step S337, Update coefficients and

[0042]

[0043]

[0044] Step S338: If the maximum number of iterations is reached or the algorithm converges, the algorithm ends; otherwise, return to step S332 for the next iteration.

[0045] The present invention has the following beneficial effects: By separating the non-local self-similar domain information, spectral domain information and spatial domain information of hyperspectral images, the present invention applies low-rank constraints to the spectral domain of the image, which effectively improves the problem of imbalance of the tensor expansion matrix, overcomes the unbalance trap problem faced by image algorithms based on tensor Tucker decomposition when dealing with the low-rank nature of the spectral domain of hyperspectral images, and makes great use of the global and local correlations in the spectral domain of hyperspectral images. Attached Figure Description

[0046] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0047] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, a hyperspectral image denoising method based on tensor-based higher-order singular value decomposition according to the present invention includes the following steps:

[0049] Step S10: Image tensor segmentation and clustering of similar blocks: non-local similar block extraction and clustering, input tensor Divide the tensor into blocks of P*P spatial size, and within a w*w window, find K+1 similar blocks for each block to generate several blocks of dimension B×P. 2 Tensor of ×(K+1) B represents the spectral domain dimension.

[0050] Step S20: Establish a hyperspectral image denoising optimization model based on the nonlocal self-similarity and global correlation in the spectral domain of the hyperspectral image.

[0051]

[0052] In the formula: express The l1-norm of the first-order difference in mode-3 (spectral domain); terms express The weighted nuclear norm of the matrix expanded along the mode-2 (non-local self-similar region), where The dimension is B*P 2 ×(K+1); Item This indicates that the dimension is B*P. 2 ×(K+1) Recombined into P 2 The sum of the weighted nuclear norms of B×(K+1) matrices; terms Guaranteed and Consistency, and protection The integrity, of which This represents a grouping tensor, which will... Blocking and clustering.

[0053] Step S30: Use the ADM algorithm to solve the hyperspectral image denoising optimization model to obtain a noise-free image patch combination;

[0054] Step S31: Introduce auxiliary variables The original problem is decomposed into parts about the Lagrange multipliers. and Subproblems:

[0055]

[0056]

[0057]

[0058] Where: Equation (4) is The matrix form expanded along mode-2;

[0059] Step S32: In order to group the operators and Separate updates and introduce auxiliary variables And use the Lagrange multiplier method to further decompose equation (2) so that ADMM (alternating direction multiplier method) can be applied later;

[0060]

[0061]

[0062] Step S33: Solve each subproblem iteratively using ADMM (Alternating Direction Multiplier Method);

[0063] Step S331, Initialization:

[0064] Step S332: Solve equation (4) using a combination of tensor Tucker decomposition and the WNNM algorithm to obtain... The low-rank estimate;

[0065] Step S333: Calculate the result of the (l+1)th iteration using the result of the l-th iteration.

[0066]

[0067] Step S334: Utilize the results of the lth iteration and renew

[0068]

[0069] Step S335: Utilize the results of the lth iteration and renew

[0070]

[0071] Step S336: Update the Lagrange multipliers and

[0072]

[0073]

[0074] Step S337, Update coefficients and

[0075]

[0076]

[0077] Step S338: If the maximum number of iterations is reached or the algorithm converges, the algorithm ends and a noise-free image patch combination is obtained; otherwise, return to step S332 for the next iteration.

[0078] The convergence condition for the algorithm is as follows:

[0079] |PSNR (l+1) -PSNR (l) |<ε

[0080] Peak signal-to-noise ratio (PSNR):

[0081]

[0082] Mean square error:

[0083]

[0084] Step S40: Obtain a noise-free image by combining noise-free image blocks.

[0085] Traditional methods for applying global correlation to hyperspectral images typically consider the sparsity of the first-order difference in the spectral domain. However, methods that consider the low-rank property of the spectral domain often suffer from unbalanced traps, failing to achieve the expected performance. This method recombines tensors containing non-local self-similarity, spectral, and spatial information, separating the spatial, spectral, and non-local self-similarity information. The recombined tensor, after expansion, has similar horizontal and vertical dimensions and good low-rank property, effectively extracting the structural information of the image.

[0086] The advantage of this method is that it takes into account both the sparsity of the first-order difference in the spectral domain and the low-rank property of the spectral domain, making full use of the global correlation in the spectral domain while eliminating the impact of unbalanced trap on the algorithm performance.

[0087] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the present invention shall still fall within the scope of the present invention.

Claims

1. A hyperspectral image denoising method based on tensor-based high-order singular value decomposition, characterized in that, Includes the following steps: Step S1: Divide the hyperspectral image tensor into blocks and merge and cluster similar blocks; The specific steps are as follows: Input a tensor, divide the tensor into blocks according to a P*P spatial size, and within a w*w window, find K+1 similar blocks for each block and generate several tensors. The tensor The dimension is B×P 2 × (K+1), where B represents the spectral domain dimension; Step S2: Establish a hyperspectral image denoising optimization model based on the nonlocal self-similarity and global correlation in the spectral domain of the hyperspectral image; The hyperspectral image denoising optimization model is as follows: In the formula: express The l1-norm of the first-order difference of the mode-3 spectral domain; express The weighted nuclear norm of the matrix expanded along the mode-2 nonlocal self-similar region; This indicates that the dimension is of Reassembled into indivual Matrix; Represents a grouping tensor; Represents noise-free image variables; This indicates a hyperspectral image contaminated with noise. Represents the i-th non-local self-similar tensor block; Step S3: Use the ADM algorithm to solve the hyperspectral image denoising optimization model to obtain a noise-free image patch combination; Step S31: Introduce auxiliary variables The hyperspectral image denoising optimization model is decomposed into components with respect to the Lagrange multiplier method. and Subproblems; Step S32: Introduce auxiliary variables And the decomposition is further performed using the Lagrange multiplier method; Step S33: Solve each subproblem using the Alternating Direction Multiplier Method (ADMM) iteratively; Step S331, Initialization: , , ; Step S332: Solve using a combination of tensor Tucker decomposition and the WNNM algorithm to obtain... The low-rank estimate; Step S333: Calculate the result of the (l+1)th iteration using the result of the l-th iteration. ; Step S334: Utilize the results of the lth iteration and renew ; Step S335: Utilize the results of the lth iteration and renew ; Step S336: Update the Lagrange multipliers and ; Step S337, Update coefficients and ; Step S338: If the maximum number of iterations is reached or the algorithm converges, the algorithm ends; otherwise, return to step S332 for the next iteration. Step S4: Obtain a noise-free hyperspectral image by combining noise-free image blocks.

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