Hyperspectral image denoising method based on manifold space sparse tensor decomposition

Abstract

The present invention discloses a method for denoising a hyperspectral image based on manifold space sparse tensor decomposition, which relates to the field of image denoising. The method comprises the following steps: S1: constructing a noisy hyperspectral image Y ; S2: Based on the orthogonal projection method, obtain noisy hyperspectral images Y On a noisy low-dimensional manifold L ; S3: Using K-NN method from low-dimensional manifold L The non-local clustered image blocks are obtained from P Indicates the number of image blocks. At this time, the image blocks are noisy. S4: Use the sparse tensor decomposition method to separate the noise in the image blocks to obtain noise-free image blocks. S5: Recombine the noise-free image blocks to obtain a noise-free low-dimensional manifold. L’ ; S6: Inverse transformation of low-dimensional manifold L’ Obtain noise-free hyperspectral images X’ The present invention not only has better detail reconstruction performance for hyperspectral images, but also can perfectly preserve the edges of the images.

Description

Technical Field

[0001] The present invention relates to the field of image denoising, and in particular to hyperspectral image denoising based on manifold space sparse tensor decomposition. Background Art

[0002] Hyperspectral image acquisition is susceptible to noise due to hardware resource limitations, atmospheric interference, and the effects of photoelectrons during transmission. This noise not only reduces the visual perceptibility of the data but also deviates from the accuracy of spatial spectrum identification, ultimately impacting the confidence and reliability of the image. Therefore, image denoising can be used to improve the data's feature representation. In theory, the negative impact of noise can be reduced by improving hardware parameters, but this increases costs and provides incomplete noise removal. A more reasonable approach leverages the advantages of image processing and intelligent algorithms to effectively remove noise through data processing, such as band-by-band k-SVD and BM3D denoising methods. However, these methods ignore inter-band correlations and, more importantly, fail to model the high-dimensional structure of the spatial spectrum, resulting in less than satisfactory denoising results.

[0003] Given the spatial distribution characteristics of signal and noise, researchers have proposed methods based on low-dimensional modeling. These methods aim to map the inseparable noise and data in high-dimensional space to a low-dimensional space. In this low-dimensional space, noise and signal are separated based on the intrinsic correlation of the data and the high-dimensional distribution of the noise. For example, hyperspectral image denoising methods based on sparse representation and low-rank regularization use joint spatial and spectral low-rank priors to optimize the clean image. Furthermore, considering the low-rank nature of the data and the sparse distribution of the noise, they can be modeled separately. Then, an alternating iterative optimization framework can be constructed to classify the noise and signal. Representative methods include robust principal component analysis. Building on this foundation, more accurate modeling of the signal component can be achieved, such as those based on total variation modeling, weighted nuclear norm regularization, nonlocal low-rank, and nonlinear manifold constraints. Although these denoising methods significantly improve the modeling of noise and signal, the two-dimensional matrix modeling approach inevitably destroys the high-dimensional structure of the hyperspectral image, and the denoising process distorts the spatial-spectral structural information.

[0004] In recent years, with the rapid development of data science, tensor modeling has attracted increasing attention from scholars and has been widely used in the field of hyperspectral image denoising. By leveraging the multilinear representation advantages of tensor low-rank modeling, it is possible to simultaneously mine the low-dimensional linear structure of both spatial and spectral data, such as methods based on Tucker decomposition and parallel factorization. Furthermore, incorporating the nonlocal information, local smoothness, and non-negativity of hyperspectral images, methods based on nonlocal tensor decomposition, nonnegative tensor decomposition, and total variation regularized tensor decomposition have also been applied to denoising applications. However, biases in tensor rank estimation can lead to unstable denoising results. Summary of the Invention

[0005] The purpose of the present invention is to provide a hyperspectral image denoising method based on manifold space sparse tensor decomposition to address the above-mentioned problems, which not only has good detail reconstruction performance for hyperspectral images, but also can preserve the edges of the image intact.

[0006] The technical solution adopted by the present invention is as follows: a hyperspectral image denoising method based on manifold space sparse tensor decomposition, comprising the following steps:

[0007] S1: Constructing noisy hyperspectral images Y Specifically, according to the three-dimensional characteristics of hyperspectral images, the additive noise of spatial and spectral dimensions is jointly considered to construct a hyperspectral image. Y Formula 1:

[0008] (Formula 1);

[0009] in, 、 and represent the noisy hyperspectral image, the hyperspectral image to be restored, and the additive noise respectively; R is the set of real numbers, H Represents the number of pixels in the horizontal direction of the spatial dimension, W Represents the number of pixels in the vertical direction of the spatial dimension, B Represents the number of bands of the spectral dimension.

[0010] S2: Obtaining noisy hyperspectral images based on orthogonal projection Y On a noisy low-dimensional manifold L ; Specifically, initialize X ,make X=Y , introduce the orthogonal projection method to estimate the noisy low-dimensional manifold L Formula 2:

[0011] (Formula 2);

[0012] in, VRepresents the projection matrix.

[0013] Furthermore, in the noise reduction problem, the process of learning the orthogonal projection matrix is ​​easily affected by noise or outliers. Therefore, in the noisy low-dimensional manifold L Introducing maximization The norm-obtained manifold learning framework is Equation 3:

[0014] (Formula 3);

[0015] in, express X Expanding the matrix in the third dimension, Represents the matrix norm.

[0016] Solve the manifold learning framework to obtain the projection matrix V The closed-form solution includes steps S21-S23;

[0017] S21: Derivative equation 3 to obtain equation 4:

[0018] (Formula 4);

[0019] S22: Constraint-based , for the matrix Perform singular value decomposition to obtain Equation 5:

[0020] (Formula 5);

[0021] in, SVD represents singular value decomposition;

[0022] S23: Calculate equation 5 to obtain the projection matrix V The closed-form solution is Equation 6:

[0023] (Equation 6).

[0024] Furthermore, substituting Equation 6 into Equation 2, we obtain the noisy low-dimensional manifold L .

[0025] S3: Using K-NN method to extract low-dimensional manifolds L The image blocks with non-local clustering are obtained from ,in P Indicates the number of image blocks. In this case, the image blocks are noisy image blocks.

[0026] S4: Using sparse tensor decomposition method to The noise in the image is separated to obtain the noise-free image block; specifically, the sparse tensor decomposition model is first introduced to approximate the noise-free data, that is, the image block of the non-local clustering After introducing sparse tensor decomposition, we get Equation 7:

[0027] (Formula 7);

[0028] in, 、 and is the feature matrix, is a sparse constraint.

[0029] Furthermore, setting , Representation weighted norm, the convex optimization problem of Equation 7 is obtained as Equation 8:

[0030] (Equation 8);

[0031] in, is the weight parameter.

[0032] Furthermore, the optimization of Equation 8 is decomposed into two sub-problems, which are Subproblems and Subproblem, and iteratively update each variable by fixing other variables, initializing it in the first iteration X ,by X=Y Iterate and get P A noise-free image block, P The noise-free image patches are reassembled to obtain a noise-free low-dimensional manifold L’ ;in,

[0033] The sub-problem is Equation 9:

[0034] (Equation 9);

[0035] Among them, Equation 9 is solved using singular value decomposition 、 and ;

[0036] Sub-question 10 is the essence:

[0037] (Equation 10);

[0038] Among them, Equation 10 is solved using the tensor weighted shrinkage threshold algorithm.

[0039] S5: Recombining the noise-free image blocks to obtain a noise-free low-dimensional manifold L’ ;

[0040] S6: Inverse Transformation of Low-Dimensional Manifolds L’ Obtain noise-free hyperspectral images X’ Specifically, use Equation 11 to obtain a noise-free hyperspectral image X’ , Equation 11 is the inverse transformation of Equation 2:

[0041] (Equation 11).

[0042] In summary, the above-mentioned hyperspectral image denoising method based on manifold space sparse tensor decomposition can be summarized using the following algorithm:

[0043] Input: noisy hyperspectral image Y , weight parameter ;

[0044] ①:for =1:10 do

[0045] ②: Use Equation 6 to learn the projection matrix V , and substitute into Equation 2 to obtain the noisy low-dimensional manifold L ;

[0046] ③: Use K-NN method to extract the low-dimensional manifold L The image blocks with non-local clustering are obtained from , construct a tensor collection ;

[0047] ④:Use sparse tensor decomposition method to Separate the noise in

[0048] ⑤:for do

[0049] ⑥: Fix other variables and iteratively update using formula 9 ;

[0050] ⑦: Fix other variables and iteratively update using formula 10 ;

[0051] ⑧:end for

[0052] 9: Recombination Get a noise-free low-dimensional manifold L’ ;

[0053] ⑩: Using Equation 11 for noise-free hyperspectral images X’ to rebuild;

[0054] ⑪:end for

[0055] Output: X’ .

[0056] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0057] The present invention considers the global correlation of hyperspectral images in the spectral dimension and performs orthogonal projection on the high-dimensional structure in the data to obtain a noisy low-dimensional manifold. L ; Then, in order to L The spatial and spectral information in the data is mined and the K-NN method is used to mine the low-dimensional manifold L The image blocks with non-local clustering are obtained from , and combined with the multilinear characteristics and sparse expression advantages of tensors, a tensor sparsity-based representation model is introduced, and the sparse tensor decomposition method is used to The noise in the image is separated to obtain a noise-free image block, and the noise-free hyperspectral image is reconstructed using the inverse manifold projection of the noise-free signal; a method is implemented to achieve not only good detail reconstruction performance for the hyperspectral image, but also good preservation of the image edge. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0059] Figure 1 It is a schematic diagram of the process of the present invention;

[0060] Figure 2 Comparison of noise reduction results. DETAILED DESCRIPTION

[0061] The image data Toy used in the present invention comes from the public Cave dataset, which has a spatial resolution of 512×512 and 31 spectral bands.

[0062] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0063] like Figure 1 As shown in the figure, a hyperspectral image denoising method based on manifold space sparse tensor decomposition proposed by the present invention is used to denoise four images with different noise intensities (the noise variances are = 10, 30, 50 and 100) for noise separation, including the following steps:

[0064] S1: Constructing noisy hyperspectral images YSpecifically, according to the three-dimensional characteristics of hyperspectral images, the additive noise of spatial and spectral dimensions is jointly considered to construct a hyperspectral image. Y Formula 1:

[0065] (Formula 1);

[0066] in, 、 represent the noisy hyperspectral image, the hyperspectral image to be restored, and the additive noise respectively; R is the set of real numbers, H Represents the number of pixels in the horizontal direction of the spatial dimension, W Represents the number of pixels in the vertical direction of the spatial dimension, B Represents the number of bands of the spectral dimension.

[0067] S2: Obtaining noisy hyperspectral images based on orthogonal projection Y On a noisy low-dimensional manifold L ; Specifically, initialize X ,make X=Y , introduce the orthogonal projection method to estimate the noisy low-dimensional manifold L Formula 2:

[0068] (Formula 2);

[0069] in, V Represents the projection matrix.

[0070] Furthermore, in the noise reduction problem, the process of learning the orthogonal projection matrix is ​​easily affected by noise or outliers. Therefore, in the noisy low-dimensional manifold L Introducing maximization The norm-obtained manifold learning framework is Equation 3:

[0071] (Formula 3);

[0072] in, express X Expanding the matrix in the third dimension, Represents the matrix norm.

[0073] Solve the manifold learning framework to obtain the projection matrix V The closed-form solution includes steps S21-S23;

[0074] S21: Derivative equation 3 to obtain equation 4:

[0075] (Formula 4);

[0076] S22: Constraint-based , for the matrix Perform singular value decomposition to obtain Equation 5:

[0077] (Formula 5);

[0078] in, SVD represents singular value decomposition;

[0079] S23: Calculate equation 5 to obtain the projection matrix V The closed-form solution is Equation 6:

[0080] (Equation 6).

[0081] Furthermore, substituting Equation 6 into Equation 2, we obtain the noisy low-dimensional manifold L .

[0082] S3: Using K-NN method to extract low-dimensional manifolds L The image blocks with non-local clustering are obtained from ,in P Indicates the number of image blocks. In this case, the image blocks are noisy image blocks.

[0083] S4: Using sparse tensor decomposition method to The noise in the image is separated to obtain the noise-free image block; specifically, the sparse tensor decomposition model is first introduced to approximate the noise-free data, that is, the image block of the non-local clustering After introducing sparse tensor decomposition, we get Equation 7:

[0084] (Formula 7);

[0085] in, 、 and is the feature matrix, is a sparse constraint.

[0086] Furthermore, , Representation weighted norm, the convex optimization problem of Equation 7 is obtained as Equation 8:

[0087] (Equation 8);

[0088] in, is the weight parameter, which can be .

[0089] Furthermore, the optimization of Equation 8 is decomposed into two sub-problems, which are Subproblems and Subproblem, and iteratively update each variable by fixing other variables, initializing it in the first iteration X ,by X=Y Iterate and get P A noise-free image block, P The noise-free image patches are reassembled to obtain a noise-free low-dimensional manifold L’ ;in,

[0090] The sub-problem is Equation 9:

[0091] (Equation 9);

[0092] Among them, Equation 9 is solved using singular value decomposition 、 and ;

[0093] Sub-question 10 is the essence:

[0094] (Equation 10);

[0095] Among them, Equation 10 is solved using the tensor weighted shrinkage threshold algorithm.

[0096] S5: Recombining the noise-free image blocks to obtain a noise-free low-dimensional manifold L’ ;

[0097] S6: Inverse Transformation of Low-Dimensional Manifolds L’ Obtain noise-free hyperspectral images X’ Specifically, use Equation 11 to obtain a noise-free hyperspectral image X’ , Equation 11 is the inverse transformation of Equation 2:

[0098] (Equation 11).

[0099] In summary, the above-mentioned hyperspectral image denoising method based on manifold space sparse tensor decomposition can be summarized using the following algorithm:

[0100] Input: noisy hyperspectral image Y , weight parameter = ;

[0101] ①:for =1:10 do

[0102] ②: Use Equation 6 to learn the projection matrix V, and substitute into Equation 2 to obtain the noisy low-dimensional manifold L ;

[0103] ③: Use K-NN method to extract the low-dimensional manifold L The image blocks with non-local clustering are obtained from , construct a tensor collection ;

[0104] ④:Use sparse tensor decomposition method to Separate the noise in

[0105] ⑤:for do

[0106] ⑥: Fix other variables and iteratively update using formula 9 ;

[0107] ⑦: Fix other variables and iteratively update using formula 10 ;

[0108] ⑧:end for

[0109] 9: Recombination Get a noise-free low-dimensional manifold L’ ;

[0110] ⑩: Using Equation 11 for noise-free hyperspectral images X’ to rebuild;

[0111] ⑪:end for

[0112] Output: X’ .

[0113] In order to quantitatively and qualitatively evaluate the noise reduction effect, this paper selects four classic hyperspectral image noise reduction methods: tensor-based hyperspectral image noise reduction methods (including LRTA and PARAFAC), low-rank matrix restoration methods (LRTV and NAILRMA), and uses the noise reduction results of these comparison methods to compare with the results of this paper. The quality comparison uses three quality evaluation indicators: PSNR (dB), SSIM and SAM. The quantitative analysis results are shown in Table 1, and the visual comparison results are shown in Table 2. Figure 2 shown.

[0114] Table 1

[0115]

[0116] It can be found from Table 1 that compared with the four comparison methods of LRTA, PARAFAC, LRTV and NAILRMA, the method of the present invention has higher PSNR, SSIM and smaller SAM values, which shows that the method of the present invention has obvious advantages in reconstructing structural information and is also better than other methods in suppressing spectral distortion.

[0117] When the noise intensity =30, the visual comparison of the noise reduction results on the Toy data is as follows: Figure 2 As shown, Figure 2 Figure a is the denoised reference image, Figure b is the noisy image without denoising, Figure c is the result of image denoising using the LRTA method, Figure d is the result of image denoising using the PARAFAC method, Figure e is the result of image denoising using the LRTA method, Figure f is the result of image denoising using the NAILRMA method, and Figure g is the result of image denoising using the method disclosed in the present invention. It is not difficult to see that all methods have a suppressive effect on noise, but upon careful observation, it is found that there is still a lot of noise in the denoising results of the LRTV and PARAFAC methods. The denoising results of LRTA and NAILRMA are better than those of LRTV and PARAFAC methods, but it is difficult to retain the structural information of the image during the denoising process. In comparison, the method of the present invention not only has better detail reconstruction performance, but also shows obvious advantages in retaining the edges of the image.

[0118] The present invention is not limited to the aforementioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.

Claims

1. A hyperspectral image denoising method based on manifold space sparse tensor decomposition, characterized by: The following steps are involved: S1: Constructing noisy hyperspectral images Y : According to the three-dimensional characteristics of hyperspectral images, the additive noise of spatial and spectral dimensions is jointly considered to construct a hyperspectral image. Y Formula 1: (Formula 1); in, 、 and represent the noisy hyperspectral image, the hyperspectral image to be restored, and the additive noise respectively; R is the set of real numbers, H Represents the number of pixels in the horizontal direction of the spatial dimension, W Represents the number of pixels in the vertical direction of the spatial dimension, B Indicates the number of bands of the spectral dimension; S2: Obtaining noisy hyperspectral images based on orthogonal projection Y Low-dimensional manifold L : initialization X ,make X=Y , a noisy low-dimensional manifold L Formula 2: (Formula 2); in, V represents the projection matrix; On a noisy low-dimensional manifold L Introducing maximization The norm-obtained manifold learning framework is Equation 3: (Formula 3); in, express X Expanding the matrix in the third dimension, Represents the matrix norm; Solve the manifold learning framework to obtain a closed-form solution of the projection matrix V, specifically steps S21-S23; S21: Derivative equation 3 to obtain equation 4: (Formula 4); S22: Constraint-based , for the matrix Perform singular value decomposition to obtain Equation 5: (Formula 5); in, SVD represents singular value decomposition; S23: Calculate equation 5 to obtain the projection matrix V The closed-form solution is Equation 6: (Equation 6); Substituting Equation 6 into Equation 2, we obtain the noisy low-dimensional manifold L ; S3: Using K-NN method to extract low-dimensional manifolds L The image blocks of non-local clusters are obtained from ,in P Indicates the number of image blocks. In this case, the image blocks are noisy image blocks. S4: Using sparse tensor decomposition method to The noise in the image is separated to obtain a noise-free image block: For non-local clustering of image patches After introducing sparse tensor decomposition, we get Equation 7: (Formula 7); in, 、 and is the feature matrix, is a sparse constraint term; set up , Representation weighted norm, the convex optimization problem of Equation 7 is obtained as Equation 8: (Equation 8); in, is the weight parameter; Decompose the optimization of Equation 8 into two sub-problems, which are Subproblems and Subproblem, and iteratively update each variable by fixing other variables, initializing it in the first iteration X ,by X=Y Iterate and get P A noise-free image block, P The noise-free image patches are reassembled to obtain a noise-free low-dimensional manifold L’ ;in, The sub-problem is Equation 9: (Equation 9); Among them, Equation 9 is solved using singular value decomposition 、 and ; The sub-problem is Equation 10: (Equation 10); Among them, Equation 10 is solved using the tensor weighted shrinkage threshold algorithm; S5: Recombining the noise-free image blocks to obtain a noise-free low-dimensional manifold L’ ; S6: Inverse transform of noise-free low-dimensional manifolds L’ Obtain noise-free hyperspectral images X’ : In step S6, the noise-free hyperspectral image is obtained using equation 11: X’ , Equation 11 is the inverse transformation of Equation 2: (Equation 11).

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