Large-scale hyperspectral image distributed recovery method and system based on graph signal processing and superpixel segmentation

Abstract

This invention discloses a large-scale distributed hyperspectral image restoration method and system based on graph signal processing and superpixel segmentation. This method utilizes superpixel segmentation technology and a distributed algorithm based on graph signal processing to obtain a large-scale HSI (hybrid noise in hyperspectral images) removal method. The underlying structure of HSI is modeled by a two-layer architecture graph: the upper layer is a skeleton graph, which effectively represents the relationships between superpixels while preserving boundary information and reducing computational complexity; the lower layer is a detail graph, composed of a series of subgraphs used to model the similarity between pixels. Based on the two-layer graph structure, the HSI restoration problem is formulated as a series of optimization problems, each corresponding to a subgraph. Utilizing the information interaction between the skeleton graph and subgraph nodes, the restoration method is a receive-send-fuse distributed algorithm. Numerical experiments on synthetic and real datasets demonstrate that this restoration algorithm is effective compared to existing methods.

Description

Technical Field

[0001] This invention relates to the fields of hyperspectral data processing and graph signal processing technology, and in particular to a method and system for large-scale distributed restoration of hyperspectral images based on graph signal processing and superpixel segmentation. Background Technology

[0002] Hyperspectral images (HSI) consist of dozens or even hundreds of grayscale images corresponding to spectral channels, possessing high spectral resolution and rich texture information. Based on these HSI characteristics, the combination of spatial images and spectral bands can provide favorable conditions for target feature extraction. Therefore, it is widely used in fields such as food quality and safety assessment, medical diagnosis and image-guided surgery, and precision agriculture. However, HSI images are often affected by various noises during acquisition and transmission. These noises pose significant challenges to subsequent analysis, especially in feature extraction and target recognition, greatly reducing processing reliability. Therefore, effectively removing HSI noise has become a crucial issue.

[0003] Currently, various denoising methods have been proposed for HSI recovery. The traditional approach to HSI denoising is to describe each band as a grayscale image and then apply two-dimensional denoising methods, such as BM3D, to remove noise band by band. However, these methods ignore the high correlation between spectral bands or spatial pixels, resulting in relatively poor recovery performance. In light of this, many HSI denoising methods have been proposed to consider these correlations, such as HSSNR, a hybrid spatial-spectral derivative domain wavelet contraction model that considers the differences in signal regularity across spatial and spectral dimensions; CTV and SSAHTV, which apply a total variational (TV) image operator to HSI recovery, effectively characterizing the spatial piecewise smooth (PWS) properties of HSI; LRMR, a method based on low-rank (LR) matrix approximation, utilizing the low-dimensional structure in high-dimensional data to remove noise; TSLRLN and LRTDTV, methods based on tensor decomposition to utilize the LR properties of HSI; and GLF, a method combining different LR attribute representations, etc. These methods effectively represent the spatial and spectral correlations of HSI. In addition, some nonlocal-based methods, such as NLTR and NGMeet, can denoise HSI in blocks. However, these methods only consider nonlocal self-similarity and ignore the PWS characteristics within the groups. TVNLRTD treats nonlocal self-similarity as a regularization term in the model and combines it with other global regularization terms (such as TV). It achieves good recovery performance through combined regularization, but it cannot simply perform block-based recovery and suffers from high computational complexity per node under large-scale HSI. Unlike nonlocal-based methods, superpixel segmentation-based methods, such as SSSB, group the pixels of the HSI into a series of uniform regions whose shapes depend on boundary information and are irregular. Therefore, superpixel segmentation-based methods can effectively preserve boundary information, while nonlocal methods cannot due to their cube-based block strategy. However, existing superpixel segmentation-based methods, such as SSSB, perform poorly in HSI recovery, partly because they do not consider the PWS characteristics of the HSI and the similarity between superpixels. Given the shortcomings of these algorithms, and considering Graph Signal Processing (GSP), a multidisciplinary research field that uses graph topology to describe the correlations between network data and comprehensively constructs the theoretical framework for network data processing, significantly expanding the theoretical boundaries of classical signal processing, a novel hyperspectral hybrid noise denoising method based on GSP and superpixel segmentation techniques can be invented.

[0004] Furthermore, existing methods typically focus on a small HSI or a sub-region of a large HSI, and due to the often centralized operators, they have poor scalability on large HSIs. Moreover, many recovery methods convert 3D HSI datasets into 2D matrices, which, due to their spatial dimension being much larger than their spectral dimension, are ill-conditioned matrices, leading to blurring and loss of detail in the denoising results. For large-scale HSIs, the loss of boundary information and texture details becomes even more severe.

[0005] Existing hyperspectral images (HSI) are frequently affected by various noises, posing significant challenges to subsequent applications. Many existing restoration algorithms do not perform well on large-scale HSIs; therefore, improving the scalability of restoration methods is a crucial issue. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a large-scale distributed restoration method for hyperspectral images based on graph signal processing and superpixel segmentation. This method utilizes superpixel segmentation technology and distributed algorithms based on graph signal processing to propose a large-scale HSI mixed noise removal method.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation provided by this invention includes the following steps:

[0009] (10) Constructing the input signal model: Performing linear normalization on the hyperspectral data;

[0010] (11) Pre-denoising: Select a hyperspectral image of a band and pre-denoise the image of the band;

[0011] (12) Superpixel segmentation: The SLIC superpixel segmentation algorithm is used to segment the hyperspectral image after pre-denoising into a series of superpixel regions;

[0012] (13) Construct a skeleton diagram based on the superpixel region;

[0013] (14) Local graph construction: Construct a local graph for all elements of each superpixel region;

[0014] (15) Subgraph construction: Based on the skeleton graph and local graph, an overlapping subgraph is constructed, with each subgraph corresponding to a computing node; in each subgraph, a distributed denoising method is used to perform distributed denoising on the hyperspectral image and solve the subgraph optimization model;

[0015] (16) Distributed denoising of the hyperspectral image is performed in each sub-image using a swapped distributed approach;

[0016] (17) Based on the subgraph, establish an optimization model for each subgraph;

[0017] (18) Repeat the above iteration. In each iteration, the optimization model in step (8) is solved by the exchange distributed method in step (7). The iteration stops when each subgraph meets the iteration convergence condition, and the update iteration ends when the subgraph that meets the condition continues to be solved in other subgraphs.

[0018] Furthermore, the skeleton diagram construction in step (4) is performed according to the following steps:

[0019] Each superpixel region is modeled as a skeleton graph node. The graph signal of each node is the average value of all pixels in the superpixel region, and the coordinates are the coordinates of the pixel whose intensity value in the superpixel region is closest to the graph signal.

[0020] Constructing a skeleton graph using a modified KNN algorithm in, This represents the set of nodes consisting of all superpixel nodes. Let be the set consisting of all edges. This represents the adjacency matrix of the skeleton graph, used to characterize the relevance weight matrix of the edges;

[0021] The element a i,j Calculated using formula (1):

[0022]

[0023] Among them, I i I represents the coordinates of the i-th superpixel; j x represents the coordinates of the j-th superpixel; i x represents the image signal of the i-th superpixel; j σ represents the image signal of the h-th superpixel; l , σ x There are two constant parameters;

[0024] get Then, set the first k largest values ​​in each row to 1 and the rest to 0. Next, symmetricize and correct the processed matrix to make it an unweighted matrix, thus obtaining the final matrix.

[0025] Furthermore, the local graph construction in step (5) is performed according to the following steps:

[0026] For each superpixel region, construct a local graph for all elements. Let K be the number of elements in the m-th superpixel region. m Each pixel is modeled as a node, forming a local graph.

[0027] in, Let represent the set of nodes consisting of all pixel nodes in the m-th superpixel. This represents the set of edges connecting each node to its four neighboring nodes. It is an unweighted four-neighbor adjacency matrix;

[0028] The signal in the local image above is a vector. The image signal of the hyperspectral image in band b is Apply local maps to hyperspectral images for each band;

[0029] The image signal representation of the hyperspectral image is obtained by concatenating the image signals of all bands into a matrix:

[0030]

[0031] Among them, X m (i,b) represents the i-th image signal in b bands of the hyperspectral image; X m,b This represents the m-th image signal in b bands of a hyperspectral image; This indicates that the dimension of the matrix is ​​K. m ×p.

[0032] Furthermore, the subgraph construction in step (6) is performed according to the following steps:

[0033] Based on the skeleton graph and local graph, overlapping subgraphs are constructed, with each subgraph corresponding to a computation node. The hyperspectral restoration problem is transformed into solving a series of small-scale problems, each of which is located on a subgraph, and each subgraph is centered on a node of the skeleton graph.

[0034] The f-th subgraph is defined according to the following formula:

[0035]

[0036] in,

[0037] This represents the f-th subgraph; This represents the set of nodes consisting of all the nodes in the subgraph. M represents the set of edges between nodes; s The subgraph represents the total number of subgraphs; f represents the f-th subgraph.

[0038] It represents the set of all neighboring nodes within d hops of node f;

[0039] ρ(f,j) represents the shortest path required to reach node j from node f;

[0040] Each subgraph contains multiple local graphs. The m-th local graph is a section of the set of all neighboring nodes within d hops of node f, i.e.

[0041] Where d represents the neighbors within d hops; m represents the m-th local graph, which is also the node of the f-th subgraph; It represents the set of nodes consisting of all pixel nodes in the m-th superpixel; Representation diagram The set of all neighboring nodes within d hops of node f;

[0042] The set of edges Define it according to the following steps:

[0043] If a partial image and If there is a boundary connection within the corresponding superpixel region, then the boundary node is connected to its four neighboring nodes, and there is an edge connecting the coordinate nodes of the two local graphs; otherwise, there is only one edge between the two local graphs, that is, there is an edge connecting the coordinate nodes of the two local graphs.

[0044] Get Laplace matrix Use the same submap for all frequency bands of the hyperspectral image region corresponding to the submap;

[0045] The nodes on the f-th subgraph The signal in the above diagram is mapped into vector form:

[0046]

[0047] in, X f (i,b) represents the subgraph in the b-th band. The graph signal at the i-th node; X f (1,b) represents the first image signal of the b-th band in the f-th sub-image; K m The total number of nodes in the m-th local graph on the f-th subgraph represents the number of pixels contained in the superpixel corresponding to the m-th local graph on the f-th subgraph; x represents the x-th band.

[0048] All bands of image signals are stitched into a matrix using the following formula:

[0049]

[0050] Obtain subgraph The hyperspectral image is represented by a graphical signal.

[0051] Furthermore, step (7) performs distributed denoising on the hyperspectral image in the following manner:

[0052] Several computational units are set up, each corresponding to a subgraph. Each computational unit is based on a skeleton graph. The edge establishes a transmission link with its adjacent computing units, and the computing unit receives the calculation results of its neighbors each time it iterates the optimization model of the subgraph;

[0053] The received results calculated at its neighboring nodes are merged with the previous calculation results calculated by itself and then averaged.

[0054] Each subgraph-based computational optimization model computes new results for itself and its neighbors;

[0055] The new calculation result and the corresponding part of the new result are transmitted to its respective neighbors.

[0056] Repeat the previous steps to iteratively solve the subgraph optimization model.

[0057] Furthermore, the optimization model in step (8) is established according to the following steps:

[0058]

[0059] in, K m This represents the number of pixels in the m-th superpixel. α and β are two parameters used to adjust the proportions of the kernel norm, GLR, and l1 norm. f This represents the modeling of sparse noise in the f-th subgraph; O f The f-th subgraph represents the original input hyperspectral image data; ε represents a very small threshold; r is a constant representing the constraint on the rank of the hyperspectral signal; f represents the f-th subgraph.

[0060] The GLR is defined as follows:

[0061]

[0062] The matrix form of GLR is defined as follows:

[0063] ||X|| GLR =[||x1|| GLR ,…,||x b || GLR ,…,||x p || GLR (5)

[0064] in, Let a represent the Laplacian matrix of the f-th subgraph; i，jx represents the (i, j)th element of the adjacency matrix of the f-th subgraph; i Represents the signal of the i-th subgraph in the f-th subgraph; ||x b || GLR This represents the GLR definition for the b-th band.

[0065] Furthermore, the optimization model in step (8) is solved in the following manner:

[0066] The augmented Lagrange multiplier method is used to solve this problem.

[0067] Equation (3) can be converted to:

[0068]

[0069] Among them, H f H represents the introduced auxiliary variable. f =X f ;

[0070] The augmented Lagrangian function of formula (6) is:

[0071]

[0072] Where γ (γ > 0) is the penalty variable, C f and D f It is a Lagrange multiplier.

[0073] The formula (7) is optimized alternately according to the following steps, and the specific updates are as follows:

[0074] 2) Update H f :

[0075]

[0076] Where (k+1) represents the (k+1)th iteration, This represents the denoised hyperspectral image of the f-th subgraph after the k-th iteration; This represents the sparse noise in the f-th subgraph during the k-th iteration; This represents the Lagrange multiplier result of the f-th subgraph in the k-th iteration;

[0077] For a given matrix Its rank is r, and it is decomposed using singular value decomposition to obtain:

[0078] Z=UE r V H E r =diag(σ i (9)

[0079] in, and It is an orthogonal matrix, E r This represents a diagonal matrix composed of singular values; singular values ​​σ i(1≤i≤r) Given a threshold φ ≥ 0, the singular value thresholding operator is defined as:

[0080]

[0081] Where η=σ i -φ, η represent the vector formed by the difference between the i-th singular value and the threshold; σ i Represents the i-th singular value after singular value decomposition; φ is a constant representing the threshold; D φ (·) denotes the solution of the singular value contraction operator; then the singular value contraction operator (10) is the solution to the following problem:

[0082]

[0083] By using the singular value contraction operator (10), the solution to the optimized formula (8) is:

[0084]

[0085] 5) Update X f :

[0086]

[0087] in, Based on the matrix form GLR in (5), formula (13) is equivalent to:

[0088]

[0089] Formula (14) is decomposed into p subproblems, which are solved band by band. The j-th subproblem is:

[0090]

[0091] Formula (15) is a least squares problem, and its analytical solution is:

[0092]

[0093] The solution to (14) is obtained by combining the solutions (16) for each band:

[0094]

[0095] Formula (17) can be rewritten in matrix form:

[0096]

[0097] Through derivation, formula (13) is equivalent to the following formula and solution:

[0098]

[0099] 6) Update S f

[0100]

[0101] By introducing a soft threshold operator:

[0102]

[0103] in, Δ>0, the solution to formula (20) can be expressed as:

[0104]

[0105] 7) Update the Lagrange multipliers and parameter γ:

[0106]

[0107] Where ρ is the growth step size, γ max It is a constant.

[0108] Furthermore, in step (9), each subgraph satisfies the iterative convergence condition calculated according to the following formula:

[0109]

[0110] Where ε1 and ε2 are two constants. H represents the introduced auxiliary variable. f =X f The solution after (k+1) iterations; Let f represent the sparse noise solution of the f-th subgraph after (k+1) iterations; Let f represent the solution of the clean hyperspectral image of the f-th subgraph after (k+1) iterations.

[0111] The large-scale hyperspectral image distributed restoration system based on graph signal processing and superpixel segmentation provided by the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the above-mentioned method.

[0112] The beneficial effects of this invention are as follows:

[0113] This invention provides a distributed method for large-scale hyperspectral image restoration based on graph signal processing and superpixel segmentation. First, the underlying structure of HSI is modeled by a two-layer architecture graph. The upper layer is a skeleton graph, a coarsened graph constructed using the k-nearest neighbor algorithm, whose nodes correspond to a series of superpixels formed by HSI segmentation. The skeleton graph can effectively represent the relationships between superpixels while preserving boundary information and reducing computational complexity. The lower layer is a detail graph, composed of a series of subgraphs used to model the similarity between pixels. Second, based on the two-layer graph structure, the HSI restoration problem is formulated as a series of optimization problems, each corresponding to a subgraph. Third, utilizing the information interaction between the skeleton graph and subgraph nodes, a distributed algorithm of send-receive-fuse is tailored for the restoration problem. This method overcomes the problem that hyperspectral images (HSI) are often affected by various noises, and the significant challenges they pose to subsequent applications.

[0114] Distributed algorithms based on graph signal processing can offer a novel approach to solving this problem. Within the graph signal processing framework, these distributed methods exchange information with neighbors during each iteration, potentially achieving better denoising performance than methods based on nonlocal or superpixel segmentation. Numerical experiments on synthetic and real datasets demonstrate that this recovery algorithm is effective compared to existing methods.

[0115] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0116] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0117] Figure 1 This is the clean original image provided by the present invention.

[0118] Figure 2 This is the image with added noise provided by the present invention.

[0119] Figure 3 This is the image after LRMR denoising provided by the present invention.

[0120] Figure 4 This is the image after LRTV denoising provided by the present invention.

[0121] Figure 5 This is the image after SSSB denoising provided by the present invention.

[0122] Figure 6 This is the image after denoising using GLRSSDA, as provided by the present invention.

[0123] Figure 7 This is a comparison chart of PSNR for each band provided by the present invention.

[0124] Figure 8 This is a comparison chart of SSIMs for different bands provided by this invention. Detailed Implementation

[0125] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0126] Example 1

[0127] The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation provided in this embodiment includes the following steps:

[0128] (1) Constructing the input signal model: The hyperspectral data is linearly normalized to the range of [0, 1], and the input signal model Y = X + S + N is constructed, where Y represents the input noise signal; X represents the clean original image; S represents sparse noise, which is used to characterize impulse noise, bad pixels, stripe noise, etc.; and N represents Gaussian noise.

[0129] (2) Pre-denoising: Select a specific or random hyperspectral image of a band and use a median filter to pre-denoise the image of that band.

[0130] (3) Superpixel segmentation: The SLIC superpixel segmentation algorithm is used to segment the hyperspectral image of a band after pre-denoising into a series of superpixel regions.

[0131] (4) Skeleton Graph Construction: Based on the segmented superpixels, a skeleton graph can be defined. Assume that after superpixel segmentation, there exists M... s Each superpixel region is modeled as a skeleton graph node. The graph signal of each node is the average value of all pixels within that superpixel region, and the coordinates are the coordinates of the pixel whose intensity value within the superpixel region is closest to the graph signal. Then, a modified KNN algorithm is used to construct the skeleton graph. in This represents the set of nodes consisting of all superpixel nodes. Let be the set consisting of all edges. element a i，j Calculated using formula (1):

[0132]

[0133] Among them, I i and x i Let σ represent the coordinates and graph signal of the i-th superpixel, respectively. l , σ x These are two constant parameters. We obtain... Then, set the first k largest values ​​in each row to 1 and the rest to 0. Next, symmetricize and correct the processed matrix to make it an unweighted matrix, thus obtaining the final matrix.

[0134] (5) Local graph construction: Construct a local graph for all elements in each superpixel region. Let K be the number of elements in the m-th superpixel region. m A local graph is defined as a set of pixels, where all pixels are modeled as nodes. in Let represent the set of nodes consisting of all pixel nodes in the m-th superpixel. This represents the set of edges connecting each node to its four neighboring nodes. Given an unweighted four-neighbor adjacency matrix, which is sparse, the signal in the local graph can be represented as a vector. Then the HSI signal of the b-th band can be represented as: By applying local maps to the HSI of each band, the HSI map signal representation can be obtained by concatenating the map signals of all bands into a matrix.

[0135] (6) Subgraph Construction: Based on the skeleton graph and local graph, overlapping subgraphs are constructed, each subgraph corresponding to a computation node. Thus, the hyperspectral reconstruction problem can be transformed into solving a series of smaller problems, each located on a subgraph, and each subgraph centered on a node of the skeleton graph. The definition of the f-th subgraph is as follows:

[0136]

[0137] in Let ρ(f,j) represent the set of all neighboring nodes within d hops of node f, and let ρ(f,j) represent the shortest path (number of hops) required to reach node j from node f. It can be seen that each subgraph contains the m-th local graph, and... The set of edges is defined as follows: if the local graph and If there is a boundary connection within the corresponding superpixel region, then the boundary node is connected to its four neighboring nodes, and there is an edge connecting the coordinate nodes of the two local graphs. Otherwise, there is only one edge between the two local graphs, that is, an edge connecting the coordinate nodes of the two local graphs. Therefore, we can obtain The Laplace matrix is ​​expressed as Note that the same subgraph is used for all frequency bands within the HSI region corresponding to the subgraph. The nodes on the f-th subgraph... The signal in the above diagram is mapped to vector form, that is... in X f (i, b) represents the subgraph in the b-th band. The graph signal at the i-th node. Then, by concatenating the graph signals of all bands into a matrix, i.e. It is possible to obtain the subgraph The HSI signal is represented graphically.

[0138] (7) Apply a distributed receive-transmit-converge (also known as switching) approach to perform distributed denoising on HSI in each subgraph. Specifically, assume there are M... s Computational units, each corresponding to a subgraph Each computational unit is based on a skeleton graph. The edge establishes a transmission link with its adjacent computing units. This M s In each iteration of the subgraph optimization model, the computational unit receives the computation results from its neighbors. Then, the node merges and averages the received results computed at its neighboring nodes with its own previous computation result. Next, it computes new results for itself and its neighbors using each subgraph-based computational optimization model. Finally, the node transmits its new computational result and corresponding portions thereof to its respective neighbors. This process is repeated iteratively to solve the subgraph optimization model.

[0139] (8) Based on the subgraph, an optimization model is established for each subgraph. The optimization model corresponding to the f-th subgraph is as follows:

[0140]

[0141] in, K m This represents the number of pixels in the m-th superpixel. α and β are two parameters used to adjust the proportions of the kernel norm, GLR, and l1 norm, where GLR is defined as:

[0142]

[0143] The matrix form of GLR is defined as follows:

[0144] ||X|| GLR =[||x1|| GLR ,…,||x b || GLR ,…,||x p || GLR (5)

[0145] Therefore, it can be regarded as a combination vector form of GLR. GLR is a quadratic form of a matrix and has many excellent properties, in which the solution of the quadratic problem can be solved by simple standard linear algebra. In addition, due to the rank constraint in the optimization model, Equation (3) is non-convex and can be solved by the augmented Lagrange multiplier method (ALM).

[0146] First, we introduce the auxiliary variable H. f Formula (3) can be equivalently transformed into:

[0147]

[0148] Then, the augmented Lagrangian function of formula (6) is:

[0149]

[0150] Where γ (γ>0) is the penalty variable, C f and D f These are Lagrange multipliers, which can optimize one variable while fixing others, performing alternating optimization of formula (7). Therefore, in the (k+1)th iteration, the variables in formula (7) are updated as follows:

[0151] 1) Update H f :

[0152]

[0153] For a given matrix Its rank is r, and it is decomposed using singular value decomposition to obtain:

[0154] Z=UE r V H E r =diag(σ i (9)

[0155] in and It is an orthogonal matrix with singular values ​​σ. i(1≤i≤r) Given a threshold φ ≥ 0, the singular value thresholding (also known as singular value shrinkage) operator can be defined as:

[0156]

[0157] Where η = σ i -φ. Then the singular value contraction operator (10) is the solution to the following problem:

[0158]

[0159] By using the singular value contraction operator (10), the solution to the optimized formula (8) is:

[0160]

[0161] 2) Update X f :

[0162]

[0163] For convenience, please note Based on the matrix form GLR in (5), formula (13) can be equivalent to:

[0164]

[0165] Then, formula (14) can be decomposed into p subproblems, which can be solved band by band. The j-th sub-formula of formula (14) is:

[0166]

[0167] Formula (15) is a least squares problem, and its analytical solution is:

[0168]

[0169] Therefore, the solution to (14) can be obtained by combining the solutions (16) for each band:

[0170]

[0171] Clearly, formula (17) can be rewritten in matrix form:

[0172]

[0173] Through derivation, formula (13) can be equivalently transformed into the following formula and solution:

[0174]

[0175] 3) Update S f

[0176]

[0177] By introducing a soft threshold operator:

[0178]

[0179] in Δ>0, the solution to formula (20) can be expressed as

[0180]

[0181] 4) Update the Lagrange multipliers and parameter γ:

[0182]

[0183] Where ρ is the growth step size, γ max It is a constant.

[0184] (9) Repeat the above iterations. In each iteration, the distributed receiving-transmission-fusion method in step (5) is used to iteratively solve the optimization model equations in step (6). When each subgraph satisfies the iterative convergence condition:

[0185]

[0186] The iteration stops when a subgraph satisfying this condition continues to be iterated over in other subgraphs, at which point the update iteration ends. Here, ε1 and ε2 are two constants.

[0187] Where ε1 and ε2 are two constants. H represents the introduced auxiliary variable. f =X f The solution after (k+1) iterations; Let f represent the sparse noise solution of the f-th subgraph after (k+1) iterations; Let f represent the solution of the clean hyperspectral image of the f-th subgraph after (k+1) iterations.

[0188] Example 2

[0189] In this embodiment, the input hyperspectral image is a clean hyperspectral image of the Washington shopping center, i.e., X, which has 191 bands and dimensions of 1280*307*191. Noise is artificially added to it, including sparse noise (including salt-and-pepper noise and dead zone noise) and Gaussian noise. The output after noise addition is Y. The noisy 3D hyperspectral image is then fed into the model of this method to obtain the denoised hyperspectral image.

[0190] In this example, the parameter settings for the specific steps are as follows: In step (2), a specific hyperspectral band is selected, and the hyperspectral data of the 50th band is taken. The window used for median filtering is [3, 3]; In step (3), the region size in the SLIC superpixel segmentation parameters is set to 30, and the regularization parameter is set to 0.05; In step (4), σ l =100, σ x =0.2, k=3; in step (6), d=1; in step (8), α=0.5, β=0.23, ε=ε1=ε2=1e-6, r=3, ρ=1.5, γ max =1e6, It is a matrix of all zeros, γ (0)=1e-2. Finally, the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) parameters of the denoised hyperspectral image X and the clean image without noise are calculated to evaluate the superiority of the denoising effect.

[0191] The noisy 3D hyperspectral image is fed into the technical solution model with predefined parameters in this patent. The patent's GLRSDA solution is then compared with the hyperspectral image restoration method based on low-rank matrix recovery (LRMR) proposed by Hongyan Zhang, the hyperspectral image restoration method based on total variational regular low-rank matrix decomposition (LRTV) proposed by Wei He, and the hyperspectral image restoration method based on superpixel segmentation of smooth bands (SSSB) proposed by Yaru Fan. The comparison images before and after denoising are shown below. Figure 1-6 As shown, Figure 1-6 This is a grayscale image, representing the depth of black; the darker the black, the smaller the grayscale value. Figure 1 The original image is clean. Figure 2 The image after adding noise. Figure 3 The image after denoising using the LRMR method. Figure 4 The image after denoising using the LRTV method. Figure 5 The image after denoising using the SSSB method. Figure 6 The image after denoising using GLRSDA according to this technical solution; Figure 1 and Figure 2 The comparison shows that this experiment incorporated significant noise, further demonstrating the effectiveness of this technical solution. Based on... Figure 3 and Figure 5 Within the frame, it can be observed that there is a loss of detail in the image. Figure 4 There is an oversmoothing phenomenon, and Figure 6 It exhibits excellent denoising capabilities, not only effectively removing noise but also demonstrating outstanding performance in edge detail, indicating that the denoising effect of this technical solution is observable. Comparing the PSNR and SSIM parameters of each band after denoising using this technical solution with the aforementioned existing technical solutions yields... Figure 7-8 Observe the two images. The solid line with a circle represents the GLRSDA curve of this technology; the solid line with a '.' sign represents the LRMR curve; the dashed line with a '+' sign represents the LRMR curve; and the dashed line with a pentagram represents the SSSB curve. Footnotes in the upper left corner of the images correspond to the line styles and technology schemes. Higher PSNR and SSIM values ​​indicate better noise reduction. Figure 7-8 Observations show that the proposed technical solutions PSNR and SSIM have better noise reduction performance than LRMR, LRTV and SSSB in most bands.

[0192] In summary, it can be observed that the proposed technical solution is superior to the aforementioned existing technical solutions. The average values ​​of PSNR and SSIM for each band of the proposed technical solution and the aforementioned existing solutions are used to obtain the MPSNR and MSSIM indices, as shown in Table 1. It can be observed that the proposed technical solution is superior to the aforementioned existing solutions.

[0193] Table 1 Comparison of Noise Reduction Effects of Different Schemes

[0194]

[0195] The method presented here is a distributed restoration approach for large-scale hyperspectral images based on graph signal processing and superpixel segmentation, which overcomes the problem that hyperspectral images (HSI) are often subject to various noise interferences.

[0196] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A large-scale hyperspectral image distributed recovery method based on graph signal processing and superpixel segmentation, characterized in that Includes the following steps: (1) Constructing the input signal model: Perform linear normalization on the hyperspectral data; construct the input signal model. ,in, This represents the input noise signal; This represents a clean original image; Represents sparse noise; Indicates Gaussian noise; (2) Pre-denoising: Select a hyperspectral image of a band and perform pre-denoising on the image of the band; (3) Superpixel segmentation: The SLIC superpixel segmentation algorithm is used to segment the pre-denoised hyperspectral image into a series of superpixel regions; (4) Construct a skeleton graph based on the superpixel regions; model each superpixel region as a skeleton graph node, where the graph signal of each node is the average value of all pixels within that superpixel region, and the coordinates are the coordinates of the pixel whose intensity value within the superpixel region is closest to the graph signal. Then, construct the skeleton graph using the modified KNN algorithm. ,in This represents the set of nodes consisting of all superpixel nodes. Let be the set consisting of all edges. The adjacency matrix is ​​the skeleton graph. (5) Local graph construction: Construct a local graph for all elements of each superpixel region; let the first... Within each superpixel region there are A local graph is defined as a set of pixels, where all pixels are modeled as nodes. ,in Indicates by the first The set of nodes consisting of all pixel nodes in a superpixel. This represents the set of edges connecting each node to its four neighboring nodes. It is an unweighted four-neighbor adjacency matrix; (6) Subgraph construction: Based on the skeleton graph and local graph, construct overlapping subgraphs, with each subgraph corresponding to a computation node; (7) Distributed denoising of the hyperspectral image is performed in each subgraph using a swapped distributed approach, and the subgraph optimization model is solved; (8) Based on the subgraph, establish an optimization model for each subgraph; the optimization model is established according to the following steps: in, Indicates the first Number of pixels in a superpixel and There are two parameters used to adjust the nuclear norm, GLR, The proportion of norms Indicates the first Modeling sparse noise in subgraphs; Indicates the first The original input hyperspectral image data in each sub-image; This represents a very small threshold. It is a constant representing a constraint on the rank of the hyperspectral signal; Indicates the first Individual charts; Indicates the first Denoising-reduced hyperspectral image of each sub-image; (9) Iterative solution: Repeat steps (7) and (8). In each iteration, the optimized model in step (8) is solved iteratively using the exchange-distributed method in step (7). The iteration stops when each subgraph meets the convergence condition, and the update iteration ends when the subgraph that meets the condition continues to be solved iteratively in other subgraphs.

2. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... The skeleton diagram construction in step (4) is performed according to the following steps: Each superpixel region is modeled as a skeleton graph node. The graph signal of each node is the average value of all pixels in the superpixel region, and the coordinates are the coordinates of the pixel whose intensity value in the superpixel region is closest to the graph signal. A modified KNN algorithm is used to construct a skeleton graph. ,in, This represents the set of nodes consisting of all superpixel nodes. Let be the set consisting of all edges. This represents the adjacency matrix of the skeleton graph, used to characterize the relevance weight matrix of the edges; The elements Calculated using formula (1): in, Indicates the first The coordinates of each superpixel; Indicates the first The coordinates of each superpixel; Indicates the first Image signal of one superpixel; Indicates the first Image signal of one superpixel; Two constant parameters; get Then, select the row with the largest value first. Set one element to 1 and the rest to 0. Then, symmetricize and correct the processed matrix to obtain an unweighted matrix, thus obtaining the final matrix. .

3. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... The local graph construction in step (5) is performed according to the following steps: For each superpixel region, construct a local graph for all elements, and let the first... Within each superpixel region there are Each pixel is modeled as a node, forming a local graph. ; in, Indicates by the first The set of nodes consisting of all pixel nodes in a superpixel. This represents the set of edges connecting each node to its four neighboring nodes. It is an unweighted four-neighbor adjacency matrix; The signal in the local image above is a vector. , No. The image signal of the hyperspectral image in each band is The local map is applied to the hyperspectral image for each band; The image signal representation of the hyperspectral image is obtained by concatenating the image signals of all bands into a matrix: in, Indicates the first The first hyperspectral image of the [band]. Individual signal; Indicates the first The first hyperspectral image of the [band]. Individual signal; The dimension of this matrix is .

4. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... The subgraph in step (6) The construction is carried out according to the following steps: Based on the skeleton graph and local graphs, overlapping subgraphs are constructed, each corresponding to a computation node. The hyperspectral reconstruction problem is transformed into solving a series of smaller problems, each located on a subgraph, and each subgraph is centered on a node of the skeleton graph. Sub-image Defined according to the following formula: in, ; Indicates the first Individual charts; This represents the set of nodes consisting of all the nodes in the subgraph. Represents the set of edges between nodes; Indicates the total number of subgraphs; Indicates the first Individual charts; This represents a node. of The set of all neighboring nodes within a hop; Indicates from node Reaching the node The required shortest path; Each subgraph contains multiple local graphs, the first... A local graph is a node of An element in the set of all neighboring nodes within a hop, i.e. ; in, express Neighbors within 10 jumps; Indicates the first The first partial image, which is also the first... The nodes of the subgraph; Indicates by the first The set of nodes consisting of all pixel nodes in a superpixel; Representation diagram nodes of The set of all neighboring nodes within a hop; The set of edges Define it according to the following steps: If a partial image and If there is a boundary connection within the corresponding superpixel region, then the boundary node is connected to its four neighboring nodes, and there is an edge connecting the coordinate nodes of the two local graphs; otherwise, there is only one edge between the two local graphs, that is, there is an edge connecting the coordinate nodes of the two local graphs. Get Laplace matrix The same submap is used for all frequency bands of the hyperspectral image region corresponding to the submap; The first Nodes on the subgraph The signal above is mapped to vector form: in, Indicates the first Sub-maps of each band In the The graph signal of each node; Indicates the first The first sub-chart The first image signal in each band; Indicates the first The first sub-chart The number of pixels contained in a superpixel corresponding to a local image; Indicates the first Each band; All band signal images are stitched into a matrix using the following formula: Obtain subgraph The hyperspectral image is represented by a graphical signal.

5. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... Step (7) involves distributed denoising of the hyperspectral image in the following manner: Several computational units are set up, each corresponding to a subgraph. Each computational unit is based on a skeleton graph. The edge of the computation unit establishes a transmission link with its adjacent computational units, and the computational unit receives the computation results of its neighbors during each iteration of the subgraph optimization model; The received results calculated at its neighboring nodes are merged with its previous calculation results and averaged. Each subgraph-based computational optimization model computes new results for itself and its neighbors; The new calculation result and its corresponding parts are transmitted to its respective neighbors. Repeat the previous steps to iteratively solve the subgraph optimization model.

6. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... The GLR is defined as follows: (4) The matrix form of GLR is defined as follows: (5) in, Indicates the first The Laplacian matrix of each subgraph; Indicates the first The adjacency matrix of the subgraphs is in the th order. One element; Indicates the first Subgraph No. Individual signal; Indicates the first GLR definition for each band.

7. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 6, characterized in that... The optimization model in step (8) is solved in the following manner: The augmented Lagrange multiplier method is used to solve this problem. Equivalent to formula (3): (6) in, This indicates the introduced auxiliary variable. ; The augmented Lagrangian function of formula (6) is: (7) in, It is a penalty variable. and It is a Lagrange multiplier. The formula (7) is optimized alternately according to the following steps, and the specific updates are as follows: 1) Update : (8) in, Indicates the first The next iteration, Indicates the first Subgraph No. The denoised hyperspectral image after the next iteration; Indicates the first Subgraph No. Sparse noise in the next iteration; Indicates the first Subgraph No. Lagrange multiplier results for the next iteration; For a given matrix and its rank Decompose it using singular value decomposition to obtain: (9) in, and It is an orthogonal matrix. Let represent a diagonal matrix composed of singular values; singular values Given a threshold The singular value threshold operator is defined as: (10) in, Indicates the first A vector consisting of the differences between each singular value and the threshold value; Represents the i-th singular value decomposition. One singular value; It is a constant representing the threshold; Let represent the solution of the singular value contraction operator; then the singular value contraction operator (10) is the solution to the following problem: (11) By using the singular value contraction operator (10), the solution to the optimized formula (8) is: (12) 2) Update : (13) in, According to the matrix form GLR in (5), formula (13) is equivalent to: (14) Formula (14) is decomposed into Each sub-problem is solved band by band. The question is: (15) Formula (15) is a least squares problem, and its analytical solution is: (16) The solution to (14) is obtained by combining the solutions (16) for each band: (17) Formula (17) can be rewritten in matrix form: (18) Through derivation, formula (13) is equivalent to the following formula and solution: (19) 3) Update (20) By introducing a soft threshold operator: (21) in, The solution to formula (20) can be expressed as: 4) Update the Lagrange multipliers and their parameters. : in, To increase the step size, It is a constant.

8. The large-scale hyperspectral image distributed restoration method based on graph signal processing and superpixel segmentation as described in claim 1, characterized in that... In step (9), each subgraph satisfies the iterative convergence condition and is calculated according to the following formula: in, They are two constants. This indicates the introduced auxiliary variable. exist The solution after iteration; Indicates the first Subgraphs in The solution for sparse noise after iteration; Indicates the first Subgraphs in Solution of the clean hyperspectral image after iteration; Indicates the first The original input hyperspectral image data in each sub-figure.

9. A large-scale hyperspectral image distributed restoration system based on graph signal processing and superpixel segmentation, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that... When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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