A spectral imaging method, system, and device

Abstract

The present invention discloses a spectral imaging method, system and device. The method includes: obtaining a hyperspectral image of a target scene, initializing the hyperspectral image, obtaining an image to be processed, evenly dividing the image to be processed into a number of three-dimensional spectral blocks, dividing the number of the three-dimensional spectral blocks into multiple clusters, and obtaining a principal component dictionary for each cluster; obtaining a number of similar blocks to be calculated for the three-dimensional spectral block, selecting a number of the most similar blocks therefrom, and obtaining a weighted sparse representation coefficient of the three-dimensional spectral block according to the dictionary; obtaining an image function according to the dictionary and the weighted sparse representation coefficient, reconstructing the image function, obtaining a target image function, and making the target image function converge by iteratively updating the dictionary and the weighted sparse representation coefficient to obtain a final image function. The weighted sum calculation of non-local similar blocks existing in the hyperspectral image is used to suppress sparse coding noise, improve the accuracy of sparse coding, and reduce the loss of details in the image reconstruction process.

Description

Technical Field

[0001] The present invention relates to a method for spectral imaging, and particularly to a method for reconstructing a spectral image. Background Art

[0002] A hyperspectral image consists of two spatial dimensions and one spectral dimension. Compared with the currently widely used RGB three-color imaging, a hyperspectral image can obtain more spectral channels, thereby obtaining more details and features of the shooting target, and is therefore widely used in fields such as remote sensing and medical imaging.

[0003] Traditional hyperspectral images are generally obtained by scanning. This method sacrifices temporal resolution in exchange for spectral resolution, and this imaging method will cause dynamic scenes to be unable to be photographed. In order to photograph a dynamic caisson, coded aperture spectral imaging has been proposed. Coded aperture spectroscopy performs sparse low-dimensional sampling on three-dimensional hyperspectral data through a single exposure, obtains aliased spectral information on a grayscale camera, and reconstructs three-dimensional spectral data through calculation, and has the ability to obtain spectral videos.

[0004] How to improve the quality of spectral image reconstruction is a key topic in coded aperture spectral imaging. Using different reconstruction algorithms to improve the reconstruction quality is a common reconstruction method, and the TV regularization algorithm is one of them. However, this algorithm will make the reconstructed image too smooth and lose image details. Summary of the Invention

[0005] In order to solve the above technical problems, the present application provides a spectral imaging method.

[0006] A spectral imaging method specifically includes:

[0007] Obtain a hyperspectral image of a target scene, initialize the hyperspectral image to obtain an image to be processed, evenly divide the image to be processed into several three-dimensional spectral blocks, divide the several three-dimensional spectral blocks into multiple clusters, and obtain the principal component dictionary of each cluster; obtain several similar blocks to be calculated of the three-dimensional spectral block, take several of the most similar blocks, and according to the dictionary, obtain the weighted sparse representation coefficient of the three-dimensional spectral block; obtain an image function according to the dictionary and the weighted sparse representation coefficient, reconstruct the image function to obtain a target image function, and iteratively update the dictionary and the weighted sparse representation coefficient to make the target image function converge to obtain a final image function.

[0008] Further, before initializing the hyperspectral image, it further includes: obtaining a grayscale image and the grayscale matrix of the grayscale image; obtaining an RGB image and the RGB matrix of the RGB image, and combining the grayscale image and the RGB image to obtain a hyperspectral image.

[0009] Further, the initialization of the high-light spectrum map specifically includes: multiplying the hyperspectral image by the transpose matrix of the matrix of the hyperspectral image.

[0010] Further, obtaining the weighted sparse representation coefficients of the three-dimensional spectral block specifically includes: taking a number of similar blocks to be calculated around the three-dimensional spectral block, comparing the pixel differences of the RGB three channels of the three-dimensional spectral block and each similar block to be calculated, distinguishing a number of most similar blocks from the number of similar blocks to be calculated according to the pixel difference size, obtaining the sparse representation coefficients of each of the most similar blocks according to the dictionary, and obtaining the weighted sparse representation coefficients of the three-dimensional spectral block according to the sparse representation coefficients.

[0011] Further, the dictionary and the weighted sparse representation coefficients are updated by iteration, where the dictionary and the weighted sparse representation coefficients are updated once every 10 - 25 iterations.

[0012] Further, dividing a number of the three-dimensional spectral blocks into multiple clusters and obtaining the dictionary of each cluster specifically includes: dividing a number of the three-dimensional spectral blocks into multiple clusters by using the K-means clustering algorithm, performing principal component analysis on each cluster, and obtaining the dictionary of each cluster.

[0013] A spectral imaging system includes:

[0014] An image processing unit, configured to obtain a hyperspectral image of a target scene, initialize the hyperspectral image, and obtain an image to be processed;

[0015] An image segmentation unit, configured to evenly divide the image to be processed into a number of three-dimensional spectral blocks, and obtain a number of similar blocks to be calculated of the three-dimensional spectral blocks;

[0016] A calculation unit, configured to divide a number of the three-dimensional spectral blocks into multiple clusters, obtain the dictionary of each cluster, obtain the most similar blocks therefrom from the similar blocks to be calculated, and obtain the weighted sparse representation coefficients of the three-dimensional spectral blocks according to the dictionary;

[0017] A reconstruction unit, configured to obtain an image function according to the dictionary and the weighted sparse representation coefficients, reconstruct the image function, and obtain a target image function.

[0018] A spectral imaging device, for obtaining a grayscale image, successively includes, according to the movement direction of light: a beam splitting prism, an objective lens, a double Amici prism, a relay lens, a coding template, a relay lens, a double Amici prism placed in reverse, a relay lens, and a grayscale camera, and the beam splitting prism, the objective lens, the double Amici prism, the relay lens, the coding template, the relay lens, the double Amici prism placed in reverse, the relay lens, and the grayscale camera are placed in a straight line.

[0019] A spectral imaging device for obtaining RGB images, successively includes a beam splitter prism, a reflecting mirror, and an RGB camera according to the direction of light movement.

[0020] A spectral imaging device includes a grayscale device and an RGB device. The grayscale device includes a beam splitter prism, an objective lens, a double Amici prism, a relay lens, a coding template, a relay lens, a double Amici prism placed in reverse, a relay lens, and a grayscale camera; the RGB device includes a beam splitter prism, a reflecting mirror, and an RGB camera; the grayscale device and the RGB device share a beam splitter prism, and the grayscale device and the RGB device are placed in parallel.

[0021] The beneficial effects of the present invention are as follows:

[0022] The spectral imaging method of the present invention improves the accuracy of sparse representation through the similarity calculation of non-local similar blocks. Since there is sparse coding noise in sparse representation, the present invention uses the weighted sum calculation of non-local similar blocks existing in the hyperspectral image to suppress the sparse coding noise, improve the accuracy of sparse coding, and reduce the detail loss in the image reconstruction process. Moreover, the present invention expands the reconstruction model, further improves the image reconstruction quality, and makes the function converge through iteration to finally obtain the image function.

[0023] In the spectral imaging device of the present invention, all components of the double Amici prism are on a straight line. Only by moving the components back and forth can the optical path be adjusted, without the need to adjust the dispersion angle, which simplifies the process of setup and debugging. A reflecting mirror is also used, so that the light is mirrored before entering the RGB camera, eliminating the mirror image relationship generated by the beam splitter prism. Description of the Drawings

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0025] Figure 1 It is a schematic flowchart of the spectral imaging method;

[0026] Figure 2 It is a schematic structural diagram of the spectral imaging device. Detailed Embodiments

[0027] In order to make the application purpose, features, and advantages of this application more obvious and understandable, the following will clearly and completely describe the technical solutions in the embodiments of this application in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the embodiments described below are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of this application. The present invention will be further clarified below in conjunction with the accompanying drawings and specific embodiments.

[0028] Embodiment 1

[0029] This embodiment provides a spectral imaging device, as Figure 2 shown, including a grayscale imaging device and an RGB imaging device.

[0030] Figure 2 In, the upper row of imaging devices finally presents a grayscale image, and the light passes through a beam splitter prism, an objective lens, a double Amici prism, a relay lens, a coding template, a relay lens, a double Amici prism placed in reverse, a relay lens, and a grayscale camera in sequence. The lower row of imaging devices finally presents an RGB image, and the light passes through a beam splitter prism, a mirror, and an RGB camera in sequence. Among them, after the light passes through the beam splitter prism, it is divided into two paths. One path is captured by the grayscale camera to form a grayscale image, and the other path is captured by the RGB camera to form an RGB image.

[0031] The dispersion device in the grayscale imaging device is a double Amici prism. After the incident light is dispersed by the double Amici prism, the light with the central wavelength still exits along the original direction, is encoded by the coding template, and then undergoes secondary dispersion through a double Amici prism placed in reverse, and finally forms a grayscale image on the grayscale camera through a relay lens.

[0032] The existing imaging devices generally use a triangular prism as the dichroic element, but using a triangular prism requires adjusting the dispersion angle, and the optical path debugging is relatively troublesome. However, in the imaging device of this embodiment, all components of the double Amici prism are on a straight line, and the optical path can be adjusted by simply moving the components back and forth, without the need to adjust the dispersion angle, which simplifies the process of building and debugging.

[0033] After the light is divided into two paths by the beam splitter prism, there will be a mirror image relationship between the split light and the original light. A mirror is added to the RGB imaging device, so that the light is mirrored before entering the RGB camera, eliminating the mirror image relationship generated by the beam splitter prism. This makes the image angle captured by the RGB camera the same as the image angle captured by the grayscale camera.

[0034] Embodiment 2

[0035] A spectral imaging method using the spectral imaging device described in Embodiment 1, as Figure 1 shown, includes the following steps:

[0036] Step 1: Obtain a hyperspectral image of the target scene and initialize the hyperspectral image.

[0037] If the target scene is X((i, j, p)), and the spatial size of X is M×N×L, then the expression of the grayscale image observed by the grayscale camera is:

[0038]

[0039] where y c represents the grayscale image, with a size of M×N; C(i, j, p) represents the encoding template matrix, which encodes the spatial and spectral dimensions of the target scene, with a size of M×N×L; ⊙ is the Hadamard product. Equation (1) is a linear transformation relationship and can be transformed into the following matrix form:

[0040] y c = Φ c X Equation (2)

[0041] where Φ c is the forward response matrix of the grayscale image, with a size of MN×MNL, representing a two-dimensional matrix size, the matrix height is M×N, and the width is M×N×L; X is the vector representation of the target scene, with a size of MNL×1, representing a one-dimensional vector with a length of M×N×L. L is the number of channels of the hyperspectral image.

[0042] Similarly, the RGB image observed by the RGB camera is:

[0043] y rgb = Φ rgb X Equation (3)

[0044] where y rgb is the RGB image observed by the RGB camera, which is a vector formed by concatenating the R, G, and B channel image vectors, y T represents the transpose of the channel matrix; Φ rgb represents the matrix obtained from the spectral curves of the RGB image, with a size of 3MN×MNL.

[0045] Combining the above two images, the model of the hyperspectral image for the entire spectral imaging can be obtained as:

[0046]

[0047] Let Then the above equation can be written as Y = ΦX, where Y represents the hyperspectral image.

[0048] Initialize the hyperspectral image, multiply the obtained hyperspectral image Y by the transpose matrix of the matrix Φ of the hyperspectral image to obtain the image to be processed Φ T Y, with dimensions M×N×L, Φ T is the matrix transpose.

[0049] It should be noted that all the above dimension expressions M, N, and L are three-dimensional tensor dimensions.

[0050] Step 2: Evenly divide the image to be processed into several three-dimensional spectral blocks, divide the several three-dimensional spectral blocks into multiple clusters, and obtain the principal component dictionary of each cluster.

[0051] Evenly divide the image to be processed into several three-dimensional spectral blocks with dimensions of n×n×L. For hyperspectral images, within a small adjacent range, the spectral curves are similar, and the spectral image similarity between different bands is also very high. The spectral reflection curve of a natural scene is a sparse signal and can be represented by 6 - 8 principal components. Therefore, this spectral block is a signal with a relatively high redundancy and high sparsity, and can be sparsely represented by a few principal components.

[0052] After block division, use the K-means clustering algorithm to divide several three-dimensional spectral blocks into multiple clusters, perform principal component analysis on each cluster, and obtain the dictionary D of each cluster k . The spectral blocks in the same cluster can be well sparsely represented by the dictionary of this cluster, and the dictionary here is an orthogonal matrix.

[0053] Step 3: Obtain several most similar blocks of the three-dimensional spectral block, and according to the dictionary in Step 2, obtain the weighted sparse representation coefficients of the three-dimensional spectral block.

[0054] In hyperspectral images, there are regions with similar colors and materials in an image, and their spectral reflection curves are also similar. This cross-space non-local similarity can be used to improve the accuracy of sparse representation.

[0055] Take several blocks to be calculated for similarity along the periphery of the three-dimensional spectral block, compare the pixel differences of the RGB three channels at the same position in the RGB image between the three-dimensional spectral block and each block to be calculated for similarity, and distinguish several most similar blocks j from m blocks to be calculated for similarity according to the pixel difference size. The value of j can be specified according to requirements, and generally 15 is taken. Specifically, it includes:

[0056] Estimate the non-local similar blocks of the three-dimensional spectral block according to the pixel difference size, and obtain:

[0057]

[0058] Among them, D im represents the pixel difference, x r，i 、xg，i , \(x\) b，i respectively represent the vector forms of the \(i\)-th three-dimensional spectral block of the RGB three channels; \(x\) r，m , \(x\) g，m , \(x\) b，m respectively represent the vector forms of the \(m\)-th block to be calculated for similarity of the three-dimensional spectral block; the \(T\) in the upper right corner represents matrix transpose.

[0059] \(D\) im represents the pixel difference and is used to estimate the similarity between two non-local similar blocks. The smaller \(D\) im is, the higher the similarity. Non-local similar blocks refer to spectral blocks with similarity at different positions in the same image.

[0060] Obtain the sparse representation coefficients of each of the most similar blocks according to the dictionary, and obtain the weighted sparse representation coefficients of the three-dimensional spectral block according to the sparse representation coefficients. Specifically, it includes:

[0061] Multiply the dictionary \(D\) k obtained in step two with the most similar blocks to obtain the sparse representation coefficients \(\alpha\) i，j of each of the most similar blocks. \(\alpha\) i，j represents the sparse representation coefficient of the \(j\)-th most similar block of the \(i\)-th three-dimensional spectral block.

[0062] The weighted sparse representation coefficient is:

[0063]

[0064] where \(\delta\) i，j represents the weighting coefficient.

[0065] Since there is sparse coding noise in the coefficient representation coefficients, non-local similar block weighting can be used to suppress the sparse coding noise and improve the accuracy of sparse coding.

[0066] Step four: Obtain an image function according to the dictionary and the weighted sparse representation coefficients, reconstruct the image function to obtain a target image function, and make the target image function converge by iteratively updating the dictionary and the weighted sparse representation coefficients to obtain a final image function.

[0067] According to the dictionary \(D\) k and the weighted sparse representation coefficients, obtain an image function:

[0068]

[0069] where \(R\) i \(X\) represents the \(i\)-th three-dimensional spectral block taken from the target scene matrix \(X\). means \(\|\alpha\) i||1 represents the sparsity constraint, and α i represents the sparse representation coefficient of the i-th three-dimensional spectral block. λ, γ, and η are regularization parameters, and C k represents the set of three-dimensional spectral blocks belonging to the k-th cluster. In the second summation term, the dictionary D in step two is used k to minimize the summation term.

[0070] To further improve the reconstruction quality, the image function is extended to obtain the target image function:

[0071]

[0072] where λ i and γ i are diagonal matrices, and the diagonal elements are λ i，l , γ i，l respectively, to weight each value of the sparse representation coefficient. l represents the l-th element of a vector or diagonal matrix, and the corresponding adaptive weights λ i，l , γ i，l are respectively:

[0073]

[0074] where C1 and C2 are preset constants that can be adjusted according to requirements; ε is a relatively small positive number used to prevent the denominator from being zero, such as 0.000001.

[0075] Solving equation (8) according to the alternating optimization method, first fix X to find α, which becomes:

[0076]

[0077] Use the iterative shrinkage algorithm to solve equation (9), and the result of the t-th iteration is as follows:

[0078]

[0079] where, τ1 and τ2 have no specific meaning, they are just a reference for convenient expression in the equation is a vector, ν il (t) is the l-th element of this vector, q is a constant, t represents the t-th iteration, and α il (t+1) represents the value of the l-th element in the (t + 1)-th iteration.

[0080]

[0081] Then, fix α and update X. The t-th update result of X is as follows:

[0082]

[0083] Update the dictionary in Step 2 and the weighted sparse representation coefficients in Step 3 every 15 iterations. The number of iterations can be determined according to specific requirements, generally taking 10 - 25 times.

[0084] Keep iterating until the objective image function formula (8) converges to obtain the final image function, which is the spectral imaging we need.

[0085] Embodiment 3

[0086] A spectral imaging system includes the following units:

[0087] An image processing unit, configured to obtain a hyperspectral image of a target scene, initialize the hyperspectral image, and obtain an image to be processed. Transfer the image to be processed to the image segmentation unit for processing.

[0088] An image segmentation unit, configured to evenly divide the image to be processed into a plurality of three-dimensional spectral blocks, and obtain a plurality of similar blocks to be calculated for the three-dimensional spectral blocks. Hand over all the three-dimensional spectral blocks and all the similar blocks to be calculated to the calculation unit for processing.

[0089] A calculation unit divides a plurality of the three-dimensional spectral blocks into a plurality of clusters, obtains a dictionary for each cluster, obtains the most similar block from the similar blocks to be calculated, and obtains the weighted sparse representation coefficients of the three-dimensional spectral blocks according to the dictionary, specifically including:

[0090] Take a plurality of similar blocks to be calculated along the periphery of the three-dimensional spectral block, compare the pixel differences of the RGB three channels of the three-dimensional spectral block and each similar block to be calculated, distinguish a plurality of the most similar blocks from the plurality of similar blocks to be calculated according to the pixel difference size, obtain the sparse representation coefficients of each of the most similar blocks according to the dictionary, and obtain the weighted sparse representation coefficients of the three-dimensional spectral block according to the sparse representation coefficients.

[0091] A reconstruction unit obtains an image function according to the dictionary and the weighted sparse representation coefficients obtained by the calculation unit, reconstructs the image function to obtain an objective image function. Hand over the objective function to the iteration unit for solution.

[0092] An iteration unit iteratively updates the dictionary and the weighted sparse representation coefficients to make the objective image function converge and obtain the final image function.

[0093] In several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the modules or units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed.

[0094] The unit may or may not be physically separated. The components shown as units can be one physical unit or multiple physical units, that is, they can be located in one place, or they can be distributed to multiple different places. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0095] In addition, the functional units in various embodiments of the present invention can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

[0096] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code, and this module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks shown can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

Claims

1. A spectral imaging method, characterized in that, Including the following steps: Obtain the hyperspectral image of the target scene, initialize the hyperspectral image, obtain the image to be processed, evenly divide the image to be processed into several three-dimensional spectral blocks, divide the several three-dimensional spectral blocks into multiple clusters, and obtain the principal component dictionary of each cluster; obtain several similar blocks to be calculated of the three-dimensional spectral block, select several of the most similar blocks therefrom, and according to the dictionary, obtain the weighted sparse representation coefficients of the three-dimensional spectral block; obtain the image function according to the dictionary and the weighted sparse representation coefficients, reconstruct the image function, obtain the target image function, and through iterative updating of the dictionary and the weighted sparse representation coefficients, make the target image function converge to obtain the final image function; Among them, obtaining the weighted sparse representation coefficients of the three-dimensional spectral block specifically includes: taking several similar blocks to be calculated along the periphery of the three-dimensional spectral block, comparing the pixel differences of the RGB three channels of the three-dimensional spectral block and each similar block to be calculated, distinguishing several of the most similar blocks from the several similar blocks to be calculated according to the pixel difference size, obtaining the sparse representation coefficients of each of the most similar blocks according to the dictionary, and obtaining the weighted sparse representation coefficients of the three-dimensional spectral block according to the sparse representation coefficients. The weighted sparse representation coefficients are: ； Among them, represents the weighted sparse representation coefficient, represents the weighting coefficient, , , represents the sparse representation coefficient of the j-th most similar block of the i-th three-dimensional spectral block, D im represents the pixel difference, , , , respectively represent the vector forms of the i-th three-dimensional spectral block in the RGB three channels; , , respectively represent the vector forms of the m-th to-be-calculated similar block of the three-dimensional spectral block; T represents matrix transpose.

2. The spectral imaging method according to claim 1, wherein Before initializing the hyperspectral image, it further includes: obtaining the grayscale image and the grayscale matrix of the grayscale image; obtaining the RGB image and the RGB matrix of the RGB image, and jointly obtaining the hyperspectral image from the grayscale image and the RGB image.

3. The spectral imaging method according to claim 2, wherein The initialization of the hyperspectral image specifically includes: multiplying the hyperspectral image by the transposed matrix of the matrix of the hyperspectral image.

4. The spectral imaging method according to claim 1, wherein Through iterative updating of the dictionary and the weighted sparse representation coefficients, where the dictionary and the weighted sparse representation coefficients are updated once every 10 - 25 iterations.

5. The spectral imaging method according to claim 1, wherein Dividing the several three-dimensional spectral blocks into multiple clusters and obtaining the dictionary of each cluster specifically includes: dividing the several three-dimensional spectral blocks into multiple clusters by using the K-means clustering algorithm, performing principal component analysis on each cluster, and obtaining the dictionary of each cluster.

6. A spectral imaging system, characterized in that, Including: An image processing unit, configured to obtain the hyperspectral image of the target scene, initialize the hyperspectral image, and obtain the image to be processed; An image segmentation unit, configured to evenly divide the image to be processed into several three-dimensional spectral blocks and obtain several similar blocks to be calculated of the three-dimensional spectral block; A calculation unit, configured to divide the several three-dimensional spectral blocks into multiple clusters, obtain the dictionary of each cluster, obtain the most similar blocks therefrom from the similar blocks to be calculated, and according to the dictionary, obtain the weighted sparse representation coefficients of the three-dimensional spectral block; A reconstruction unit, configured to obtain the image function according to the dictionary and the weighted sparse representation coefficients, reconstruct the image function, and obtain the target image function; An iterative unit, through iterative updating of the dictionary and the weighted sparse representation coefficients, makes the target image function converge to obtain the final image function; Among them, obtaining the weighted sparse representation coefficients of the three-dimensional spectral block specifically includes: taking a number of similar blocks to be calculated around the three-dimensional spectral block, comparing the pixel differences of the RGB three channels of the three-dimensional spectral block and each similar block to be calculated, distinguishing a number of most similar blocks from the number of similar blocks to be calculated according to the pixel difference size, obtaining the sparse representation coefficients of each of the most similar blocks according to the dictionary, and obtaining the weighted sparse representation coefficients of the three-dimensional spectral block according to the sparse representation coefficients. The weighted sparse representation coefficients are: ； Among them, represents the weighted sparse representation coefficient, represents the weighting coefficient, , , represents the sparse representation coefficient of the j-th most similar block of the i-th three-dimensional spectral block, D im represents the pixel difference, , , , respectively represent the vector forms of the i-th three-dimensional spectral block in the RGB three channels; , , respectively represent the vector forms of the m-th to-be-calculated similar block of the three-dimensional spectral block; T represents matrix transpose.

Images