Panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization

Abstract

The application discloses a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization, which comprises the following steps: obtaining a panchromatic image and a multispectral image under the same scene; inputting the panchromatic image into a sub-pixel displacement decomposition model for decomposition to obtain a panchromatic sub-pixel displacement sub-image with the same spatial resolution as the multispectral image; performing sparse representation on the multispectral image and the panchromatic sub-pixel displacement sub-image based on a spectral dictionary to obtain a spectral dictionary solution and a sub-image sparse coefficient matrix under joint optimization with sparse and low-rank constraints; and fusing the spectral dictionary solution and a spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix to obtain a fused high spatial resolution multispectral remote sensing image. The application realizes efficient and high-precision fusion of high spatial resolution panchromatic and low spatial resolution multispectral remote sensing images.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of remote sensing image processing, and particularly relates to a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization. BACKGROUND

[0002] High spatial resolution multispectral remote sensing images can provide rich spatial and spectral information, and can be widely applied to the fields of environment monitoring, ground object classification and the like. However, due to the mutual restriction of spatial resolution, spectral resolution and signal-to-noise ratio, most remote sensing satellites usually obtain high-resolution panchromatic remote sensing images and low-resolution multispectral remote sensing images through two different sensors. The former has higher spatial resolution, while the latter can provide richer spectral information. Considering that rich spatial and spectral information is indispensable in many remote sensing application fields, how to fuse and reconstruct high spatial resolution multispectral remote sensing images based on existing panchromatic and multispectral remote sensing images has important practical significance.

[0003] By fusing the panchromatic image sharpening method of the same scene panchromatic and multispectral remote sensing images, an effective solution is provided for fusing and reconstructing high spatial resolution multispectral remote sensing images. However, at present, the method based on component substitution (CS) can cause serious spectral distortion, while the method based on multi-resolution analysis (MRA) can reduce spectral distortion but usually loses spatial detail information; the method based on variational optimization (VO) and the method based on deep learning (DL) have better panchromatic image sharpening performance, but need a large amount of training data and training time; in addition, the method based on sparse representation (SR) uses image blocks to learn a spatial dictionary, and the reconstruction of spectral information is not accurate enough; the above problems make the existing methods unable to obtain satisfactory panchromatic image sharpening results. SUMMARY

[0004] The present application aims to at least solve one of the technical problems in the related art to some extent.

[0005] In order to overcome the above-mentioned defects of the prior art, the present application aims to provide a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization, which firstly decomposes the panchromatic image into a plurality of sub-images with the same spatial resolution as the multi-spectral remote sensing image by constructing a sub-pixel displacement decomposition scheme; secondly, solves the closed-form solution of the spectral dictionary and the sub-image sparse coefficient by constructing the spectral and spatial correspondence between the sub-images and between the sub-images and the multi-spectral image, and jointly optimizing; finally, obtains the high spatial resolution multi-spectral image by the product of the spectral dictionary and the sub-image sparse coefficient reverse synthesis matrix. The present application utilizes the spectral information provided by the multi-spectral image, the spatial information provided by the panchromatic sub-image, and the spectral similarity of the pixels at the same position, constructs the joint optimization learning process of the spectral dictionary and the sub-image sparse coefficient under strict theoretical derivation, and realizes the efficient and high-precision fusion of the high spatial resolution panchromatic and low spatial resolution multi-spectral remote sensing images.

[0006] Another object of the present application is to provide a panchromatic image sharpening system based on sub-pixel displacement decomposition and joint optimization.

[0007] To achieve the above object, in one aspect, the present application provides a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization, comprising:

[0008] acquiring a panchromatic image and a multi-spectral image under the same scene; wherein the panchromatic image comprises a high spatial resolution panchromatic remote sensing image, and the multi-spectral image comprises a low spatial resolution multi-spectral remote sensing image;

[0009] inputting the panchromatic image into a sub-pixel displacement decomposition model for decomposition, to obtain a panchromatic sub-pixel displacement sub-image with the same spatial resolution as the multi-spectral image;

[0010] performing sparse representation on the multi-spectral image and the panchromatic sub-pixel displacement sub-image based on a spectral dictionary, to obtain a spectral dictionary solution and a sub-image sparse coefficient matrix by joint optimization under sparse and low-rank constraints;

[0011] fusing the spectral dictionary solution and a spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix, to obtain a fused high spatial resolution multi-spectral remote sensing image.

[0012] To achieve the above object, in another aspect, the present application provides a panchromatic image sharpening system based on sub-pixel displacement decomposition and joint optimization, comprising:

[0013] an image acquisition module, configured to acquire a panchromatic image and a multi-spectral image under the same scene; wherein the panchromatic image comprises a high spatial resolution panchromatic remote sensing image, and the multi-spectral image comprises a low spatial resolution multi-spectral remote sensing image;

[0014] an image decomposition module configured to decompose the panchromatic image into sub-pixel displacement sub-images with the same spatial resolution as the multi-spectral image;

[0015] a matrix solving module configured to jointly optimize a spectral dictionary and a sub-image sparse coefficient matrix under sparse and low-rank constraints based on the spectral dictionary to sparsely represent the multi-spectral image and the sub-pixel displacement sub-images, to obtain a spectral dictionary solving result;

[0016] a data fusion module configured to fuse the spectral dictionary solving result and a spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix, to obtain a fused high spatial resolution multi-spectral remote sensing image.

[0017] The panchromatic image sharpening method and system based on sub-pixel displacement decomposition and joint optimization according to the embodiments of the present application utilize the spectral information provided by the multi-spectral image, the spatial information provided by the panchromatic sub-image, and the spectral similarity of pixels at the same position, construct a joint optimization learning process of a spectral dictionary and a sub-image sparse coefficient under strict theoretical derivation, and realize efficient and high-precision fusion of high spatial resolution panchromatic and low spatial resolution multi-spectral remote sensing images.

[0018] The present application has the following advantages:

[0019] 1) The present application establishes a new panchromatic image sharpening system under a sub-pixel displacement decomposition scheme, and models the fusion of multi-spectral and panchromatic images at different resolutions as panchromatic image sharpening of multi-spectral images and multiple panchromatic sub-pixel displacement sub-images at the same resolution.

[0020] 2) The present application introduces the spectral information of the multi-spectral image into the panchromatic image sharpening system in the form of a spectral dictionary by utilizing the same ground object coverage of the multi-spectral image and the panchromatic sub-image, and effectively improves the high spatial resolution multi-spectral image fusion reconstruction precision.

[0021] 3) The present application utilizes the spatial information of the panchromatic sub-pixel displacement sub-image and the spectral similarity of pixels at the same position under sparse and low-rank constraints, and realizes high-precision and high-stability high spatial resolution multi-spectral image reconstruction precision.

[0022] 4) The present application is not only suitable for panchromatic image sharpening of remote sensing images, but also suitable for panchromatic image sharpening of general digital images.

[0023] Additional aspects and advantages of the present application will be made apparent from the following description. BRIEF DESCRIPTION OF DRAWINGS

[0024] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description of embodiments, taken in conjunction with the references to the following drawings, of which:

[0025] Figure 1 is a flow chart of a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization according to an embodiment of the present application;

[0026] Figure 2 is a framework diagram of a panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization according to an embodiment of the present application;

[0027] Figure 3 is a structural schematic diagram of a panchromatic image sharpening system based on sub-pixel displacement decomposition and joint optimization according to an embodiment of the present application. DETAILED DESCRIPTION

[0028] It should be noted that the embodiments and features of the embodiments in the present application can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0029] In order to enable persons skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work should belong to the scope of protection of the present application.

[0030] The panchromatic image sharpening method and system based on sub-pixel displacement decomposition and joint optimization according to the embodiments of the present application will be described below with reference to the accompanying drawings.

[0031] The framework of the present application is as follows Figure 2As shown, a high spatial resolution panchromatic remote sensing image and a low spatial resolution multispectral remote sensing image under the same scene are input; the panchromatic image is decomposed into a plurality of panchromatic sub-images with the same spatial resolution as the multispectral remote sensing image by constructing a sub-pixel displacement decomposition scheme; then, the closed-form solution of the spectral dictionary and the sub-image sparse coefficient is solved by jointly optimizing under the sparse and low-rank constraints through the spectral and spatial correspondence between the sub-images and between the sub-image and the multispectral image; finally, the high spatial resolution multispectral image is obtained by the product of the spectral dictionary and the sub-image sparse coefficient reverse synthesis matrix. Under the sparse and low-rank framework, the spectral information provided by the multispectral image, the spatial information provided by the panchromatic sub-image and the spectral similarity of the pixels at the same position are used to invent the joint optimization learning process of the spectral dictionary and the sparse coefficient under strict theoretical derivation, and the efficient and high-precision fusion of the high spatial resolution panchromatic and low spatial resolution multispectral remote sensing images is realized.

[0032] Figure 1 The flowchart of the panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization of the embodiments of the present application is shown in the figure.

[0033] As shown in the figure, the method includes but is not limited to the following steps: Figure 1

[0034] Step S1, obtaining a panchromatic image and a multispectral image under the same scene; wherein the panchromatic image includes a high spatial resolution panchromatic remote sensing image, and the multispectral image includes a low spatial resolution multispectral remote sensing image.

[0035] Specifically, a high spatial resolution panchromatic remote sensing image P an and a low spatial resolution multispectral remote sensing image M s under the same scene are input.

[0036] Further, a high spatial resolution panchromatic remote sensing image P and a low spatial resolution multispectral remote sensing image M under the same scene are input, and the ratio of the spatial dimensions is d=N / n.

[0037] In this embodiment, the spectral image adopts the panchromatic and multispectral remote sensing images obtained by WorldView-4 satellite, and the spatial resolutions are 1.84m and 0.46m respectively. In order to perform full-reference quantitative evaluation, the multispectral image with a size of 512x512x4 is required as a reference image, and the panchromatic image with a size of 512x512x1 and the multispectral image with a size of 128x128x4 generated by degradation are input in this embodiment.

[0038] ​Step S2, input the panchromatic image into the sub-pixel displacement decomposition model to obtain panchromatic sub-pixel displacement sub-images with the same spatial resolution as the multi-spectral image.

[0039] Specifically, by constructing a sub-pixel displacement decomposition scheme, the panchromatic image P an is decomposed into d panchromatic sub-pixel displacement sub-images P s with the same spatial resolution as the multi-spectral remote sensing image M an H i .

[0040] Further, the constructed sub-pixel displacement decomposition scheme means that each pixel in the panchromatic remote sensing image P an is labeled from 1 to d in an image block with a size of The sub-pixel displacement sub-image P an H i (i = 1, …, d) is composed of pixels with the same label in each image block. Wherein, represents a sub-pixel displacement decomposition operator.

[0041] In an embodiment of the present application, d = 16.

[0042] Step S3, sparse representation of the multi-spectral image and the panchromatic sub-pixel displacement sub-image based on the spectral dictionary, to jointly optimize the spectral dictionary solution and the sub-image sparse coefficient matrix under sparse and low rank constraints.

[0043] Specifically, the multi-spectral remote sensing image M s input in step S1, and the panchromatic sub-pixel displacement sub-image P an H i solved in step S2 are simultaneously sparse represented under the spectral dictionary D s , and the spectral dictionary D s and the sub-image sparse coefficient

[0044] Further, step S3, the multi-spectral remote sensing image M s input in step S1, and the panchromatic sub-image P an H i solved in step S2 are simultaneously sparse represented under the spectral dictionary D s , specifically including the following process: first, the multi-spectral image M s and the panchromatic sub-image P an H i are modeled as spectral and spatial degradation of the pseudo-reconstructed high spatial resolution multi-spectral image :

[0045] Ms = XB + N M

[0046]

[0047] wherein, denotes a joint matrix of a series of decomposed sub-images, denotes a spatial blur and down-sampling matrix, denotes a spectral response function, N M and N Pi denotes zero-mean Gaussian noise in the degradation model. Secondly, a spectral dictionary D is used to sparsely represent the pseudo-reconstructed high spatial resolution multi-spectral image X:

[0048] X = D s A (2)

[0049] wherein, denotes a spectral sparse coefficient matrix. Finally, combining equation (1) and equation (2) can obtain the multi-spectral remote sensing image M s , and the panchromatic sub-image P an H i under the sparse representation of the spectral dictionary D s

[0050] M s = D s AB + N M

[0051]

[0052] wherein, and denote block diagonal matrices with the spectral response function and the spectral dictionary D s as elements, respectively, denotes a sub-image sparse coefficient matrix.

[0053] Further, in step S3, the spectral dictionary D s and the sub-image sparse coefficient are solved by jointly optimizing under the sparse and low-rank constraints. It is pointed out that, considering the spatial continuity of the ground cover, the spectra of the same position pixels of the panchromatic sub-image have similarity, and the spectral dictionary D s denotes that, the sub-image sparse coefficient is subjected to sparse and low-rank constraints, and the spectral dictionary D s and the sub-image sparse coefficient are solved by the following equation:

[0054]

[0055] wherein, γ, λ, η are regularization parameters; || || F is F-norm constraint, || || 1 is 1-norm constraint, || || 2 is 2-norm constraint, and || || * is kernel norm constraint. F * is kernel norm constraint. In the solving process, two sub-problems containing D s and are respectively optimized by using convergence iterative strategy, so as to obtain the following accurate closed-form solution:

[0056]

[0057] wherein, C i = D s AH i , and denote split variables, V i , and are Lagrange multipliers (i = 1, …, d).

[0058] In an embodiment of the present application, the column number of the spectral dictionary D s is 20, and the regularization parameters are respectively set as γ = 10 -5 , λ = 10 -1 , η = 10 2 .

[0059] Step S4, the spectral dictionary solving result and the spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix are fused to obtain a fused high spatial resolution multi-spectral remote sensing image.

[0060] Specifically, the fused high spatial resolution multi-spectral image is obtained by the product of the spectral dictionary D s and the spectral coefficient inverse synthesis matrix A, that is, X = D s A.

[0061] Further, in step S4, the spectral coefficient inverse synthesis matrix A refers to that the sub-image sparse coefficient matrix A is pixel by pixel synthesized into the spectral sparse coefficient matrix by the inverse process of sub-pixel displacement decomposition.

[0062] In an embodiment of the present application, the ERGAS of the panchromatic image sharpened high spatial resolution multi-spectral image is 1.1397, and the spectral angle SAM is 1.7937, and it can be known that a high-quality multi-spectral image is obtained.

[0063] ​​According to the embodiments of the present invention, the panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization utilizes the spectral information provided by multispectral images, the spatial information provided by panchromatic sub-images, and the spectral similarity of pixels at the same position within a sparse and low-rank framework. Under rigorous theoretical derivation, a joint optimization learning process for spectral dictionaries and sparse coefficients is invented, realizing efficient and high-precision fusion of high spatial resolution panchromatic and low spatial resolution multispectral remote sensing images.

[0064] To achieve the above embodiments, such as Figure 3 As shown, this embodiment also provides a panchromatic image sharpening system 10 based on sub-pixel displacement decomposition and joint optimization. The system 10 includes an image acquisition module 100, an image decomposition module 200, a matrix solving module 300, and a data fusion module 400.

[0065] The image acquisition module 100 is used to acquire panchromatic images and multispectral images of the same scene; wherein, the panchromatic images include high spatial resolution panchromatic remote sensing images, and the multispectral images include low spatial resolution multispectral remote sensing images.

[0066] The image decomposition module 200 is used to input the panchromatic image into the sub-pixel displacement decomposition model for decomposition to obtain multiple panchromatic sub-pixel displacement sub-images with the same spatial resolution as the multispectral image.

[0067] The matrix solving module 300 is used to perform sparse representation of multispectral images and panchromatic sub-pixel shifted sub-images based on the spectral dictionary, so as to obtain the spectral dictionary solution results and the sparse coefficient matrix of the sub-images under the joint optimization under the sparsity and low-rank constraints.

[0068] The data fusion module 400 is used to fuse the spectral dictionary solution results and the spectral sparse coefficient matrix obtained from the sparse coefficient matrix of the sub-image to obtain a fused high spatial resolution multispectral remote sensing image.

[0069] Furthermore, the image decomposition module 200 described above is also used to decompose the panchromatic image P an Each pixel in the image has a size of The image blocks are labeled from 1 to d, and a panchromatic sub-pixel shift sub-image P is obtained based on the pixels with the same label in each image block. an H i (i = 1, ..., d); where, (N / n = d, i = 1, ..., d) represents the subpixel shift decomposition operator.

[0070] Furthermore, the matrix solving module 300 described above is also used for:

[0071] Multispectral image M s P with panchromatic sub-pixel displacement sub-imagean H i Modeling for reconstructing high spatial resolution multispectral images Spectral and spatial degradation:

[0072] M s =XB+N M

[0073]

[0074] in, This represents the joint matrix of a series of decomposed sub-images. Representing spatial ambiguity and the downsampling matrix, N represents the spectral response function. M With N Pi Zero-mean Gaussian noise in the degradation model is represented using a spectral dictionary. Using the sparse model X=D s A represents the high spatial resolution multispectral image X to be reconstructed. The spectral sparse coefficient matrix is ​​represented by equation (1), and the multispectral image M is obtained according to equation (1). s And the panchromatic sub-pixel displacement sub-image P an H i In the spectral dictionary D s Sparse representation of the following:

[0075] M s =D s AB+N M

[0076]

[0077] in, and Represented by the spectral response function With spectral dictionary D s A block diagonal matrix of elements. This represents the sparse coefficient matrix of the sub-image.

[0078] Furthermore, the matrix solving module 300 described above is also used in the spectral dictionary D s The following represents the sparse coefficient matrix of the sub-image. Apply sparsity and low-rank constraints, and solve for the spectral dictionary D. s With the sparse coefficient matrix of the sub-image

[0079]

[0080] Where γ, λ, and η are regularization parameters, || || Fis a nuclear norm constraint. * is a nuclear norm constraint.

[0081] Further, the matrix solving module 300 is further configured to utilize a convergence iterative strategy to respectively optimize two sub-problems containing D s and to obtain a closed-form solution:

[0082]

[0083] wherein, A Hi = AH i , A B = AB, C i = D s AH i , and denote split variables, V i , and are Lagrange multipliers (i = 1, …, d).

[0084] According to the panchromatic image sharpening system based on sub-pixel displacement decomposition and joint optimization, under a sparse and low rank framework, spectral information provided by a multi-spectral image, spatial information provided by a panchromatic sub-image, and spectral similarity of pixels at the same position are utilized, a joint optimization learning process of a spectral dictionary and sparse coefficients is invented under strict theoretical derivation, and efficient and high-precision fusion of high spatial resolution panchromatic and low spatial resolution multi-spectral remote sensing images is realized.

[0085] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0086] Furthermore, the terms "first", "second", "third", "fourth", "fifth" and "sixth" are used herein for descriptive purposes only and are not to be construed as indicating or implying relative importance or a significant nature of so described technical features. It is to be understood that a technical feature described with the "first", "second", "third", "fourth", "fifth" or "sixth" can implicitly or explicitly include at least one of the technical features described with the "first", "second", "third", "fourth", "fifth" or "sixth". In the description of the present application, the meaning of "a plurality" is at least two, for example, two, three, etc., unless otherwise specifically defined.

Claims

1. A panchromatic image sharpening method based on sub-pixel displacement decomposition and joint optimization, characterized in that, The method comprises the following steps: obtaining a panchromatic image and a multispectral image under the same scene; wherein the panchromatic image comprises a high spatial resolution panchromatic remote sensing image, and the multispectral image comprises a low spatial resolution multispectral remote sensing image; inputting the panchromatic image into a sub-pixel displacement decomposition model for decomposition to obtain a panchromatic sub-pixel displacement sub-image with the same spatial resolution as the multispectral image; performing sparse representation on the multispectral image and the panchromatic sub-pixel displacement sub-image based on a spectral dictionary to jointly optimize a spectral dictionary solution and a sub-image sparse coefficient matrix under sparse and low-rank constraints; fusing the spectral dictionary solution and a spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix to obtain a fused high spatial resolution multispectral remote sensing image; panchromatic image Each pixel in the image has a size of [size missing]. Image blocks from 1 to Labeling is performed, and panchromatic sub-pixel shift sub-images are obtained based on pixels with the same label in each image patch. ( );in, ( , ) represents the subpixel shift decomposition operator; the sparse representation on the multispectral image and the panchromatic sub-pixel displacement sub-image based on the spectral dictionary comprises: The multispectral image with panchromatic sub-pixel displacement sub-images Modeling to simulate reconstruction of high spatial resolution multispectral images Spectral and spatial degradation: (1) wherein, denotes a joint matrix of the series of decomposed sub-images, denotes a spatial blur and down-sampling matrix, denotes a spectral response function, and denotes a zero-mean Gaussian noise in the degradation model, using a spectral dictionary by means of a sparse model denotes a pseudo-reconstructed high spatial resolution multispectral image , denotes a spectral sparse coefficient matrix, the multispectral image being obtained from equation (1) , and the panchromatic sub-pixel displacement sub-image under a sparse representation of the spectral dictionary : （2） wherein, with denote the spectral response function and the spectral dictionary is a block diagonal matrix of elements, denotes a sub-image sparse coefficient matrix; the expression for jointly optimizing the spectral dictionary solution and the sub-image sparse coefficient matrix under sparse and low-rank constraints is: （3） wherein, , , is a regularization parameter, is an F-norm constraint, is a 1-norm constraint, is a kernel-norm constraint; The method further comprises optimizing two sub-problems containing and respectively using a convergent iterative strategy to obtain a closed-form solution: （4） wherein , , , , , and denote split variables, , and are Lagrange multipliers ( ).

2. A panchromatic image sharpening system based on sub-pixel displacement decomposition and joint optimization, characterized in that, comprise: an image acquisition module configured to obtain a panchromatic image and a multispectral image under the same scene; wherein the panchromatic image comprises a high spatial resolution panchromatic remote sensing image, and the multispectral image comprises a low spatial resolution multispectral remote sensing image; an image decomposition module configured to input the panchromatic image into a sub-pixel displacement decomposition model for decomposition to obtain a plurality of panchromatic sub-pixel displacement sub-images with the same spatial resolution as the multispectral image; a matrix solution module configured to perform sparse representation on the multispectral image and the panchromatic sub-pixel displacement sub-image based on a spectral dictionary to jointly optimize a spectral dictionary solution and a sub-image sparse coefficient matrix under sparse and low-rank constraints; a data fusion module configured to fuse the spectral dictionary solution and a spectral sparse coefficient matrix obtained according to the sub-image sparse coefficient matrix to obtain a fused high spatial resolution multispectral remote sensing image; The image decomposition module is further configured to mark each pixel in the panchromatic image in an image block with a size of from 1 to and obtain a panchromatic sub-pixel displacement sub-image based on pixels with the same label in each image block ; wherein and , and represent a sub-pixel shift decomposition operator. the matrix solution module is further configured to: The multispectral image with panchromatic sub-pixel displacement sub-images Modeling to simulate reconstruction of high spatial resolution multispectral images spectral and spatial degradation: (1) wherein, denotes a joint matrix of a series of decomposed sub-images, denotes a spatial blur and down-sampling matrix, denotes a spectral response function, and denotes zero-mean Gaussian noise in the degradation model, using a spectral dictionary by sparse modeling denotes a pseudo-reconstructed high spatial resolution multispectral image , denotes a spectral sparse coefficient matrix, from which a multispectral image , and a panchromatic sub-pixel shifted sub-image is obtained under sparse representation of the spectral dictionary : （2） wherein, with denote the spectral response function and the spectral dictionary is a block diagonal matrix with elements denotes a sub-image sparse coefficient matrix; The matrix solving module is further configured to solve the spectral dictionary subject to sparse coefficient matrix of sub-images subject to sparse and low-rank constraints, and solve the spectral dictionary and sparse coefficient matrix of sub-images : （3） wherein, , , is a regularization parameter, is an F-norm constraint, is a 1-norm constraint, is a kernel-norm constraint; The matrix solving module is further configured to utilize a convergence iteration strategy to respectively optimize two sub-problems containing and to obtain a closed-form solution. （4） wherein , , , , , and denote split variables, , and are Lagrange multipliers ( ).

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