Hybrid noise hyperspectral image restoration method combining double low rank and spectral empty total variation

Abstract

The application provides a mixed noise hyperspectral image restoration method combining double low rank and empty spectrum total variation, which uses low rank tensor approximation and low rank matrix approximation model of each band respectively to excavate low rank properties of noise-free hyperspectral remote sensing image and strip noise, simultaneously introduces anisotropic spatial spectrum total variation model, establishes a hyperspectral remote sensing image multi-type mixed noise removal model combining double low rank approximation and anisotropic spatial spectrum total variation, and uses an alternating direction multiplier method to obtain noise-free hyperspectral remote sensing image. The application is applied to mixed noise removal of hyperspectral remote sensing image of Gaofen 5, and real hyperspectral remote sensing image experiments of Gaofen 5 show that the application can more effectively remove multi-type, high-intensity mixed noise in the hyperspectral remote sensing image of Gaofen 5, simultaneously protects high-dimensional structure information of the image, and greatly improves the quality of the hyperspectral remote sensing image of Gaofen 5.

Description

Technical Field

[0001] This invention relates to the field of mixed noise removal technology for hyperspectral remote sensing images, and particularly to a technical solution that constructs a double low-rank approximation model by performing low-rank tensor approximation on the noiseless hyperspectral remote sensing image and low-rank matrix approximation on the strip noise, and combines it with anisotropic spatial spectral total variation. The method of solving the optimization problem using the alternating direction multiplier method is used to separate the noiseless hyperspectral remote sensing image from various types of noise, thereby achieving the removal of mixed noise of multiple types in hyperspectral remote sensing images. Background Technology

[0002] Since the 1980s, hyperspectral imaging technology has made continuous breakthroughs, making significant contributions to Earth observation and remote sensing, and has become a key factor in international scientific and technological competition. Hyperspectral remote sensing images can finely describe the spatial spectral characteristics of observed targets, enabling more accurate and robust characterization, identification, and classification of land cover with very high spectral resolution, providing an effective means for observing and distinguishing land features. Therefore, hyperspectral remote sensing image data is becoming a valuable tool for land surface monitoring and is widely used in fields such as medical imaging, ecological science, hydrology, and environmental monitoring.

[0003] However, due to the influence of observation conditions (such as atmospheric environment and topographic relief), differences in band energy distribution, and sensor limitations (interference or malfunction of detection elements), hyperspectral remote sensing imaging is highly susceptible to interference from various types of noise, including Gaussian noise, impulse noise, dead pixels, dead lines, and stripes. These diverse and complex mixed noises coexist in both the spatial and spectral domains of hyperspectral images, severely degrading their quality and limiting the accuracy of subsequent processing applications. Therefore, developing techniques for removing mixed noise from hyperspectral remote sensing images to improve image quality and enhance the application value and social benefits of hyperspectral remote sensing satellite data is of great significance.

[0004] Over the past two decades, scholars both domestically and internationally have conducted a series of studies and explorations on noise removal from hyperspectral remote sensing images. Generally speaking, current hyperspectral remote sensing image denoising methods can be mainly divided into three categories: spatial domain-based, spectral domain-based, and spatial-spectral joint methods. Spatial domain-based methods treat each band as an independent grayscale image and use one-dimensional signal or two-dimensional image restoration methods for pixel-by-pixel or band-by-band denoising. However, due to neglecting the high correlation between spectral bands in the image, artifacts or distortions can be introduced. Spectral domain-based methods extract spectral and noise features from the spectral domain to achieve noise removal. However, the lack of effective utilization of spatial information and features often leads to the destruction of structural and detail information. In recent years, strategies that simultaneously explore spatial structural information and spectral curve features have become mainstream, and researchers have successively proposed more advanced spatial-spectral joint denoising methods, such as those based on transform domain, multidimensional analysis, and prior constraints such as total variation and nonlocality. However, due to the lack of deeper prior information mining of hyperspectral remote sensing images, most of the above methods are only applicable to one or two specific types of noise, or low-intensity mixed noise environments of simple types and distributions. In complex mixed noise situations, they usually lead to low-quality denoising results.

[0005] In recent years, low-rank constraints have become a mainstream research direction and hot topic in hyperspectral image denoising due to their superior performance in removing mixed noise from hyperspectral images. Clean hyperspectral images exhibit strong correlations between adjacent bands, revealing a potential low-rank structure. Denoising methods based on low-rank joint sparse matrix recovery (LRMR) first apply low-rank constraints to hyperspectral image denoising, demonstrating highly competitive performance in removing mixed noise of Gaussian and sparse noise. Building upon the low-rank matrix recovery framework, researchers have combined spatial prior constraints, tensor decomposition, and other techniques to further improve the model's denoising effectiveness.

[0006] For the problem of mixed noise removal in hyperspectral images, denoising methods based on low-rank constraints are an effective approach. However, in environments with multiple types of mixed noise, especially when high-intensity, complexly distributed strip noise exists, existing low-rank constraint-based methods struggle to effectively remove various types of noise and preserve the original high-dimensional structural information of the image due to neglecting the effective utilization of prior information on strip noise and the potential high-dimensional structural information of the hyperspectral image. This leads to problems such as incomplete noise removal, loss of image details, and spectral distortion. Furthermore, hyperspectral remote sensing images are inevitably contaminated by various types of mixed noise during actual acquisition. For example, HYDICE Urban and Gaofen-5 satellite imagery data are severely damaged by strip, Gaussian, and impulse noise. Strip noise, in particular, has high intensity and complex distribution. Existing methods perform poorly in removing mixed noise of multiple types, including strip noise, thus limiting the subsequent applications of remote sensing images.

[0007] Therefore, this invention takes into account the intrinsic features of hyperspectral remote sensing images and the prior constraints of multiple types of noise, and proposes a hyperspectral remote sensing image multi-type mixed noise removal method (ATVDLR) that combines the double low-rank approximation and anisotropic spatial spectral total variation, which is of great significance. Summary of the Invention

[0008] The purpose of this invention is to address the problem of poor denoising performance of existing low-rank constraint-based hyperspectral remote sensing image noise removal methods in the case of mixed noise of multiple types. This invention provides a method for removing mixed noise of multiple types from hyperspectral remote sensing images by combining double low-rank approximation and anisotropic spatial spectral total variation. A double low-rank approximation model is established by applying low-rank tensor approximation to the noise-free image and low-rank matrix approximation to the strip noise. An anisotropic spatial spectral total variation model is then introduced to construct a joint denoising model. The method of solving the optimization problem using alternating direction multipliers is employed to separate the noise-free signal from various types of noise, thus achieving the removal of mixed noise of multiple types from hyperspectral remote sensing images.

[0009] The technical solution of this invention provides a method for restoring hybrid noise hyperspectral images by combining dual low-rank and spatial-spectral total variation, comprising the following steps:

[0010] Step 1: The low-rank properties of noiseless hyperspectral remote sensing images and strip noise are mined by low-rank tensor approximation and band-by-band low-rank matrix approximation models, respectively. The sparsity characteristics of sparse noise are constrained by sparse regularization to establish a dual low-rank approximation model.

[0011] Step 2: For the double low-rank approximation model obtained in Step 1, the anisotropic spatial spectral total variation model (ASSTV) is introduced into its denoising framework to establish a hyperspectral remote sensing image multi-type mixed noise removal model that combines the double low-rank approximation and anisotropic spatial spectral total variation.

[0012] Step 3: The hyperspectral remote sensing image multi-type mixed noise removal model obtained in Step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, is optimized and solved using the alternating direction multiplier method (ADMM) to obtain a noise-free hyperspectral remote sensing image.

[0013] Furthermore, in step 1, a low-rank tensor approximation is performed on the noiseless hyperspectral remote sensing image using the weighted sum tensor nuclear norm (WSTNN), a low-rank matrix approximation is performed on the strip noise in each band of the hyperspectral remote sensing image using the nuclear norm, and a sparse constraint is applied to the sparse noise using the l1 norm, thus establishing a double low-rank approximation model, including the following steps:

[0014] Step 1.1: The observed 3D hyperspectral remote sensing image is modeled as a collection of noise-free hyperspectral remote sensing image, sparse noise, striped noise, and Gaussian noise, i.e. in, This represents a three-dimensional hyperspectral remote sensing image, where m, n, and p are the width, height, and number of bands of the hyperspectral remote sensing image, respectively. and All are size and A consistent three-dimensional tensor represents noise-free hyperspectral remote sensing imagery, sparse noise (impulse noise, bad pixels, and dead lines), strip noise, and Gaussian noise, respectively.

[0015] Step 1.2: Utilize weighted sums and tensor nuclear norms to analyze the noise-free hyperspectral remote sensing image. We perform a low-rank tensor approximation and use the nuclear norm to approximate the strip noise. Band-by-band low-rank matrix approximation is performed, and the l1 norm is used to approximate sparse noise. By applying sparsity constraints, a double low-rank approximation model is established:

[0016]

[0017] Among them, the weighted sum tensor norm ||·|| WSTNN Defined as the weighted sum of the nuclear norms of each mode-k1k2 expanded tensor, 1≤k1 <k2≤3,k1, The l1 norm ||·||1 represents the sum of the non-zero elements in the matrix; Let be the stripe noise matrix in the i-th band of the hyperspectral remote sensing image; λ and β are regularization parameters that control the trade-offs between each regularization term, and rank(·) represents the rank of the vector. t (·) denotes the Tubal rank of the tensor, where r is the tensor. The upper rank of the mode-13 and mode-23 expanded tensors, r b B represents the band-by-band strip noise matrix. i The upper rank of ε is given by ε, where ε represents the intensity of the Gaussian noise.

[0018] Furthermore, in step 2, the anisotropic spatial spectral total variation model is introduced into the denoising framework of the dual low-rank approximation model obtained in step 1, establishing a multi-type hybrid noise removal model for hyperspectral remote sensing images that combines the dual low-rank approximation and anisotropic spatial spectral total variation, including the following steps:

[0019] Step 2.1: Using linear first-order discrete difference operators to constrain the gradients along the spatial horizontal and spectral directions of the noise-free hyperspectral remote sensing image and the spatial vertical direction of the strip noise, an anisotropic spatial spectral total variation model is established:

[0020]

[0021] Here, τ1, τ2, and τ3 are regularization parameters used to measure the gradient contribution along different directions. Operator D h D v and D s These are linear first-order discrete difference operators along the horizontal, vertical, and spectral directions, respectively.

[0022] Step 2.2: Introduce the anisotropic spatial spectral total variation model into the double low-rank approximation model to establish a multi-type hybrid noise removal model for hyperspectral remote sensing images that combines the double low-rank approximation and anisotropic spatial spectral total variation:

[0023]

[0024] Furthermore, in step 3, the hyperspectral remote sensing image multi-type mixed noise removal model obtained in step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, is optimized using the alternating direction multiplier method to obtain a noise-free hyperspectral remote sensing image, including the following steps:

[0025] Step 3.1: For the hyperspectral remote sensing image multi-type hybrid noise removal model obtained in Step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, firstly... and Five auxiliary variables are introduced into the minimization problem, and the minimization of model (3) is equivalent to the following formula:

[0026]

[0027] Step 3.2: Solve using the alternating direction multiplier method, which minimizes the following augmented Lagrangian function:

[0028]

[0029] Where μ is the penalty parameter, and It is a Lagrange multiplier.

[0030] Step 3.3 involves iteratively optimizing the augmented Lagrangian function (5) on one variable while keeping other variables fixed. Specifically:

[0031] Step A. In the (k+1)th iteration, update The variables are as follows:

[0032]

[0033] The tensor singular value threshold (t-SVT) operator is defined as follows:

[0034]

[0035] in, and

[0036] Step B. In the (k+1)th iteration, update The variables are as follows:

[0037]

[0038] The soft threshold shrinkage operator is expressed as:

[0039]

[0040] Step C. In the (k+1)th iteration, update The variables are as follows:

[0041]

[0042] in,

[0043]

[0044] in, Represents the Fast Fourier Transform. It is its inverse transformation.

[0045] Step D. In the (k+1)th iteration, update and The variables are as follows:

[0046]

[0047]

[0048] Step E. In the (k+1)th iteration, update The variables are as follows:

[0049]

[0050] Among them, H i X i S i T i ,、M hi and M bi Let represent a matrix of size m×n in the i-th band. The singular value contraction operator follows:

[0051]

[0052] Step F. In the (k+1)th iteration, update The variables are as follows:

[0053]

[0054] Step G. In the (k+1)th iteration, update The variables are as follows:

[0055]

[0056] Step H. In the (k+1)th iteration, update the Lagrange multipliers. and as follows:

[0057]

[0058] Step I. In the (k+1)th iteration, update the penalty parameter μ as follows:

[0059] μ:=min(ρμ,μ max (19)

[0060] Step J. In the (k+1)th iteration, check whether the following convergence condition is met:

[0061]

[0062] If the convergence condition is met, output a noise-free hyperspectral remote sensing image; if the convergence condition is not met, set k = k + 1 and repeat steps A to J.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] The proposed method for removing mixed noise from hyperspectral remote sensing images by combining the dual low-rank approximation and anisotropic spatial spectral total variation, reconstructs the mixed noise removal model of hyperspectral remote sensing images based on the current low-rank constraint-based mixed noise removal method. The mixed noise removal model is solved by the alternating direction multiplier method, and finally noise-free hyperspectral remote sensing images are obtained. This method addresses the issue that existing hyperspectral remote sensing images (such as HYDICEUrban and Gaofen-5 satellite images) are inevitably subject to severe damage from complex mixed noise containing multiple types and high-intensity strip noise. Furthermore, current methods for removing mixed noise from hyperspectral remote sensing images are ineffective in handling this type of high-intensity mixed noise. This method constrains the low-rank properties of both the noise-free hyperspectral image and the strip noise by utilizing low-rank tensor approximation and band-by-band low-rank matrix approximation, combining them into a dual low-rank approximation model. Simultaneously, an anisotropic spatial spectral total variation model is introduced into the denoising framework, thus re-establishing a multi-type mixed noise removal model for hyperspectral remote sensing images. Compared to current hyperspectral remote sensing image mixed noise removal models, this new model demonstrates superior performance in handling multi-type, high-intensity mixed noise and preserving image features.

[0065] The proposed method for removing multi-type mixed noise from hyperspectral remote sensing images, combining the dual low-rank approximation and anisotropic spatial spectral total variation, is more effective than current methods for removing mixed noise from hyperspectral remote sensing images in removing Gaussian noise, impulse noise, dead line noise, bad pixels, and high-intensity, complexly distributed stripe noise. This significantly improves the quality of hyperspectral remote sensing images, enabling them to provide valuable data for subsequent applications. Therefore, this method for removing multi-type mixed noise from hyperspectral remote sensing images, combining the dual low-rank approximation and anisotropic spatial spectral total variation, not only has significant academic value but also important practical implications. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0067] Figure 2 This is a flowchart of the algorithm for step 3 of an embodiment of the present invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the following, in conjunction with the accompanying drawings, provides a more detailed description of a method for removing multi-type mixed noise from hyperspectral remote sensing images using a combination of dual low-rank approximation and anisotropic spatial spectral total variation, according to an embodiment of the present invention. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0069] This invention addresses the problem that existing hyperspectral remote sensing images are inevitably severely damaged by complex mixed noise of multiple types and high-intensity strip noise, and that current methods for removing mixed noise from hyperspectral remote sensing images perform poorly in handling such noise. The invention constructs a dual low-rank approximation model by applying low-rank tensor approximation to the noise-free image and band-by-band low-rank matrix approximation to the strip noise. It also introduces an anisotropic spatial spectral total variation model to re-establish the mixed noise removal model for hyperspectral remote sensing images. Finally, the model is solved using the alternating direction multiplier method to obtain a noise-free hyperspectral remote sensing image.

[0070] like Figure 1 The implementation of the hybrid noise hyperspectral image restoration method combining dual low-rank and spatial-spectral total variation provided in the embodiments includes the following processing steps:

[0071] Step 1: The low-rank properties of noiseless hyperspectral remote sensing images and strip noise are mined by low-rank tensor approximation and band-by-band low-rank matrix approximation models, respectively. The sparsity characteristics of sparse noise are constrained by sparse regularization to establish a dual low-rank approximation model.

[0072] Step 2: For the double low-rank approximation model obtained in Step 1, the anisotropic spatial spectral total variation model (ASSTV) is introduced into its denoising framework to establish a hyperspectral remote sensing image multi-type mixed noise removal model that combines the double low-rank approximation and anisotropic spatial spectral total variation.

[0073] Step 3: The hyperspectral remote sensing image multi-type mixed noise removal model obtained in Step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, is optimized and solved using the alternating direction multiplier method (ADMM) to obtain a noise-free hyperspectral remote sensing image.

[0074] Furthermore, in step 1, a low-rank tensor approximation is performed on the noiseless hyperspectral remote sensing image using the weighted sum tensor nuclear norm (WSTNN), a low-rank matrix approximation is performed on the strip noise in each band of the hyperspectral remote sensing image using the nuclear norm, and a sparse constraint is applied to the sparse noise using the l1 norm, thus establishing a double low-rank approximation model, including the following steps:

[0075] Step 1.1: The observed 3D hyperspectral remote sensing image is modeled as a collection of noise-free hyperspectral remote sensing image, sparse noise, striped noise, and Gaussian noise, i.e. in, This represents a three-dimensional hyperspectral remote sensing image, where m, n, and p are the width, height, and number of bands of the hyperspectral remote sensing image, respectively. and All are size and A consistent three-dimensional tensor represents noise-free hyperspectral remote sensing imagery, sparse noise (impulse noise, bad pixels, and dead lines), strip noise, and Gaussian noise, respectively.

[0076] Step 1.2: Utilize weighted sums and tensor nuclear norms to analyze the noise-free hyperspectral remote sensing image. We perform a low-rank tensor approximation and use the nuclear norm to approximate the strip noise. Band-by-band low-rank matrix approximation is performed, and the l1 norm is used to approximate sparse noise. By applying sparsity constraints, a double low-rank approximation model is established:

[0077]

[0078] Among them, the weighted sum tensor norm ||·|| WSTNN Defined as the weighted sum of the nuclear norms of each mode-k1k2 expanded tensor (1≤k1) <k2≤3,k1, The l1 norm ||·||1 represents the sum of the non-zero elements in the matrix. Let be the stripe noise matrix in the i-th band of the hyperspectral remote sensing image; λ and β are regularization parameters that control the trade-offs between each regularization term, and rank(·) represents the rank of the vector. t(·) denotes the Tubal rank of the tensor, where r is the tensor. The upper rank of the mode-13 and mode-23 expanded tensors, r b B represents the band-by-band strip noise matrix. i The upper rank of ε is given by ε, where ε represents the intensity of the Gaussian noise.

[0079] The implemented Gaofen-5 hyperspectral remote sensing image has a size of 600×400×330. In the Gaofen-5 hyperspectral remote sensing image noise removal model, m×n=600×600 and p=330.

[0080] Furthermore, in step 2, the anisotropic spatial spectral total variation model is introduced into the denoising framework of the dual low-rank approximation model obtained in step 1, establishing a multi-type hybrid noise removal model for hyperspectral remote sensing images that combines the dual low-rank approximation and anisotropic spatial spectral total variation, including the following steps:

[0081] Step 2.1: Using linear first-order discrete difference operators to constrain the gradients along the spatial horizontal and spectral directions of the noise-free hyperspectral remote sensing image and the spatial vertical direction of the strip noise, an anisotropic spatial spectral total variation model is established:

[0082]

[0083] Here, τ1, τ2, and τ3 are regularization parameters used to measure the gradient contribution along different directions. Operator D h D v and D s These are linear first-order discrete difference operators along the horizontal, vertical, and spectral directions, respectively.

[0084] Step 2.2: Introduce the anisotropic spatial spectral total variation model into the double low-rank approximation model to establish a multi-type hybrid noise removal model for hyperspectral remote sensing images that combines the double low-rank approximation and anisotropic spatial spectral total variation:

[0085]

[0086] Furthermore, in step 3, the hyperspectral remote sensing image multi-type mixed noise removal model obtained in step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, is optimized using the alternating direction multiplier method to obtain a noise-free hyperspectral remote sensing image, including the following steps:

[0087] Step 3.1: For the hyperspectral remote sensing image multi-type hybrid noise removal model obtained in Step 2, which combines the dual low-rank approximation and anisotropic spatial spectral total variation, firstly... and Five auxiliary variables are introduced into the minimization problem, and the minimization of model (3) is equivalent to the following formula:

[0088]

[0089] Step 3.2: Solve using the alternating direction multiplier method, which minimizes the following augmented Lagrangian function:

[0090]

[0091] Where μ is the penalty parameter, and It is a Lagrange multiplier.

[0092] Step 3.3, Input variables: Input the observed Gaofen-5 hyperspectral remote sensing image. The input is of size m×n×p; the input regularization parameters λ, β, τ1, τ2, and τ3 are 0.02, 0.5, 0.0015, 0.10, and 0.0030, respectively; the input is the upper rank r of the low-rank tensor and the upper rank r of the striped noise matrix. b The values ​​of ε and 3 are respectively; the value of the input stopping criterion ε is 10. -6 ;

[0093] In this example, the input is a 600×400×330 Gaofen-5 hyperspectral remote sensing image. Before denoising, the gray values ​​of the hyperspectral image are normalized band by band to the range of [0,1].

[0094] Step 3.4, Initialize variables: Initialize variables and Create a zero tensor of size m×n×p; initialize the Lagrange multipliers. and Let m be a zero tensor of size m×n×p; initialize the penalty parameter μ to 10. -2 Initialize the parameter μ used to update the penalty parameter. max The values ​​of ρ and 10 are respectively. 6 1.1; Initialize the iteration count k to 0;

[0095] In this embodiment, the initial size of each three-dimensional tensor is 600×400×330.

[0096] Step 3.5 involves iteratively optimizing the augmented Lagrangian function (5) on one variable while keeping other variables fixed. Specifically:

[0097] Step A. In the (k+1)th iteration, update The variables are as follows:

[0098]

[0099] The tensor singular value threshold (t-SVT) operator is defined as follows:

[0100]

[0101] in, and

[0102] Step B. In the (k+1)th iteration, update The variables are as follows:

[0103]

[0104] in,

[0105]

[0106] Step C. In the (k+1)th iteration, update The variables are as follows:

[0107]

[0108] in,

[0109]

[0110] in, Represents the Fast Fourier Transform. It is its inverse transformation.

[0111] Step D. In the (k+1)th iteration, update and The variables are as follows:

[0112]

[0113]

[0114] Step E. In the (k+1)th iteration, update The variables are as follows:

[0115]

[0116] Among them, H i X i S i T i ,、M hi and M bi Let represent a matrix of size m×n in the i-th band. The singular value contraction operator follows:

[0117]

[0118] In this embodiment, the variables of size 600×400×330 are converted into 330 matrices of size 600×600, and variable B is then processed. i The update then involves 330 matrices B, each of size 600×600. i Reconstruct it into a variable of size 600×400×330.

[0119] Step F. In the (k+1)th iteration, update The variables are as follows:

[0120]

[0121] Step G. In the (k+1)th iteration, update The variables are as follows:

[0122]

[0123] Step H. In the (k+1)th iteration, update the Lagrange multipliers. and as follows:

[0124]

[0125] Step I. In the (k+1)th iteration, update the penalty parameter μ as follows:

[0126] μ:=min(ρμ,μ max (19)

[0127] Step J. In the (k+1)th iteration, check whether the following convergence condition is met:

[0128]

[0129] If the convergence condition is met, output a noise-free hyperspectral remote sensing image; if the convergence condition is not met, set k = k + 1 and repeat steps A to J.

[0130] In this embodiment, after the convergence condition is met, a noise-free Gaofen-5 hyperspectral remote sensing image with a size of 600×400×330 is output.

[0131] The embodiments of this invention use Gaofen-5 hyperspectral remote sensing imagery, but are not limited to Gaofen-5 hyperspectral remote sensing imagery. It has broad applicability to other hyperspectral images damaged by mixed noise, regardless of the intensity of Gaussian noise, impulse noise, dead line noise, bad pixels, or stripe noise, and is less restricted by objective factors. Experimental results using real Gaofen-5 hyperspectral remote sensing imagery demonstrate that this method has superior performance compared to other methods in removing multiple types of high-intensity mixed noise and protecting high-dimensional structural information.

[0132] It should be noted and understood that various modifications and improvements can be made to the invention described in the above detailed description without departing from the spirit and scope of the invention as claimed in the appended claims. Therefore, the scope of the claimed technical solutions is not limited to any specific exemplary teachings given.

Claims

1. A method for mixed noise hyperspectral image restoration by combining dual low-rank and spectral empty total variation, characterized in that, The method comprises the following steps: Step 1, establishing a double low-rank approximation model; Step 2, introducing an anisotropic spatial spectral total variation model into the denoising framework of the double low-rank approximation model obtained in step 1, and establishing a hyperspectral remote sensing image multi-type mixed noise removal model combining double low-rank approximation and anisotropic spatial spectral total variation; Step 3, using an alternating direction multiplier method to optimize and solve the hyperspectral remote sensing image multi-type mixed noise removal model combining double low-rank approximation and anisotropic spatial spectral total variation obtained in step 2, to obtain a noise-free hyperspectral remote sensing image; The specific implementation of step 3 comprises the following steps: Step 3.1, for the hyperspectral remote sensing image multi-type mixed noise removal model of combined double low rank approximation and anisotropic spatial spectrum total variation obtained in step 2, first introduce five auxiliary variables into the minimization problem, and the minimization of the multi-type mixed noise removal model is equivalent to the following formula: , , , and five auxiliary variables are introduced into the minimization problem, and the minimization of the multi-type mixed noise removal model is equivalent to the following formula: (4) Step 3.2, using the alternating direction multiplier method to solve, which minimizes the following augmented Lagrangian function: (5) wherein is a penalty parameter, , , , , and is a Lagrange multiplier; Step 3.3, iteratively optimizing the augmented Lagrangian function (5) on one variable while fixing other variables, specifically: Step A. In the first iteration, update k+ 1 = 1 the variables as follows: (6) Wherein, the tensor singular value threshold (t-SVT) operator is defined as follows: (7) wherein , and ; Step B. In the first iteration, update k+ 1 = 1 the variables as follows: (8) Wherein, the soft threshold shrinkage operator is represented as: (9) Step C. In the first iteration, update k+ 1 = 1 the variables as follows: (10) Wherein, (11) wherein denotes the fast Fourier transform, is its inverse transform; Step D. In the first iteration, update k+ 1 = 1 and variable as follows: (12) (13) Step E. In the 1st iteration, update k+ 1 = 1 the variables as follows: (14) where , , , , and denote the matrix of size i on the th band, and the singular value shrinkage operator obeys: (15) Step F. In the 1st iteration, update k+ 1st iteration, update the variables as follows: (16) Step G. In the first iteration, update k+ 1 = 1 the variables as follows: (17) Step H. In the 1st iteration, update the Lagrange multiplier k+ 1 、 、 、 、 and the Lagrange multiplier as follows: (18) Step I. At the end of each k+ 1 iteration, update the penalty parameter as follows: (19) Step J. In the first iteration, check if the following convergence condition is met: k+ 1 iteration, check if the following convergence condition is met: (20) If the convergence condition is satisfied, the noise-free hyperspectral remote sensing image is output; if the convergence condition is not satisfied, the step A-J is repeated. and repeating steps A-J.

2. The method of claim 1, wherein the method is a joint low-rank and spatially adaptive total variation (LRTV) method. In step 1, the low-rank tensor approximation of the noise-free hyperspectral remote sensing image is performed by using the weighted sum and the tensor kernel norm, the low-rank matrix approximation of the strip noise in each band of the hyperspectral remote sensing image is performed by using the kernel norm, and the sparse constraint of the sparse noise is performed by using the norm, so as to establish a double low-rank approximation model.

3. The method of claim 1, wherein the method is characterized by: The specific implementation of step 1 is as follows: Step 1.1, model the observed three-dimensional hyperspectral remote sensing image as a set of noise-free hyperspectral remote sensing image, sparse noise, strip noise and Gaussian noise, i.e. wherein, denotes the three-dimensional observed hyperspectral remote sensing image, , and are the width, height and band number of the hyperspectral remote sensing image, respectively, , , and are three-dimensional tensors with the same size and represent noise-free hyperspectral remote sensing image, sparse noise, strip noise and Gaussian noise, respectively; Step 1.

2. Denoising hyperspectral remote sensing images using weighted sum and tensor nuclear norm Low-rank tensor approximation with nuclear norm for striping noise Waveband-wise low-rank matrix approximation with norm for sparse noise Sparse constraint, and a double low-rank approximation model (1) where the weighted sum of the tensor core norms is defined as the rank of each mode- k 1 k 2 tensor, ; norm is the sum of non-zero elements in a matrix; is the banding noise matrix in the th band of the hyperspectral remote sensing image; and are regularization parameters to control the trade-off between each regularization term, denotes the rank of a vector, denotes the Tubal rank of a tensor, is the mode and mode -13 of a tensor -23 is the upper bound rank of the unfolded tensor, denotes the upper bound rank of the band-wise banding noise matrix , and denotes the intensity of the Gaussian noise.

4. The method of claim 1, wherein the method is a joint low-rank and spectral void total variation (LRTV) method. The specific implementation of step 2 comprises the following steps: Step 2.1, using a linear first-order discrete difference operator to constrain the gradients along the spatial horizontal direction and spectral direction of the noise-free hyperspectral remote sensing image, the spatial vertical direction of the strip noise, and establishing an anisotropic spatial spectral total variation model: (2) wherein, , and are regularization parameters for measuring gradient contributions along different directions, the operators , and are linear first-order discrete difference operators along horizontal, vertical and spectral directions, respectively; Step 2.2, introducing the anisotropic spatial spectral total variation model into the double low-rank approximation model, and establishing a hyperspectral remote sensing image multi-type mixed noise removal model combining double low-rank approximation and anisotropic spatial spectral total variation: (3)。 5. The method of claim 1, wherein the method is a joint low-rank and spatially adaptive total variation (LRTV) method. Initialize variables before step 3.3: initialize variables , , , , , , and to zero tensors of size ; initialize Lagrange multipliers , , , , and to zero tensors of size ; initialize penalty parameter to ; initialize parameters for updating the penalty parameter and to values of size and 1.1, respectively; initialize the number of iterations to 0.

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