CN106408530A - Sparse and low-rank matrix approximation-based hyperspectral image restoration method - Google Patents

Abstract

The invention relates to a sparse and low-rank matrix approximation-based hyperspectral image restoration method and belongs to the image processing field. The method includes the following steps that: a hyperspectral data sequence affected by mixed noises is acquired, or simulated mixed noises are artificially added into a clear hyperspectral image sequence, so that hyperspectral data to be processed can be obtained; the multi-band hyperspectral image data are segmented into a plurality of small data blocks, and each three-dimensional data block is pieced into one two-dimensional data matrix; a weighted Schatten p-normal type low-rank matrix approximation model is constructed for each two-dimensional data matrix; an extended Lagrange multiplier method is adopted to solve the model to obtain mixed noise-removed two-dimensional data matrixes; each two-dimensional data matrix is restored into three-dimensional hyperspectral data, so that a mixed noise-removed multi-band hyperspectral image can be obtained; and the above steps are repeated by using an iteration method to obtain a better restoration effect. The method can be effectively applied to fields such as remote sensing, geography, agriculture and military fields.

Description

Hyperspectral image recovery method based on sparse and low-rank matrix approximation

Technical Field

The invention relates to image processing, in particular to a hyperspectral image recovery method based on sparse and low-rank matrix approximation.

Background

The hyperspectral imaging technology is an earth observation technology developed from the 20 th century, and has high practical value in the aspects of military affairs, geological survey, agricultural detection and the like. The hyperspectral image data is three-dimensional image data, and besides a two-dimensional image, the hyperspectral image data also has a waveband dimension, and is mainly characterized in that the traditional image space and spectral information are fused into a whole. The hyperspectral image data contains abundant surface feature spectrum information, and the target recognition of the surface features and the like can be realized.

Although with the development of computer technology and spectral imaging technology, the imaging quality of hyperspectral image data is greatly improved. But inevitably, hyperspectral images are affected by mixing noise due to imager physical imperfections, atmospheric pollution, transmission losses and calibration problems. These mixed noises include gaussian noise, impulse noise, stripe noise, and dead lines. Therefore, the denoising problem of the hyperspectral image needs to be solved urgently, and the method is an important preprocessing work of the hyperspectral image data in the subsequent information analysis.

At present, many image denoising techniques are applied to the denoising of hyperspectral images. Inspired by a grayscale Image denoising method, a non-local mean method, an SVD method, a BM3D method proposed by Dabov et al in "Image differentiating by 3-D transform-domain communicating filtering. IEEE Trans. on Image processing", and an SSATV method proposed by Yuan et al in "hyper spectral Image differentiating applying dynamic total variation model. IEEE geographic information. However, these methods are not satisfactory because they ignore the correlation between different bands of the hyperspectral image. In order to utilize the correlation between images in different wave bands, some researchers propose to divide large three-dimensional data into small three-dimensional data, convert the small three-dimensional data into two-dimensional data, and then perform low-rank matrix recovery by using the low-rank property of a noise-free matrix, so as to achieve the denoising effect. For example, Zhang et al, in "Hyperspectral Image retrieval Using Low-Rank Matrix recovery. IEEE Trans. on Geosunce and Remote Sensing" proposed LRMR method.

Disclosure of Invention

The invention aims to provide a hyperspectral image recovery method based on sparse and low-rank matrix approximation, which removes most of noise and also reserves abundant image details.

The invention comprises the following steps:

(1) setting a group of multiband hyperspectral image data d, wherein the size of d is MxNxB, M and N respectively represent the length and width of the hyperspectral image of each waveband, B represents the number of the shared wavebands, and the estimated noise level of d is eta;

(2) initializing variables, denoised dataNoisy dataGaussian noise level η⁽⁰⁾＝η；

(3) Initializing iteration, enabling a loop variable K to be 1, and setting the maximum outer loop times K;

(4) iterative regularization

(5) Taking the central coordinate position as (i, j), wherein i and j respectively represent the horizontal and vertical coordinates of the central point, and extracting data with the size of w × h × BWherein w and h represent the width and height of the data block and B is the number of hyperspectral data bands;

(6) combining three-dimensional dataConverting the two-dimensional matrix into a two-dimensional matrix D with the size of wh × B;

(7) constructing a weighted Schatten-p normal form low-rank matrix approximation model for the D;

(8) solving the weighted Schatten-p normal form low-rank matrix approximate model constructed in the step (7) by using an extended Lagrange multiplier method to obtain a matrix A after denoising;

(9) update noise level η^(k)；

(10) Taking all the center coordinates (i, j) according to a certain step length, repeating the steps (5) to (9) to respectively obtain corresponding A_(i,j)；

(11) All A with the size of wh × B_(i,j)Convert back to three dimensional data of size w × h × B

(12) All will beSplicing complete three-dimensional data with size M × N × B

(13) Taking K > K as a cycle termination condition, if K does not meet the condition of being more than K, returning to the step (4) after increasing the value of K by 1, otherwise, directly executing the step (14);

(14) will be provided withAnd finally removing all noise to obtain the hyperspectral image data.

In step (5), the extraction size is a number of w × h × BAccording toThe method comprises the steps of taking out image blocks with the size of w × h and the center of (i, j) of M × N hyperspectral images of B wave bands respectively, and then laminating the image blocks to obtain a three-dimensional data block with the size of w × h × B.

In step (6), the three-dimensional data is processedThe two-dimensional matrix D converted into wh × B is a rectangle D in which B image blocks of w × h are arranged in sequence into a pixel column of wh × 1, and then, a wh × B is formed.

In step (7), the weighted Schatten-p-norm low rank matrix approximation model is as follows:

s.t D＝A+E+N,||N||_F≤η

where C and λ are coefficients, A represents clean image data unaffected by noise, E represents a mixture of impulse noise, dead lines, and stripe noise, N represents Gaussian noise with a noise level η set artificially | | · | | Y |₁Represents the 1 norm of the matrix, | · | | non-woven phosphor_FA Frobenius norm representing a matrix;represents a weighted Schatten-p paradigm, the specific form is as follows:

wherein p is more than 0 and less than or equal to 1, r is min { wh, B }, and sigma is_iIs the i-th singular value of a,wherein sigma_i(D) Representing the ith singular value of D.

In the step (8), the specific steps of solving the weighted Schatten-p normal form low-rank matrix approximation model constructed in the step (7) by using the extended lagrange multiplier method to obtain the denoised matrix a are as follows:

(8.1) initializing variables:^k＝D，A^k＝E^k＝0，β_kgreater than 0, rho > 1, k is 0, lagrange multiplier, β_kThe penalty coefficient of the constraint term in the kth iteration is, rho is a penalty coefficient iteration factor, and k is the current iteration number;

(8.2) updateWherein

(8.3) update

(8.4) update

(8.5) update^k+1＝^k-β_k(A^k+1+E^k+1+N^k+1-D)；

(8.6) order β_k+1＝ρ*β_k；

(8.7) letting k be k + 1;

(8.8) if | purple^k-^k-1||₁< convergence, wherein convergence is convergence parameter, executing step (8.9), otherwise executing step (8.2);

(8.9) adding A^k+1As denoised matrix a.

In step (8.3), the updatingThe method comprises the following steps:

let matrix E^k+1Each element of (a):

(E^k+1)_ij＝sign(X_ij)·max(|X_ij|-λ,0)

wherein,(·)_ijand (3) representing the element of the ith row and the jth column of the matrix, wherein sign () is a sign function.

In step (8.4), the updateThe method comprises the following specific steps:

(8.4.1) orderCarrying out SVD on Y to obtain Y ═ U ∑ V^ΤWherein Σ ═ diag (σ)₁,...,σ_r) I.e. sigma_iSingular values for Y;

(8.4.2) initializing iteration, setting a loop variable i to be 1, and setting the maximum outer loop times r;

(8.4.3) use of σ_i,ω_iP, obtaining A by generalized soft threshold method^k+1Is estimated from the ith singular value of the matrix_i；

(8.4.4) if i is greater than or equal to r, directly executing the step (8.4.5), otherwise, making i equal to i +1, and executing the step (8.4.3);

(8.4.5) let the variable Δ ═ diag (d:)₁,..._r) Wherein diag (·) is a matrix diagonal permutation function;

(8.4.6) order A^k+1＝UΔV^Τ；

In step (8.4.3), the utilization σ_i,ω_iP, obtaining A by generalized soft threshold method^k+1Is estimated from the ith singular value of the matrix_iThe method comprises the following specific steps:

(8.4.3.1) let the variable σ be σ ═ σ_iThe variable ω ═ ω_iLet us orderThis is a function of ω and p;

(8.4.3.2) if | < sigma | < tau_p(ω), let function S_p(σ; ω) is 0, performing step (8.4.3.8); otherwise, executing step (8.4.3.3);

(8.4.3.3) initializing a thresholding variable to⁽⁰⁾＝|σ|；

(8.4.3.4) initializing iteration, making a loop variable t equal to 0, and setting the maximum outer loop times J;

(8.4.3.5) let^(t+1)＝|σ|-ωp(^(t))^p-1；

(8.4.3.6) if t ≧ J, directly executing step (8.4.3.7), otherwise, let t ═ t +1, execute step (8.4.3.5);

(8.4.3.7) setting function S_p(σ；ω)＝sgn(σ)^(t)Wherein sgn is a sign function;

(8.4.3.8) let_i＝S_p(σ；ω)。

In step (9), the update noise level η^(k)The method comprises the following steps:

where γ is a scaling factor.

In step (12), all ofSplicing complete three-dimensional data with size M × N × BComprises the specific steps ofIs put backWith (i, j) as the center and w × h × B as the size position, respectivelyThe overlapping portions are averaged.

The invention adopts a novel method to remove mixed noise generated in the acquisition and transmission process of the hyperspectral image, wherein the noise is mixed Gaussian noise, impact noise, stripe noise and dead lines, and aiming at the property of the hyperspectral image, the invention realizes a hyperspectral image recovery method by sparse and low-rank matrix approximation, thereby not only removing most of noise, but also reserving abundant image details.

The invention provides an iterative hyperspectral image recovery method based on low-rank matrix decomposition, which is characterized in that a low-rank matrix approximate model is constructed by using the low-rank property of a processed data matrix and a weighted schatten p-paradigm, and a solving method of the low-rank matrix approximate model is provided. The low-rank regular term of the unique weighted schatten-p paradigm has obvious improvement on the effect of a low-rank matrix approximation model, and then the estimation of the noise level is automatically estimated and updated in the solving process, so that different noises can be processed in a self-adaptive mode. Through the novel technical means, the mixed noise can be well removed, the image information with useful value is greatly reserved, and the effect of the method is superior to that of the currently popular hyperspectral image restoration method.

The invention has the following technical effects:

1. according to the method, the low rank property of the processed hyperspectral image is utilized to construct an extended robust principal component analysis model, and the low rank property and the sparsity of the model are well reserved. For the low-rank regularization term of the model, a novel weighted Schatten-p paradigm is used, the paradigm is controlled by giving different weight to rank components, so that the noise is adapted to different degrees, and the low-rank regularization term is better realized, so that the denoising effect is better achieved theoretically and practically.

2. Aiming at the difficult-to-solve non-convex optimization denoising model, the method adopts an expanded Lagrange multiplier method and a generalized soft threshold method to solve the difficult-to-solve non-convex optimization denoising model. Moreover, the invention also uses an iterative regularization frame, and the whole model can adaptively cope with the recovery problem of different hyperspectral data by estimating and adjusting the noise level.

Drawings

FIG. 1 is an image obtained after atmospheric disturbance removal of a real video frame of a chimney using three methods of the present invention and the prior art;

fig. 2 is an image obtained by taking out atmospheric disturbance from a simulated disturbance video of a city by using the method of the present invention and the existing method in the third place.

Detailed Description

The method comprises the following specific implementation steps:

step 1, acquiring hyperspectral image data affected by mixed noise.

A group of multiband hyperspectral image data d is obtained by using a hyperspectral imager and is normalized to [0,1 ]. The size of the hyperspectral image is M multiplied by N multiplied by B, wherein M and N respectively represent the length and width of the hyperspectral image of each wave band, and B represents how many wave bands are in total. The estimated noise level for this set of data is η 20/255.

And step 2, initializing iteration variables.

(2a) Order de-noised dataNoisy dataGaussian noise level η⁽⁰⁾＝η。

(2b) And initializing iteration, wherein the loop variable k is 1, the central horizontal and vertical coordinates are i and 10, and j is 10.

Step 3, iterative regularization

And 4, acquiring two-dimensional data of the low-rank model to be established.

(4a) For M × N hyperspectral images of B wave bands, image blocks with the size of 20 × 20 and the size of (i, j) as the center are respectively taken out and then are laminated together to obtain a three-dimensional data block with the size of 20 × 20 × B

(4b) B20 × 20 image blocks are respectively connected in series in sequence to form a 400 × 1 pixel column, and then a 400 × B rectangle D is formed by splicing.

And 5, constructing a weighted Schatten-p normal form low-rank matrix approximation model as follows:

s.t D＝A+E+N,||N||_F≤η

wherein C is 0.007, λ is 1.2, and p is 0.7.p＝0.7，r＝min{400,B}，σ_iIs the i-th singular value of a,wherein sigma_i(D) Representing the ith singular value of D.

And 6, solving the model by using an expanded Lagrange multiplier method.

(6a) Initializing variables:^h＝D，A^h＝E^h＝0，β_h> 0, ρ > 1, h ═ 0, lagrange multiplier, β_hAnd the penalty coefficient of the constraint term in the h iteration, rho is a penalty coefficient iteration factor, and h is the current iteration number.

(6b) UpdatingWherein

(6c) Update E^h+1Let's matrix E^h+1Each element (E) of^h+1)_ij＝sign(X_ij)·max(|X_ijL- λ,0), wherein

(6d) Update A^h+1The following were used:

(6d.1) orderCarrying out SVD on Y to obtain Y ═ U ∑ V^Τ，Σ＝diag(σ₁,...,σ_r)。

(6d.2) initialize the iteration, let loop variable q be 1, set the maximum skin loop number r, as described in step 5.

(6d.3) Using ω defined in step 5_qAnd p, σ in step (6d.1)_qA is obtained by the following generalized soft threshold method^h+1Of the estimation matrix of (2) q-th singular value_q：

(6d.3a) let variable σ ═ σ_qThe variable ω ═ ω_qOrder function

(6d.3b) if [ sigma ] is less than or equal to tau_p(ω), let variable S_p(σ; ω) is 0, performing step (8.8); otherwise, step (8.3) is executed.

(6d.3c) order initialization threshold method variable⁽⁰⁾＝|σ|。

(6d.3d) initialize the iteration, let the loop variable t be 0, set the maximum skin loop number J50.

(6d.3e) order^(t+1)＝|σ|-ωp(^(t))^p-1。

(6d.3f) if t is not less than J, directly executing the step (6d.3g), otherwise, making t equal to t +1, and executing the step (6 d.3e).

(6d.3g) setting function S_p(σ；ω)＝sgn(σ)^(t)。

(6d.3h) order_q＝S_p(σ；ω)。

(6d.4) if q ≧ r, directly executing step (6d.5), otherwise, if q ≧ q +1, executing step (6 d.3).

(6d.5) let the matrix variable Δ ═ diag (d: (d.5)₁,..._r) Where diag (·) is a matrix diagonal permutation function.

(6d.6) order A^h+1＝UΔV^Τ。

(6e) Updating^h+1＝^h-β_h(A^h+1+E^h+1+N^h+1-D)。

(6f) Let β_h+1＝ρ*β_h。

(6g) Let h be h + 1.

(6h) Hollow if |)^h-^h-1||₁< convergent, wherein the convergent parameter convergent is 10^-7Then step (5.9) is performed, otherwise step (5.2) is performed.

(6i) A is to be^h+1As denoised matrix A_(i,j)。

Step 7, updating the noise level

Step 8, taking all the central coordinates (i, j) according to the step length of 4 for the horizontal and vertical coordinates, repeating the steps (4) to (7) to respectively obtain the corresponding A_(i,j)。

And 9, obtaining the denoising hyperspectral data of the iteration of the current round.

(9a) All A with the size of 400 × B_(i,j)Conversion back to three-dimensional data of size 20 × 20 × B

(9b) All will beIs put backIn (c) at positions where w × h × B is the size and the center is (i, j) corresponding to eachThe overlapping parts are averaged to obtain a value of M × N × B

And step 10, taking k > 6 as a cycle termination condition, if not, returning to the step 3 after increasing the value of k by 1, otherwise, executing the step 11.

Step 11, mixingAnd finally removing all noise to obtain the hyperspectral image data.

The invention is proved by the following experiments.

1. The experimental conditions are as follows:

laboratory desktop parameters: the CPU is Inter (R) core (TM) i7-2600, the main frequency is 3.40GHz, the memory is 4G, the operating system is a Win 764 bit system, and the experimental platform is Matlab2014 b.

2. Experimental results and analysis of results:

experiment one, the invention and the existing method are used for restoring the real hyperspectral image data.

Downloading a group of real hyperspectral image data Urban influenced by mixed noise from a network, wherein the size of the hyperspectral image data Urban is 307 multiplied by 188, subtracting a minimum pixel from each pixel, and dividing the difference between a maximum pixel value and a minimum pixel value to obtain data normalized to [0,1 ]. Then, the method provided by the invention is used for denoising, and the BM3D, SSATV and LRMR methods mentioned in the background art are used for comparison experiments. The experimental results are shown in fig. 2, wherein fig. 2(a) is one of the original hyperspectral image data, fig. 2(b) is the BM3D method effect, fig. 2(c) is the SSATV method effect, fig. 2(d) is the LRMR method effect, and fig. 2(e) is the invention effect.

The experimental results of fig. 2 illustrate that: from the visual perspective, fig. 2(b) and fig. 2(c) remove most of the noise, but also lose much detail information, and fig. 2(b) also has obvious denoising traces. The result of fig. 2(d) is also much unremoved noise. The denoising effect of the method in fig. 2(e) is obvious, noise is well removed, and rich detail information is reserved to a great extent.

And experiment II, the invention and the existing method are used for recovering the simulated hyperspectral image data.

A set of hyperspectral images unaffected by noise is downloaded from the network, with a size of 256 × 256 × 191. Gaussian noise, impulse noise, banding noise and dead lines are artificially added randomly to all frames. And then, carrying out denoising treatment by using the method provided by the invention, and carrying out a comparison experiment by using three methods, namely BM3D, SSATV and LRMR. The experimental results are shown in fig. 3, where fig. 3(a) is a clear hyperspectral image data, fig. 3(b) is a hyperspectral image after adding a simulation noise, fig. 3(c) is the BM3D method effect, fig. 3(d) is the SSATV method effect, fig. 3(e) is the LRMR method effect, and fig. 3(f) is the effect of the present invention. Table 1 shows the comparison of the mean peak signal-to-noise ratio (MPSNR) and the Mean Structural Similarity (MSSIM) of the present invention with the three methods described above.

The experimental results of fig. 3 and table 1 illustrate that: fig. 3(b) is affected by mixed noise, the visual effect is very poor, and the information interference is much; FIG. 3(c) loses a lot of detail information, with little effect on dead-line noise; all noise removal in FIG. 3(d) is unsatisfactory, fuzzy and dead; the results of fig. 3(e) are all better than the previous figures, but there is still a black imprint remaining in the part of the figure circled by the green dashed line, which is the result of the incomplete processing of dead line noise. In fig. 3(f), the method of the present invention not only removes various noises including dead lines well, but also retains rich detailed information to a great extent, and is closest to and has the best effect compared with the original data image.

TABLE 1

	BM3D	SSATV	LRMR	The invention
					MPSNR	24.958	17.344	27.474	30.303
MSSIM	0.6177	0.2752	0.8114	0.8711

As shown in table 1, the MPSNR and MSSIM values of the present invention are higher than those of the existing three methods.

Claims (10)

1. The hyperspectral image recovery method based on sparse and low-rank matrix approximation is characterized by comprising the following steps of:

(1) setting a group of multiband hyperspectral image data d, wherein the size of d is MxNxB, M and N respectively represent the length and width of the hyperspectral image of each waveband, B represents the number of the shared wavebands, and the estimated noise level of d is eta;

(2) initializing variables, denoised dataNoisy dataGaussian noise level η⁽⁰⁾＝η；

(3) Initializing iteration, enabling a loop variable K to be 1, and setting the maximum outer loop times K;

(4) iterative regularization

(5) Taking the central coordinate position as (i, j), wherein i and j respectively represent the horizontal and vertical coordinates of the central point, and extracting data with the size of w × h × BWherein w and h represent the width and height of the data block and B is the number of hyperspectral data bands;

(6) combining three-dimensional dataConverting the two-dimensional matrix into a two-dimensional matrix D with the size of wh × B;

(7) constructing a weighted Schatten-p normal form low-rank matrix approximation model for the D;

(8) solving the weighted Schatten-p normal form low-rank matrix approximate model constructed in the step (7) by using an extended Lagrange multiplier method to obtain a matrix A after denoising;

(9) update noise level η^(k)；

(10) Taking all the center coordinates (i, j) according to a certain step length, repeating the steps (5) to (9) to respectively obtain corresponding A_(i,j)；

(11) All A with the size of wh × B_(i,j)Convert back to three dimensional data of size w × h × B

(12) All will beSplicing complete three-dimensional data with size M × N × B

(13) Taking K > K as a cycle termination condition, if K does not meet the condition of being more than K, returning to the step (4) after increasing the value of K by 1, otherwise, directly executing the step (14);

(14) will be provided withAnd finally removing all noise to obtain the hyperspectral image data.

2. The sparse-and-low-rank matrix approximation-based hyperspectral image restoration method according to claim 1, wherein in step (5), the extraction of data with the size of w × h × BThe method comprises the steps of taking out image blocks with the size of w × h and the center of (i, j) of M × N hyperspectral images of B wave bands respectively, and then laminating the image blocks to obtain a three-dimensional data block with the size of w × h × B.

3. The sparse-and-low-rank matrix approximation-based hyperspectral image recovery method of claim 1, wherein in step (6), the three-dimensional data is processedThe two-dimensional matrix D converted into wh × B is a rectangle D in which B image blocks of w × h are arranged in sequence into a pixel column of wh × 1, and then, a wh × B is formed.

4. The sparse-and-low-rank matrix approximation-based hyperspectral image restoration method according to claim 1, wherein in step (7), the weighted Schatten-p-norm low-rank matrix approximation model is as follows:

$\begin{array}{ccc}\underset{A,E}{\min }C\left|\right|A|{|}_{w,S_p}^p+\mathrm{\&lambda;}|\left|E\right|{|}_1& s.t& D=A+E+N,\left|\right|N|{|}_F\&le;\mathrm{\&eta;}\end{array}$

where C and λ are coefficients, A represents clean image data unaffected by noise, E represents a mixture of impulse noise, dead lines, and stripe noise, N represents Gaussian noise with a noise level η set artificially | | · | | Y |₁Represents the 1 norm of the matrix, | · | | non-woven phosphor_FA Frobenius norm representing a matrix;represents a weighted Schatten-p paradigm, the specific form is as follows:

$\left|\right|A|{|}_{w,S_p}^p={\mathrm{\&Sigma;}}_{i=1}^r{\mathrm{\&omega;}}_i{\mathrm{\&sigma;}}_i^p$

wherein p is more than 0 and less than or equal to 1, r is min { wh, B }, and sigma is_iIs the i-th singular value of a,wherein sigma_i(D) Representing the ith singular value of D.

5. The sparse-and-low-rank matrix approximation-based hyperspectral image restoration method according to claim 1 is characterized in that in step (8), the specific steps of solving the weighted Schatten-p-norm low-rank matrix approximation model constructed in step (7) by using the extended Lagrange multiplier method to obtain the denoised matrix A are as follows:

(8.1) initializing variables:^k＝D，A^k＝E^k＝0，β_kgreater than 0, rho > 1, k is 0, lagrange multiplier, β_kThe penalty coefficient of the constraint term in the kth iteration is, rho is a penalty coefficient iteration factor, and k is the current iteration number;

(8.2) updateWherein

(8.3) update

(8.4) update

(8.5) update^k+1＝^k-β_k(A^k+1+E^k+1+N^k+1-D)；

(8.6) order β_k+1＝ρ*β_k；

(8.7) letting k be k + 1;

(8.8) if | purple^k-^k-1||₁< convergence, wherein convergence is convergence parameter, executing step (8.9), otherwise executing step (8.2);

(8.9) adding A^k+1As denoised matrix a.

6. The sparse-and-low-rank matrix approximation-based hyperspectral image recovery method according to claim 5, wherein in step (8.3), the updatingThe method comprises the following steps:

let matrix E^k+1Each element of (a):

(E^k+1)_ij＝sign(X_ij)·max(|X_ij|-λ,0)

wherein,(·)_ijand (3) representing the element of the ith row and the jth column of the matrix, wherein sign () is a sign function.

7. As claimed in claimThe hyperspectral image recovery method based on sparse and low-rank matrix approximation is characterized in that in step (8.4), the hyperspectral image is updatedThe method comprises the following specific steps:

(8.4.1) orderCarrying out SVD on Y to obtain Y ═ U ∑ V^ΤWherein Σ ═ diag (σ)₁,...,σ_r) I.e. sigma_iSingular values for Y;

(8.4.2) initializing iteration, setting a loop variable i to be 1, and setting the maximum outer loop times r;

(8.4.3) use of σ_i,ω_iP, obtaining A by generalized soft threshold method^k+1Is estimated from the ith singular value of the matrix_i；

(8.4.4) if i is greater than or equal to r, directly executing the step (8.4.5), otherwise, making i equal to i +1, and executing the step (8.4.3);

(8.4.5) let the variable Δ ═ diag (d:)₁,..._r) Wherein diag (·) is a matrix diagonal permutation function;

(8.4.6) order A^k+1＝UΔV^Τ。

8. The sparse-and-low-rank matrix approximation-based hyperspectral image recovery method of claim 7, wherein in step (8.4.3), the utilizing σ is_i,ω_iP, obtaining A by generalized soft threshold method^k+1Is estimated from the ith singular value of the matrix_iThe method comprises the following specific steps:

(8.4.3.1) let the variable σ be σ ═ σ_iThe variable ω ═ ω_iLet us orderThis is a function of ω and p;

(8.4.3.2) if | < sigma | < tau_p(ω), let function S_p(σ; ω) is 0, performing step (8.4.3.8);otherwise, executing step (8.4.3.3);

(8.4.3.3) initializing a thresholding variable to⁽⁰⁾＝|σ|；

(8.4.3.4) initializing iteration, making a loop variable t equal to 0, and setting the maximum outer loop times J;

(8.4.3.5) let^(t+1)＝|σ|-ωp(^(t))^p-1；

(8.4.3.6) if t ≧ J, directly executing step (8.4.3.7), otherwise, let t ═ t +1, execute step (8.4.3.5);

(8.4.3.7) setting function S_p(σ；ω)＝sgn(σ)^(t)Wherein sgn is a sign function;

(8.4.3.8) let_i＝S_p(σ；ω)。

9. The sparse-and-low-rank matrix approximation-based hyperspectral image restoration method according to claim 1, wherein in step (9), the update noise level η^(k)The method comprises the following steps:

${\mathrm{\&eta;}}^{(k+1)}=\mathrm{\&gamma;}\sqrt{{\left({\mathrm{\&eta;}}^{\left(k\right)}\right)}^2-\frac{1}{B}\underset{i=1}{\overset{B}{\&Sigma;}}\left|\right|d_i-d_i^{\left(k\right)}|{|}_2^2}$

where γ is a scaling factor.

10. The sparse-and-low-rank matrix approximation-based hyperspectral image recovery method of claim 1, wherein in step (12), the method applies all the sparse-and-low-rank matrix approximationsSplicing complete three-dimensional data with size M × N × BComprises the specific steps ofIs put backWith (i, j) as the center and w × h × B as the size position, respectivelyThe overlapping portions are averaged.