CN110400276B - Hyperspectral image denoising method and device - Google Patents

Abstract

A hyperspectral image denoising method is characterized in that a low-rank matrix recovery model is established based on ground feature classes according to local space low-rank prior, spectrum low-rank prior and global spectrum low-rank prior in hyperspectral image data; partitioning the hyperspectral images according to different ground object categories; removing noise in the local blocks of the hyperspectral image; and removing noise in the whole hyperspectral image space data and the whole spectral data again.

Description

Hyperspectral image denoising method and device

Technical Field

The invention belongs to the technical field of image processing, and particularly relates to a hyperspectral image denoising method and device.

Background

Hyperspectral image (HSI) is a three-dimensional (3D) data cube, where the first two dimensions represent spatial information and the third dimension represents spectral information [1]. However, in practical HSI applications, the observed HIS is contaminated by different noise sources, which requires denoising of the hyperspectral image to generate a noiseless hyperspectral image HSI [2].

In the existing denoising method, HSI data are represented by different dimensions for denoising, and the method comprises three modes of one-dimensional pixels, two-dimensional spectral bands and three-dimensional cubes; the three-dimensional cube mode is integral processing, and denoising is respectively carried out on a spatial domain, a spectral domain and space-spectrum combination. The development of HSI data in a denoising method utilizes different-dimension data information for denoising. In short, the one-dimensional pixels are used for selecting data for each pixel to be denoised in turn, and the two-dimensional spectral bands are used for selecting data for denoising according to each band. And three-dimensional data cube, whole image or part of whole image (local block) is selected.

Meanwhile, different noise types exist in the HSI data, including gaussian noise, sparse noise (impulse noise, dead lines and stripes), and mixed noise. In denoising using two-dimensional spectral band representation (expression of data information of HSI), since HSI includes hundreds of bands, each band is regarded as a spatial grayscale image, and the grayscale image denoising method is extended to HSI denoising. Block matching and 3D filtering BM3D 3, obtaining basic estimation of image blocks through 3D conversion after matching the image blocks in a certain wave band, then filtering noise, and obtaining de-noised images again through 3-D inverse conversion; the video block matching and 3D filtering VBM3D [4] method is an extension of BM3D method, and is used for the case of denoising a single image into a multi-channel image. The method has the advantage of 'spectrum integration' 1 in the aspect of representing denoising by using a three-dimensional cube, wherein denoising of a spatial domain is equivalent to denoising of a circulating two-dimensional spectral band. The denoising of the spectral domain is to divide the whole cube into innumerable sub-cubes and utilize the high correlation among spectral bands. By combining the operation of the space-spectrum domain, on the basis of the spectrum domain, the utilization of local spatial similarity or the addition of spatial constraint and the like are considered. Different technologies such as Total Variation Regularization (TVR), sparse Representation (SR), and Tensor Decomposition (TD) are also combined for denoising.

In the spectral domain denoising method, according to the fact that HSI has a potential LR (Low Rank) structure in the spectral domain, the method is widely applied to denoising hyperspectral images nowadays, and good effect is achieved. Document [5] proposes an idealized problem of "robust principal component analysis" RPCA (robust principal component analysis), which divides a data matrix into the sum of a low-rank matrix and a sparse matrix (sparse error). Document [6] finds and applies LR property of HSI data for the first time, converts the recovery problem into low-rank matrix recovery (LRMR), divides the whole HSI into overlapped sub-cubes patch, and removes mixed noise for the first time on hyperspectral images by using two GoDec [7] (Go Decomposition) algorithms and an ALM (Augmented Lagrange Multiplier) numerical optimization algorithm, and the effect of removing sparse noise is the best. But the removing effect is poor for the noise with higher density. A PARAFAC (Parallel Factor Analysis) 8 method is provided based on TD, and denoising is performed by utilizing correlation among all wave bands in local, but spatial non-local similarity is ignored. GLRR [9] (Group Low-Rank registration) in dividing HSI into countless overlapping subcubes, clustering similar patches into a Group, and using the LRR method, using GoDec algorithm to reconstruct the Group as a whole.

In the denoising method combined with the space-spectral domain, correlation among spectra is utilized according to low-rank characteristics, meanwhile, a TVR can utilize a space segmentation smooth structure, and an LR decomposition and TVR (Total-variance-regularized low-rank matrix factorization, LRTV [10 ]) integration algorithm is provided, but local edges are blurred, texture details are lost, and adaptability is poor. In combination with SR, in order to fully utilize redundancy and correlation of the global spectrum domain, a spectrum global penalty constraint is added in the SR framework, and a method of sparse representation and spectrum low-rank penalty is provided, which is called SRLR [11] (SR and LR) for short. Further enhancing the utilization of Spatial information, improving the Low-Rank penalty attribute of the joint space and spectrum, proposing an SSLR (Spatial and Spectral Low-Rank) [12] model, and then effectively eliminating Gaussian noise in the Spectral domain by utilizing the Spectral similarity. Meanwhile, a non-local spatial LR regularization method is adopted to solve the problem of a sparse coding method, and the reduction of spatial noise can be better realized. HSI can be expressed as a third order Tensor, and there are two types of TD commonly used in the literature, tucker decomposition and PARAFAC. A denoising method based on the Tucker decomposition is LRTA (lower rank transducer approximation) [13]. In a newer document, LR constraint is combined with a sparse Tensor decomposition technique, and prior information of a hyperspectral image is used to provide a Low-order Tensor Recovery (LRTR) 0.

In the denoising method, when only two-dimensional spectral band operation is adopted, the specific spectral information among the HSI pixels is ignored, so the denoising effect of the method is poor. When only three-dimensional cube operation is adopted, the utilization of spatial information and spectral information in HSI can be ensured, and the noise removal effect is superior to that of a two-dimensional spectral band denoising mode. The trend in recent technological development is to gradually turn to the combined use of mixed noise models, but there is a difference in the removal effect for different types of mixed noise of different degrees, whether spatial and spectral information is fully utilized. In the method combining sparse representation, sparse dictionary learning occupies more time, and the performance of the algorithm is lower; the method combined with the tensor technology aims to decompose and obtain a low-rank part, and not only is the realization difficult, but also more resources are required to be occupied.

The references referred to in this application are as follows:

[1] zhang, hyperspectral image processing and information extraction leading edge [ J ] remote sensing academic report, 2016,20 (05): 1062-1090.

[2]Rasti B,Scheunders P,Ghamisi P,et al.Noise Reduction in Hyperspectral Imagery:Overview and Application[J].Remote Sensing,2018,10(3):482.

[3]Dabov,K.,A.Foi,V.Katkovnik,and K.Egiazarian,Image denoising by sparse 3-D transform-domain collaborative filtering.Ieee Transactions on Image Processing,2007.16(8):pp.2080-2095.

[4]K.Dabov,A.Foi,and K.Egiazarian,"Video denoising by sparse 3D transform-domain collaborative filtering,"European Signal Processing Conference(EUSIPCO-2007),September 2007.

[5]J.Wright,A.Ganesh,S.Rao,Y.Peng,and Y.Ma,“Robust principal component analysis:Exact recovery of corrupted low-rank matrices via convex optimization,”in Proc.NIPS,2009,pp.2080–2088.

[6]Zhang,H.Y.,W.He,L.P.Zhang,H.F.Shen,and Q.Q.Yuan,Hyperspectral Image Restoration Using Low-Rank Matrix Recovery.Ieee Transactions on Geoscience and Remote Sensing,2014.52(8):pp.4729-4743.

[7]T.Zhou and D.Tao,“Godec:Randomized low-rank&sparse matrix decomposition in noisy case,”in Proc.28th ICML,2011,pp.33–40.

[8]Liu,X.F.,S.Bourennane,and C.Fossati,Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis.Ieee Transactions on Geoscience and Remote Sensing,2012.50(10):pp.3717-3724.

[9]Wang,M.D.,J.Yu,J.H.Xue,and W.D.Sun,Denoising of Hyperspectral Images Using Group Low-Rank Representation.Ieee Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2016.9(9):pp.4420-4427.

[10]He,W.,H.Y.Zhang,L.P.Zhang,and H.F.Shen,Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration.Ieee Transactions on Geoscience and Remote Sensing,2016.54(1):pp.176-188.

[11]Zhao,Y.Q.and J.X.Yang,Hyperspectral Image Denoising via Sparse Representation and Low-Rank Constraint.Ieee Transactions on Geoscience and Remote Sensing,2015.53(1):pp.296-308.

[12]Xue,J.Z.,Y.Q.Zhao,W.Z.Liao,and S.G.Kong,Joint Spatial and Spectral Low-Rank Regularization for Hyperspectral Image Denoising.Ieee Transactions on Geoscience and Remote Sensing,2018.56(4):pp.1940-1958.

[13]Renard,N.,S.Bourennane,and J.Blanc-Talon,Denoising and dimensionality reduction using multilinear tools for hyperspectral images.Ieee Geoscience and Remote Sensing Letters,2008.5(2):pp.138-142.

[14]Fan,H.Y.,Y.J.Chen,Y.L.Guo,H.Y.Zhang,and G.Y.Kuang,Hyperspectral Image Restoration Using Low-Rank Tensor Recovery.Ieee Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2017.10(10):pp.4589-4604.

Disclosure of Invention

The invention provides a hyperspectral image denoising method which is used for improving and optimizing a hyperspectral image denoising effect for remote sensing image processing.

One embodiment of the present invention is a hyperspectral image denoising method, including:

establishing a low-rank matrix recovery model based on the ground feature category according to local space low-rank prior, spectrum low-rank prior and global spectrum low-rank prior in hyperspectral image data;

blocking the hyperspectral images according to different ground object categories;

removing noise in the local blocks of the hyperspectral image;

and removing noise in the whole hyperspectral image space data and the whole spectral data again.

In the embodiment of the invention, a mixed noise denoising method more conforming to actual HSI is realized by utilizing high correlation between spectral bands and based on a ground feature type and a low-rank prior HSI denoising algorithm, wherein for a real noisy hyperspectral image, a real image polluted by noise in a data set is adopted, and the mixed noise mainly comprises random noise, sparse noise and some unknown noise. In the verification experiment, the noise is added according to the mixed noise.

Drawings

The above and other objects, features and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description read in conjunction with the accompanying drawings. Several embodiments of the present invention are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which:

fig. 1 is a schematic diagram of an HSI denoising process according to one embodiment of the present invention.

Fig. 2 is a schematic diagram of HSI low rank characteristics according to one embodiment of the invention.

Detailed Description

The most significant difference between the so-called hyperspectral image and the normal image is spectral information, and it has been found that spectral bands that are highly correlated in the hyperspectral image HSI are very useful for improving the denoising of HSI. According to one or more embodiments, the hyperspectral image denoising method combining the ground object class and the low-rank characteristic comprises the steps of data preprocessing, co-object space spectrum low-rank and denoising calculation. And selecting blocks according to different ground object types, wherein each type represents a local block, which means that the local information selected under the whole hyperspectral homogeneous type is converted into a two-dimensional matrix. After blocking, the two-dimensional matrix is separated by space and spectrum by denoising.

First, data preprocessing is performed, which specifically includes the following steps:

firstly, washington DC Mall data is adopted as simulation data, and then the actual noise-polluted Indian Pines real data set is adopted for comparison and verification. The simulated Washington DC Mall image data experiment and the actual noise-polluted Indian image data processing refer to two different processing processes, wherein the two different processing processes are respectively denoised, and the results are compared with other related methods such as LRMR and the like. Where the former consists of 1208 × 307 pixels and 210 bands, each band corresponding to a 0.4 to 2.4 micron region of the visible and infrared spectrum, the bands in the 0.9 and 1.4 micron regions where the atmosphere is opaque are omitted from the data set, leaving 191 bands, the hyperspectral image being a three-dimensional cube map made of red, green and blue of 60, 27 and 17 bands respectively. Since Washington DC Mall images are too large, there are limitations to computer storage and cropping is required. And carrying out normalization operation on the intercepted Washington DC Mall image and the intercepted real image Indian Pines by using matlab, carrying out denoising by using a denoising algorithm, and restoring the obtained result data. Before denoising, the simulation experiment data is mostly cut, and then normalization is carried out. The actual noise-polluted Indian image experiment only needs to be normalized before denoising. Both data need inverse operation after denoising-inverse normalization. Then different local blocks are selected according to different ground object categories, the low rank of the co-object space spectrum is generated, and denoising is carried out in each local block.

And (3) analyzing and proposing a low-rank attribute between the cube and the local cube under the label by referring to a singular value decomposition technology under the condition of selecting the same patch block size in the HSI image. The comparison modes of the selection blocks are respectively selected according to the pixels of the same type and the pixels of continuous space. In this case, the low rank property is stronger.

The clipped Washington DC Mall data size was 256 × 256 × 191, and the blocking manner was selected by consecutive spatial pixels using LRMR (Low-Rank Matrix Recovery) method. Such as the upper half of fig. 1, and the combined feature type block is shown in the lower half of fig. 2. The local block size of LRMR which obtains the optimal solution according to repeated experiments is 20 multiplied by 191, and in the combined ground object type block, according to the same type of pixel selection mode, when the selected pixel number is less than 191 wave bands, the correlation between matrix rows and columns is stronger than that of the LRMR optimal local block, namely, the low rank is stronger. When the number of pixels is substantially equal to 20 × 20=400, the low rank characteristics of the two modes are shown in fig. 2:

the consistency of the inter-homologies and local block correlations at the same magnitude is indicated by the steep decay trend of the curves in fig. 2. Wherein, in FIG. 2, the cumulative energy ratios of the first k singular values define [12] in the reference background]，

σ _i Representing the ith singular value. In the graph, the first 10 singular values in fig. 2 (a) reach a ratio of 0.9522, the first 56 singular values reach a ratio of 0.9903, the first 12 singular values in fig. 2 (b) reach a ratio of 0.9520, and the first 63 singular values reach a ratio of 0.9902. These values show that, when the partitions are approximately the same size, the proposed local block correlation and the homomorphic local block correlation have consistency, and both have almost the same strong correlation, which is defined as a low rank homomorphic spatial spectrum.

Finally, as for the algorithm of denoising calculation, an LRMR model based on ground object categories and low-rank prior is adopted. Assume that the original HSI image cube is

Where w × h represents the number of rows and columns in the spatial dimension of the image, and b represents the spectral dimension of the image. Converting into the linear gradient magnetic resonance (LRMR) model by using global spectral correlation according to a low-order matrix conversion formula in the LRMR model

Where k = w × h, each column is composed of one band image data. One of the subcubes B is selected, and the size of the subcubes B is m multiplied by n multiplied by B, wherein m multiplied by n is space information in the subcubes, and B represents all wave band numbers of HSI.

Assuming that the HSI is contaminated by signal independent and sparse mixed noise, the LRMR degradation model in the form of a two-dimensional matrix is:

D＝U+S+N (1)

wherein

Which represents the original HSI, is shown,

representing noise having a sparse characteristic and representing noise,

representing signal density noise.

According to the feature type information of the HSI, assuming that there are L in total in the image, expressed as Σ = i =1,2,l, L. When all pixels with class index i are selected to form a cube B: ( ⁱ⁾ When using spatial correlation between patch pixels within an image block, i.e. forming a matrix

|B ⁽ⁱ⁾ And | represents all the pixel numbers of the class symbol i in the preceding and following rows. Since the spectral curves in a certain category have stronger consistency, the spectral correlation among pixels in an image block can be utilized, namely, the matrix is formed

LRMR model representation based on terrain category:

in the above formula, | · the luminance | | _* Representing a kernel norm matrix, i.e. the sum of matrix singular values; i | · | purple wind ₁ Represents a 1 norm matrix, i.e. the sum of the absolute values of the matrix; λ is a regularization parameter used to balance the relative contribution between the kernel-norm and the 1-norm. Candelas, and the like. [14]The probability of recovering the low-rank matrix L and the sparse matrix S is proved to be very high when the rank of the matrix L and the sparsity and distribution of the matrix S meet certain conditions.

The equality constraint optimization problem for equation (2):

for each subcube B ⁽ⁱ⁾ Constructive augmented lagrange function:

solving equation (8), firstly, solving calculation A ⁽ⁱ⁾ Then solve for E ⁽ⁱ⁾ ，

A ⁽ⁱ⁾ _k+1 ＝argminL(A ⁽ⁱ⁾ ,E ⁽ⁱ⁾ _k ,Λ _k ⁽ⁱ⁾ ,μ _k ) (5)

E ⁽ⁱ⁾ _k+1 ＝argminL(A ⁽ⁱ⁾ _k+1 ,E ⁽ⁱ⁾ ,Λ _k ⁽ⁱ⁾ ,μ _k ) (6)

Λ ⁽ⁱ⁾ _k+1 ＝Λ ⁽ⁱ⁾ _k +μ(B ⁽ⁱ⁾ -A ⁽ⁱ⁾ _k+1 -E ⁽ⁱ⁾ _k+1 ) (7)

The above (5) and (6) have closed type solutions, and an IALM algorithm is adopted, namely

Wherein (U, S, V) = svd (W), W = B ⁽ⁱ⁾ _k -E ⁽ⁱ⁾ _k +μ ^-1 Λ ⁽ⁱ⁾ _k U and V represent left and right singular value matrices, respectively, and S represents a singular value diagonal matrix.

Representing the soft threshold (shrink) operator and epsilon represents the associated parameter.

According to one or more embodiments, the HIS denoising method combining the ground feature category and the low rank prior comprises the following specific steps:

regarding the value of the parameter λ, the optimal parameter λ = 1/(max (mn, b)) ^1/2 ；

When exploiting spectral correlation in a matrix, the parameters use default parameters in the function

Where mn represents the total number of pixels within a certain image block.

Inputting:

and (3) outputting: a. The ^w×h×b

Initialization: λ = 1/(max (mn, b)) ^1/2 Or

(1) Pair of hyperspectral images by means of label information

Blocking, generating block B = { B = { (B) } ⁽¹⁾ ,B ⁽²⁾ ,L,B ^(L) }

(2) In each block B ⁽ⁱ⁾ In the construction matrix

p＝|B ⁽ⁱ⁾ | represents all the pixels of the class labeled i

(3) Using IALM algorithm, from the original matrix D ⁽ⁱ⁾ In sequence, recover the signal matrix A ₁ ⁽ⁱ⁾

(1) When p < min (w, h). Times.2, { A } is used ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ⁽ⁱ⁾ )

(2) When in use

Using { A ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ^(i)′ )

(3) Taking spatial low rank as a main point, adopting (1); mainly based on the low rank of the spectrum, then (2)

(4) Reverting to low rank part according to original position of label

(5) Will be a low rank part ^w×h×b Conversion to D ∈ A ^k×b Restoring the signal matrix A again ₂ ^k×b

(6) Obtaining A after noise reduction ^w×h×b Data of

Aiming at the denoising problem of hyperspectral remote sensing data, the spatial low-rank prior and the spectral low-rank prior in local and the spectral low-rank prior in global in the data are analyzed. On the basis of the prior knowledge, ground object type information is introduced to the hyperspectral image denoising problem, a low-rank matrix recovery model is built based on the ground object types, and hyperspectral image blocking is carried out on different ground object types. Firstly, removing mixed noise in a local block; and then the mixed noise is removed again in the global spectral block.

The method of the embodiment of the invention can obviously remove the sparse noise and also can effectively remove the high-density noise. Meanwhile, the proposed algorithm model not only has better effect of removing mixed noise, but also takes less time. According to the embodiment of the invention, through enhancing the low-rank characteristic, the similar space spectrum low-rank is explored, and the original data is better estimated from the original observed data; the method based on the low-rank recovery model is solved by using an IALM algorithm, and the size of a local patch block is not required to be repeatedly confirmed through experiments; the algorithm computation time is less time-consuming compared to classical LRMR and nairma methods.

According to the denoising method provided by the embodiment of the invention, experiments are carried out and compared with different types of denoising/Recovery methods to prove the superiority of the denoising/Recovery methods, wherein the denoising/Recovery methods are a relatively classical hyperspectral image denoising/Recovery method based on Low Rank characteristics, namely an LRMR (Low-Rank Matrix Recovery) method and a Noise correction iteration Low-order Matrix Approximation NAILRMA (Noise-Adjusted Iterative Low-Rank Matrix application). Evaluation indexes after denoising are compared as follows.

In the noise condition 1, on the data set of the selection experiment, different noises from 0 to 0.1 of random Gaussian variance are added to each wave band, and some wave bands are selected to be added with impulse noise. The currently selected band 20 through band 25, and the 9 total selected bands 140 through 142 add an impulse noise variance of 0.15. The final input SNR is 6.4483dB and the input MPSNR is 14.2516dB.

Noise condition 2, gaussian variance 0-0.1, the added mean value of 1-2, 20-21, 50-51, 73-74, 120-121, 142-143 and 188-189 wave bands selected from the hyperspectral spectrum wave bands is 0, variance 0-0.1 Gaussian variance (the random variance corresponding to the wave bands is the same as that of noise condition 1), the final input SNR is 15.6367dB, and the input MPSNR is 1.3644dB.

Noise case 3, gaussian noise with 0-0.2 random variance added per band, 17 bands (20, 21,22,23,24,25,26,27,28,29,30,70,71,73,140,141, 142) were selected to add impulse noise with a density of 0.2. The input SNR was 12.7994dB. The input SNR for the individual pulses was 15.3862dB. The average SNR of the gaussian alone is 3.3992dB. The final input SNR was 12.7994dB and the input MPSNR was 0.7990dB.

For the denoising results of the simulated noise under the three conditions, under the noise condition 1, the denoising effect of the embodiment of the invention is not obviously improved, but indexes of the MSSIM and the MFSIM are respectively improved by 0.04 and 0.02 to the maximum. However, in the noise case 2 and the noise case 3, the denoising effect of the embodiment of the invention is better. Particularly, when mixed noise pollution is more serious, MPSNR is respectively improved by more than 4dB, and indexes of MSSIM and MFSIM are respectively improved by 0.03 and 0.02.

In the gray scale image processing display of each wave band of the original Indian Pines image, 1,2, 3, 61, 75, 76, 103, 104, 105, 106, 107, 144, 145, 146, 198, 199 and 200 wave bands with mixed noise can be found, and the total of 17 wave bands are accumulated. The effect of the 17 wave bands in the de-noising data result is improved to a certain extent.

Embodiments of the present invention, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention essentially or partially contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk, and various media capable of storing program codes.

While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. A hyperspectral image denoising method is characterized by comprising the following steps:

establishing a low-rank matrix recovery model based on ground object categories according to local space low-rank prior, spectrum low-rank prior and global spectrum low-rank prior in hyperspectral image data;

partitioning the hyperspectral images according to different ground object categories;

removing noise in local blocks of the hyperspectral image;

removing noise in the whole hyperspectral image space data and the whole hyperspectral image spectral data again;

the denoising method further comprises the following steps:

initialization λ = 1/(max (mn, b)) ^1/2 Or

Pair of hyperspectral images by means of tag information

Blocking, generating block B = { B = { (B) } ⁽¹⁾ ,B ⁽²⁾ ,L,B ^(L) }；

In each block B ⁽ⁱ⁾ In, construct the matrix

p＝|B ⁽ⁱ⁾ L represents all the pixel numbers with the class label i;

using IALM algorithm, from the original matrix D ⁽ⁱ⁾ In-sequence recovery of the signal matrix a ₁ ⁽ⁱ⁾ The following are also provided:

(1) when p < min (w, h). Times.2, { A ] is used ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ⁽ⁱ⁾ )

(2) When in use

Using { A ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ^(i)′ )

(3) Taking spatial low rank as a main mode, (1) and taking spectral low rank as a main mode, (2);

reverting to low rank part according to original position of label

Will be a low rank part ^w×h×b Conversion to D ∈ A ^k×b Restoring the signal matrix A again ₂ ^k×b ；

Obtaining A after noise reduction ^w×h×b The data of the data is transmitted to the data receiver,

wherein, w x h represents the number of rows and columns of the image space dimension, b represents the spectral dimension of the image,

converting into the linear gradient magnetic resonance (LRMR) model by using global spectral correlation according to a low-order matrix conversion formula in the LRMR model

Where k = w × h, each column is composed of one band image data, where one subcube B is selected, and the size is m × n × B, where m × n is spatial information in the subcube.

2. A hyperspectral image denoising apparatus, characterized in that the apparatus comprises a memory; and

a processor coupled to the memory, the processor configured to execute instructions stored in the memory, the processor to:

initialization λ = 1/(max (mn, b)) ^1/2 Or

Pair of hyperspectral images by means of tag information

Blocking, generating block B = { B = { (B) } ⁽¹⁾ ,B ⁽²⁾ ,L,B ^(L) }；

In each block B ⁽ⁱ⁾ In, construct the matrix

p＝|B ⁽ⁱ⁾ L represents all the pixel numbers with the class label i;

using IALM algorithm, from the original matrix D ⁽ⁱ⁾ In-sequence recovery of the signal matrix a ₁ ⁽ⁱ⁾ The following are also provided:

(1) when p < min (w, h). Times.2, { A ] is used ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ⁽ⁱ⁾ )

(2) When in use

Using { A ₁ ⁽ⁱ⁾ ,E ₁ ⁽ⁱ⁾ }＝IALM(D ^(i)′ )

(3) Taking spatial low rank as a main mode, (1) and taking spectral low rank as a main mode, (2);

reverting to low rank part according to original position of label

Low rank fraction A ^w×h×b Conversion to D ∈ A ^k×b Restoring the signal matrix A again ₂ ^k×b ；

Obtaining A after noise reduction ^w×h×b The data of the data is transmitted to the server,

wherein, w x h represents the number of rows and columns of the image space dimension, b represents the spectral dimension of the image,

converting into the linear gradient magnetic resonance (LRMR) model by using global spectral correlation according to a low-order matrix conversion formula in the LRMR model

Where k = w × h, each column is composed of one band image data, where one subcube B is selected, and the size is m × n × B, where m × n is spatial information in the subcube.

Images