CN111369457B - Remote sensing image denoising method for sparse discrimination tensor robustness PCA - Google Patents
Remote sensing image denoising method for sparse discrimination tensor robustness PCA Download PDFInfo
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Abstract
The invention discloses a remote sensing image denoising method of sparse discrimination tensor robustness PCA, aiming at providing a denoising method capable of more effectively removing noise in a hyperspectral image, and the method is realized by the following technical scheme: carrying out image segmentation on an input hyperspectral remote sensing image, and segmenting the hyperspectral remote sensing image into non-overlapping tensor data blocks according to a fixed size; and (3) respectively carrying out sparse judgment tensor robustness principal component analysis on each tensor data block: decomposing a tensor data block into a low-rank component, a sparse discriminant component and a sparse noise component, constructing a sparse discriminant tensor robustness principal component analysis model, and iteratively solving the model to obtain a denoised tensor data block to obtain a denoised image; and dividing the reconstructed and denoised noiseless data into a training set and a testing set according to a proportion, finally inputting the training set and the testing set into a classifier, and outputting the class marks of all the testing samples through the classifier to realize the evaluation of the denoising effect of the hyperspectral remote sensing image.
Description
Technical Field
The invention relates to the field of image processing, in particular to a hyperspectral remote sensing image denoising method based on sparse discrimination tensor robustness Principal Component Analysis (PCA) in the technical field of remote sensing image processing.
Background
In the modern highly information-oriented society, graphics and images play an increasingly greater role in information dissemination, and images are an important information source and can help people to know the content of information through image processing. However, the image is often degraded by interference and influence of various noises during the generation and transmission processes, which will adversely affect the processing (such as segmentation, compression, image understanding, etc.) of the subsequent images. The noise is of many kinds, such as: electrical noise, mechanical noise, channel noise, and other noise. Generally, the energy of an image is mainly concentrated in a low frequency, and the detailed part of the image is concentrated in a high frequency region. Since noise is often generated during access, digitization, and transmission of images, and the interference information is mainly concentrated in a high frequency region, a common method for eliminating noise is to attenuate high frequency components by using low pass filtering. However, the negative influence caused by the negative influence also attenuates the details of the image to a certain extent, and the image is blurred in visual effect compared with the image before processing. How to acquire more effective and reliable information from the hyperspectral images polluted by noise is an important problem to be solved urgently. In order to suppress noise, improve image quality, and facilitate higher-level processing, it is necessary to perform denoising preprocessing on an image. The task of removing image noise is called image filtering or smoothing. Digital image noise removal relates to the fields of optical systems, microelectronic technology, computer science, mathematical analysis and the like, and is edge science with strong comprehensiveness. In theory, the noise can be defined as "unpredictable random error which can only be recognized by a probability statistical method", so that the image noise is regarded as a multi-dimensional random process, and the method for describing the noise can borrow the description of the random process, namely, the probability distribution function and the probability density distribution function of the random process. In many cases, however, such a description is complicated or even impossible. In practical applications, its numerical characteristics, i.e., mean variance, correlation function, etc., are commonly used. Since these numerical characteristics may all reflect the characteristics of the noise in some way. The effect of noise on the amplitude and phase of the image signal is complex, some noises and image signals are independent and uncorrelated, some noises are correlated, and the noises themselves may also be correlated. The remote sensing image is often influenced by a lot of noises in the processes of imaging, obtaining and transmitting, wherein the most common noises are gaussian noise, cloud noise, fog noise and the like. Noise in the remote sensing image has randomness and uncertainty, and the existence of the noise can reduce the quality of the image, inhibit useful information, influence the accuracy of the information, and even cause wrong judgment. The blurring of the details such as the edge texture of the image brings certain difficulties to the identification and analysis of the remote sensing image. In order to obtain clear and high-quality remote sensing images, noise reduction pretreatment is required. The remote sensing image denoising aims at removing noise to the maximum extent and improving the readability and effectiveness of data on the premise of protecting image detail information. The essence of the remote sensing image denoising method is to keep balance in removing noise and maintaining image details. The hyperspectral image is three-dimensional data consisting of two-dimensional spatial information and one-dimensional spectral information, and is considered as a 3D tensor which corresponds to the expression form of a third-order tensor. Generally, the size of the original hyperspectral image is large, and tensor operation is not suitable for being directly performed. The quality of the hyperspectral image is influenced by various complex factors, and a large amount of noise, such as thermal noise, photon noise and the like, is introduced in the acquisition and transmission processes of the hyperspectral image. The noises not only affect the visual effect of the image, but also affect the subsequent processing and application (such as hyperspectral image feature extraction, classification, mixed pixel decomposition, target detection and the like).
In recent years, hyperspectral satellite remote sensing data with different spatial resolutions can be acquired more and more. However, the hyperspectral image is difficult to avoid being polluted by noise during the acquisition and propagation process. In order to obtain a high-quality remote sensing image, the degraded image needs to be restored to improve the quality of the remote sensing image. Most of the existing image restoration algorithms are established on the premise that the point spread function of the blurred image and the image noise are known. However, in the actual imaging process, the degradation factor of the remote sensing image is complex, and the image fuzzy kernel function and the noise distribution of the remote sensing image cannot be accurately known.
The hyperspectral image contains hundreds of wave bands and has abundant spectral information, and in addition, the hyperspectral image is composed of two space dimensions and one spectral dimension, so the hyperspectral image has good spatial structure information. That is, there is a high probability that the spatial neighborhood pixels of a pixel are homologous and represent the same feature. Chen et al assume that the test pixel and its neighborhood pixels have the same sparse structure, and propose a joint sparse representation classification algorithm. The influence of noise can also be suppressed to some extent by utilizing the similarity of the neighborhood pixels. And Y.J.Deng et al propose a tensor local preserving projection method, and utilize neighborhood pixel blocks to assist in improving the separability of the low-dimensional features of the central pixels, so that a better effect is achieved. Camps-Valls et al propose a combined kernel support vector machine classification algorithm, which fully utilizes the spatial characteristics of the hyperspectral data by constructing a spectrum kernel and a space-spectrum kernel, and regards the hyperspectral data as a third-order tensor. However, the above methods all consider the spatial neighborhood information from the perspective of a single task (classification, feature extraction, etc.) in a targeted manner, thereby reducing the influence of noise on performance. From the viewpoint of wide application, this approach has certain limitations; from the viewpoint of processing noise, this method merely suppresses the negative influence of noise and does not eliminate the noise. Another method for processing noise in hyperspectral data is a denoising algorithm, and a hyperspectral image denoising technology is also a research hotspot in the technical field of remote sensing image processing. H.Y.Zhang et al propose a hyperspectral image restoration algorithm based on low-rank matrix recovery, and can remove various noises such as Gaussian noise, impulse noise, stripe noise and the like. In order to utilize the spatial structure information of the hyperspectral data, a variational regularized low rank matrix decomposition algorithm is subsequently proposed. Similarly, with the purpose of effective utilization of spectral information and spatial information, j.z.xue et al propose a space-spectrum joint low-rank regularization denoising algorithm, taking into account the low-rank characteristic of a spectral domain and the non-local low-rank characteristic of a spatial domain. In the field of image denoising, the most classical method, namely robust principal component analysis, also exists, a robust principal component analysis model is constructed by decomposing original data into a low-rank component and a sparse noise component, and the low-rank component obtained after model solution is used as noise-free data. Based on a robust principal component analysis model, the S.H.Mei et al designs a spectral domain denoising method and a spatial domain denoising method, and estimates the denoising effect from the perspective of classification performance. On one hand, however, the robust principal component analysis model can only process two-dimensional data, and the three-dimensional hyperspectral data can only be converted into a matrix form for processing, so that the subspace structure of the original data is lost; on the other hand, the robustness principal component analysis model decomposes the original data into a low-rank component and a sparse noise component, ignores the inherent judgment information of each subspace, and reduces the separability of the denoised data. The useful information part and the noise in the image are overlapped on the frequency band, which is the root cause of the defects of the traditional denoising method based on the frequency characteristic difference of the useful information and the noise.
Due to the complexity of noise intensity distribution of each wave band of the hyperspectral image, the traditional characteristic dimension reduction denoising method cannot meet the denoising requirement of hyperspectral remote sensing data. The traditional hyperspectral remote sensing image denoising method can be basically divided into two categories: 1) noise removal is performed in the spatial or frequency domain. For example, a spectrum-space domain adaptive total variation denoising model proposed by Yuan and the like, and Rasti and the like propose a hyperspectral image denoising method based on sparse rank reduction regression wavelet, and the method fully considers two-dimensional space information of hyperspectral data, but fails to fully utilize the spectrum information among all bands of the hyperspectral data. 2) And denoising by using a characteristic dimension reduction method. For example, Stephan and the like perform denoising processing on a hyperspectral image by using Principal Component Analysis (PCA), Green and the like put forward a Minimum Noise separation (MNF) theory, the method fully considers the correlation among various bands of the hyperspectral image, but the denoising effect is not ideal due to the lack of consideration on the details (namely two-dimensional space information) of a single image. The method combines a multi-scale geometric transformation technology to be applied to hyperspectral image denoising on the basis of PCA, but a dictionary obtained when the multi-scale geometric transformation is applied to sparse representation of an image has a specific analytical formula, and the method can be implicitly and quickly realized; however, the corresponding sparse dictionary structure is fixed, and the attribute of the image is not fully considered, so that the self-adaptability of the image is limited when the hyperspectral remote sensing image with special image content is denoised.
At present, sparse representation is widely applied to the field of image denoising, and how to construct a proper dictionary is an important link for sparse representation. Dictionary construction methods can be mainly divided into two main categories: one is a fixed dictionary construction method, such as Discrete Cosine Transform (DCT) dictionary, wavelet dictionary, etc., which are commonly used. The method has the disadvantage that the effect difference is large when the same sparse base is used for carrying out sparse representation on the image with large difference of detail characteristics. The second method is to design an adaptive redundant dictionary. The method makes up the defects of the first method, and can adaptively select sparse bases according to the characteristics of the images, thereby realizing accurate sparse approximation of various images. Among them, the K-Singular Value Decomposition (K-SVD) algorithm proposed by Aharon et al is the most representative and widely applied adaptive dictionary learning algorithm at present. Based on the K-SVD algorithm, Elad et al also propose a denoising model for denoising images by using the K-SVD algorithm. The use of this algorithm has the premise that the noise intensity of the image is known. The traditional PCA denoising method is to select a plurality of larger principal component components for PCA transformation denoising, and because the image characteristics of a noise-containing image group generated by PCA transformation are complex, a fixed sparse basis is difficult to accurately carry out sparse representation on the image, more detail information of the image is lost, and the image distortion in the denoising process is serious, so that the detail information of the fused image is lost. In practical application, the noise intensity of an unknown image needs to be estimated first, and then the denoising operation can be continued. Compared with the PCA method, the edge information of the image denoised by the PCA-Bish and PCA-Contourlet methods is well reserved, but the detail information of the image, especially the loss in the contrast aspect is serious, which is mainly caused by that the detail information of the fused image is lost due to the fact that a fixed sparse basis is used during denoising by the Bish wavelet threshold shrinking method and the Contourlet method.
At present, various methods are provided for the hyperspectral image denoising problem. These methods are mainly classified into 3 types: band-by-band processing, a joint spectral-spatial domain transform method, and a tensor-based decomposition method.
The band-by-band processing method respectively processes the two-dimensional images of each band of the hyperspectral image, but the method ignores the spectral correlation. The BwK-SVD method by bands does not consider the noise intensity of each band and the difference of different pixel spatial information, the denoised image is over smooth, and partial noise still exists in the smooth area.
The method combines a spectrum-space domain transformation method to carry out specific transformation on the space domain and the spectrum domain of the hyperspectral image so as to carry out denoising. The method mainly comprises a mixed space-spectrum wavelet shrinkage denoising (HSSNR) method, a hyperspectral image denoising method by using a wavelet shrinkage and PCA method and a spectrum-space self-adaptive total variation (SSAHTV) model, a hyperspectral image denoising method by non-local spectrum-space structure sparse representation and the like. Although the method can effectively denoise the hyperspectral image, the operation time is long.
Based on a tensor decomposition method, after TUCKER3 decomposition is carried out on hyperspectral data, wiener filtering is carried out to realize denoising. For example, a Low Rank Tensor Approximation (LRTA) method is characterized in that a hyperspectral image low rank approximation is obtained through a Tucker decomposition for denoising, but artifacts are generated in a reconstruction process. Although the relevance of each wave band of the hyperspectral image is considered by taking the whole hyperspectral image as a tensor based on the tensor method, the non-local similarity of the spatial information of the hyperspectral image is ignored, the image structure information is not reflected, partial detail information is lost, and the denoising result is smooth.
Disclosure of Invention
The invention aims to provide a denoising method capable of effectively removing noise in a hyperspectral image, in particular to a sparse discrimination tensor robustness PCA denoising method suitable for a hyperspectral remote sensing image, aiming at the defects that the noise distribution of each wave band image of the hyperspectral image is complex and the traditional denoising method is difficult to achieve an ideal effect.
The object of the invention can be achieved by the following measures, and the remote sensing image denoising method of sparse discrimination tensor robustness PCA is characterized by comprising the following steps: carrying out image segmentation on an input hyperspectral remote sensing image, and segmenting the hyperspectral remote sensing image into non-overlapping tensor data blocks according to a fixed size; and (3) respectively carrying out sparse judgment tensor robustness principal component analysis on each tensor data block: decomposing tensor data blocks into low-rank components, sparse discriminant components and sparse noise components, performing component decomposition on the cut tensor data blocks one by one, constructing a sparse discriminant tensor robustness principal component analysis model according to a component matrix formed by the tensor data blocks, iteratively solving the model to obtain denoised tensor data blocks, reconstructing combined image blocks, and performing sparse discriminant tensor robustness principal component analysis denoising on each tensor data block to obtain a denoised image; and dividing the reconstructed and denoised noiseless data into a training set and a testing set according to a proportion, finally inputting the training set and the testing set into a classifier, and outputting the class marks of all testing samples through the classifier to realize the evaluation of the denoising effect of the hyperspectral remote sensing image.
The effective gain of the invention is that:
(1) according to the method, by utilizing the spatial structure information with good hyperspectral data, mining the spatial structure information of each data block in a tensor expression mode, fixing the size, and segmenting a hyperspectral remote sensing image into non-overlapping tensor data blocks; and (3) respectively carrying out sparse judgment tensor robustness principal component analysis on each tensor data block: the intrinsic structure of the data can be well characterized, and powerful support is provided for removing noise in the data.
(2) According to the method, the original hyperspectral data are decomposed into a low-rank component, a sparse discriminant component and a sparse noise component, and discriminant information of each subspace is effectively reserved. Compared with a two-component decomposition mode of a low-rank component and a sparse noise component of the robust principal component analysis model, the three-component data decomposition mode of the low-rank component, the sparse discriminant component and the sparse noise component is adopted, so that valuable information in original hyperspectral data is kept as much as possible, useful information can be better separated from noise, and the data quality of the denoised hyperspectral image is obviously improved.
(3) According to the method, through tensor expression, the intrinsic structure of data is mined by utilizing spatial neighborhood information, and then a three-component data decomposition mode is utilized, so that useful information formed by low-rank components and sparse discrimination components in original data is reserved, interference information of sparse noise components is removed, and the discrimination capability of the data is enhanced. The experimental result of the invention on the basis of disclosing the hyperspectral data set shows that the performance of the method is superior to that of other image denoising algorithms, such as a classical robust principal component analysis method, a spatial-spectral joint representation method and the like.
Since the core of the present invention is the multiple decomposition of data components and the efficient use of spatial neighborhood information, the present invention is effective as far as image noise removal and image restoration are concerned. The hyperspectral image is composed of pixels representing different surface feature types and noise, the pixels of the same surface feature type show low-rank characteristics, the noise shows sparse characteristics, the pixels of different types have respective discrimination information, the sparse characteristics shown by the discrimination information are used for decomposing data into low-rank components, sparse discrimination components and sparse noise components, a sparse discrimination tensor robustness principal component analysis model is constructed, valuable components of the data can be more accurately reserved, and interference components such as the noise are removed. The sparse judgment tensor robustness PCA model fully excavates intrinsic structure information of data in a tensor expression mode, and reconstructs the data in a blocking mode through a combined image to obtain a de-noised image; and dividing the reconstructed and denoised noiseless data into a training set and a testing set according to a proportion, finally inputting the training set and the testing set into a classifier, and outputting the class marks of all the testing samples through the classifier to realize the evaluation of the denoising effect of the hyperspectral remote sensing image. The result shows that the method has positive effect, and the denoising effect is superior to that of the classical robust principal component analysis and the extension method thereof from the perspective of classification performance evaluation.
The sparse discrimination tensor robustness PCA model established by the invention is suitable for hyperspectral remote sensing images and can be popularized and applied to general image denoising.
Drawings
FIG. 1 is a flowchart of a sparse discriminant tensor robustness principal component analysis based denoising method of the present invention.
Fig. 2 is a flow chart of a solution of the sparse discriminative tensor robust principal component analysis model of fig. 1.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Detailed Description
See fig. 1. According to the method, the input hyperspectral remote sensing image is subjected to image segmentation, and the hyperspectral remote sensing image is segmented into non-overlapping tensor data blocks according to a fixed size; and (3) respectively carrying out sparse judgment tensor robustness principal component analysis on each tensor data block: decomposing tensor data blocks into low-rank components, sparse discriminant components and sparse noise components, performing component decomposition on the cut tensor data blocks one by one, constructing a sparse discriminant tensor robustness principal component analysis model according to a component matrix formed by the tensor data blocks, iteratively solving the model to obtain denoised tensor data blocks, reconstructing combined image blocks, and performing sparse discriminant tensor robustness principal component analysis denoising on each tensor data block to obtain a denoised image; and dividing the reconstructed and denoised noiseless data into a training set and a testing set according to a proportion, finally inputting the training set and the testing set into a classifier, and outputting the class marks of all testing samples through the classifier to realize the evaluation of the denoising effect of the hyperspectral remote sensing image.
The method specifically comprises the following steps:
step 1, because the original hyperspectral image is a three-dimensional data matrix with a larger size, directly processing the original data brings higher complexity. Carrying out image segmentation on an input hyperspectral remote sensing image; in this embodiment, the original data is scaled according to a certain scale r × rHSegmenting into non-overlapping sub-tensor data blocksX. Tensor data blockXContaining common information of the same categoryLMay be characterized by low rank characteristics, referred to as low rank components; discrimination information specific to each subspaceSCan be characterized by sparse characteristics, called sparse discriminant components; noise component in dataETypically exhibit sparse characteristics, referred to as sparse noise components.
And 2, carrying out sparse judgment tensor robustness principal component analysis denoising on each tensor data block.
The step 2 is shown in fig. 2, and further comprises the following steps: in sparse discriminant tensor robustness principal component analysis model solution, the common information of the same category pixels in the data is usedLDiscrimination information unique to each class pixelSNoise interferenceEBlock of tensor dataXDecompose as follows:
X＝L+S+E (1)
then decomposing the modulus according to the tensor data block compositionFormula (II)X＝L+S+ESolving each component corresponding to the image block, and for the cut tensor data blockXAnd (3) performing component decomposition one by one, and constructing the following sparse discrimination tensor robustness principal component analysis model according to the composed component matrix:
in the formula, | · the luminance | |*Representing tensor kernel norm, | ·| non-woven phosphor1Is represented by1Norm, β and λ represent regularization parameters, and s.t. represents the constraint of the subject to post-objective function.
In an alternative embodiment, according to an algebraic theory, a Lagrange multiplier is introduced into the sparse discriminant tensor robustness principal component analysis model (2) for solvingDConstructing a Lagrangian function of a sparse discriminant tensor robustness principal component analysis model (2), and then solving the Lagrangian function l by using an alternating direction method to obtain a low-rank componentLSparse discriminant componentSAnd sparse noise componentEAnd updating a Lagrange multiplier and a penalty coefficient mu, and writing a Lagrange function of the following sparse discriminant tensor robustness principal component analysis model (2):
wherein l represents a Lagrangian function, mu represents a penalty factor, and F represents a Frobenius norm.
Optimizing a sparse discriminant tensor robustness principal component analysis model (2) by adopting an alternate iteration strategy, and solving a Lagrangian function (3); in this embodiment, an Alternating Direction Method (ADM) is used to optimally solve the lagrangian function (3), and the lagrangian multiplier is updatedDAnd a penalty factor mu, the core idea is that only the low rank component is updated each time other variables are kept unchangedLSparse discriminant componentSAnd sparse noise componentEAnd (4) alternately and iteratively solving for one variable in the step (a). The updated expression of each variable is as follows:
the updated expression of the Lagrange multiplier is:D (l)＝D (l-1)+μ(l-1)(X-L (l)-S (l)-E (l))，
the updated expression of the penalty factor mu is as follows: mu.s(l)＝min(ρμ(l-1),106)，
Wherein, rho is 1.1,
indicates a threshold value of
The soft threshold operation of (2).
After the alternate iteration is solved, judging whether the iteration termination condition that the change quantity of the iteration variables in the two times is sufficiently small or the maximum iteration times is reached is met, if not, returning to the alternate direction method for optimization solution; if yes, terminating iteration and outputting the denoised noiseless tensor data block (L+S) And then judging whether the denoising operation of all tensor data blocks is finished: otherwise, continuing to execute the tensor data block component decomposition modeX＝L+S+E(1) Solving a sparse discriminant tensor robustness principal component analysis model (2) with alternating iteration; if yes, the circulation is terminated, and the noiseless data corresponding to the original data scale is output
Step 3, evaluating the denoising effect of the sparse discrimination tensor robustness principal component analysis model (2) according to the classification performance, and reconstructing the noiseless data
Divided into training and test sets.
The training set, also called a dictionary, is a data matrix composed of a certain number of data with class labels. Let the training set as
Composed of N samples of dimension D, wherein the ith sample is
Is a one-dimensional vector, and as such, the test set is
The ith test sample is
And test set Y contains samples of M unknown class labels, where,
representing a real space.
And 4, outputting the class marks of all the test samples through the classifier. The classifier may be a nearest neighbor classifier, a support vector machine classifier, a combined kernel support vector machine classifier, or the like. And inputting the training set and the test set into a specified classifier, outputting a class label of the test sample, and comparing the label of the test sample to obtain the classification precision of the classifier so as to evaluate the denoising effect of the proposed denoising model.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A remote sensing image denoising method of sparse discrimination tensor robustness PCA is characterized by comprising the following steps: carrying out image segmentation on an input hyperspectral remote sensing image, and segmenting the hyperspectral remote sensing image into non-overlapping tensor data blocks according to a fixed size; and (3) respectively carrying out sparse judgment tensor robustness principal component analysis on each tensor data block: decomposing tensor data blocks into low-rank components, sparse discriminant components and sparse noise components, performing component decomposition on the cut tensor data blocks one by one, constructing a sparse discriminant tensor robustness principal component analysis model according to a component matrix formed by the tensor data blocks, iteratively solving the model to obtain denoised tensor data blocks, reconstructing combined image blocks, and performing sparse discriminant tensor robustness principal component analysis denoising on each tensor data block to obtain a denoised image; and dividing the reconstructed and denoised noiseless data into a training set and a testing set according to a proportion, finally inputting the training set and the testing set into a classifier, and outputting the class marks of all testing samples through the classifier to realize the evaluation of the denoising effect of the hyperspectral remote sensing image.
2. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 1, wherein: tensor data blockXContaining common information of the same categoryLLow rank component, each subspace having unique discrimination informationSThe sparse characteristic is characterized as a sparse discrimination component, a noise component in the dataEExhibits a sparse characteristic, referred to as a sparse noise component.
3. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 1 or 2, wherein: in sparse discriminant tensor robustness principal component analysis model solution, the common information of the same category pixels in the data is usedLDiscrimination information unique to each class pixelSNoise interferenceENumber of tensorsAccording to blockXDecompose as follows:
X＝L+S+E (1)
then decomposing the model according to the tensor data block compositionX＝L+S+ESolving each component corresponding to the image block, and for the cut tensor data blockXAnd (3) performing component decomposition one by one, and then constructing the following sparse judgment tensor robustness principal component analysis model according to a component matrix composed of tensor data blocks:
wherein | · | charging*Expressing tensor nuclear norm, | · | counting1Represents l1Norm, β and λ represent regularization parameters, and s.t. represents the constraint of the subject to post-objective function.
4. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 3, wherein: according to an algebraic theory, a Lagrange multiplier is introduced into the sparse discriminant tensor robustness principal component analysis model (2)DConstructing a Lagrangian function of the sparse discriminant tensor robustness principal component analysis model (2), and then solving the Lagrangian function by using an alternating direction method
Obtaining a low rank componentLSparse discriminant componentSAnd sparse noise componentEAnd updating a Lagrange multiplier and a penalty coefficient mu, and writing a Lagrange function of the following sparse discriminant tensor robustness principal component analysis model (2):
wherein F represents a Frobenius norm.
5. The method of claim 4The remote sensing image denoising method of sparse discrimination tensor robustness PCA is characterized by comprising the following steps: adopting an alternate iteration strategy to optimize a sparse discrimination tensor robustness principal component analysis model to solve a Lagrangian function; then adopting an alternative direction method ADM to optimize and solve the Lagrange function, and updating the Lagrange multiplierDAnd a penalty factor mu for updating only the low rank component each time keeping the other variables unchangedLSparse discriminant componentSAnd sparse noise componentEAlternately iterating to solve one variable; lagrange multiplierDThe update expression of (1) is:D (l)＝D (l-1)+μ(l-1)(X-L (l)-S (l)-E (l))，
the updated expression of the penalty factor mu is as follows: mu.s(l)＝min(ρμ(l-1),106)，
Wherein, rho is 1.1,
indicates a threshold value of
The soft threshold operation of (2).
6. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 5, wherein: after the alternate iteration is solved, judging whether the iteration termination condition that the change quantity of the iteration variables in the two times is sufficiently small or the maximum iteration times is reached is met, if not, returning to the alternate direction method for optimization solution; if yes, terminating iteration and outputting the denoised noiseless tensor data block (L+S) And then judging whether the denoising operation of all tensor data blocks is finished: otherwise, continuing to execute the tensor data block component decomposition modeX＝L+S+ESolving a sparse judgment tensor robustness principal component analysis model with alternative iteration; if yes, the loop is terminated, and the noise-free data corresponding to the original data scale is output.
7. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 1, wherein: the training set is a dictionary and is a data matrix formed by a certain amount of data with class labels.
8. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 1, wherein: training set
Composed of N samples with dimension D, wherein the ith sample is
Is a one-dimensional vector, and as such, the test set is
The ith test sample is
And test set Y contains samples of M unknown class labels, where,
representing a real space.
9. The method for denoising remote sensing images of sparse discrimination tensor robustness PCA as claimed in claim 1, wherein: the classifier is one of a nearest neighbor classifier, a support vector machine classifier and a combined kernel support vector machine classifier.
10. The method for denoising remote sensing images of sparse discrimination tensor robust PCA as claimed in claim 1, wherein: inputting the training set and the test set into a specified classifier, outputting class labels of the test samples through the classifier, and obtaining the classification precision of the classifier by comparing the labels of the test samples so as to evaluate the denoising effect of the proposed denoising model.
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