CN111951186B - Hyperspectral image denoising method based on low-rank and total variation constraint - Google Patents

Hyperspectral image denoising method based on low-rank and total variation constraint Download PDF

Info

Publication number
CN111951186B
CN111951186B CN202010683866.2A CN202010683866A CN111951186B CN 111951186 B CN111951186 B CN 111951186B CN 202010683866 A CN202010683866 A CN 202010683866A CN 111951186 B CN111951186 B CN 111951186B
Authority
CN
China
Prior art keywords
image
noise
hyperspectral image
rank
image block
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010683866.2A
Other languages
Chinese (zh)
Other versions
CN111951186A (en
Inventor
尹海涛
陈海涛
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Posts and Telecommunications
Original Assignee
Nanjing University of Posts and Telecommunications
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Posts and Telecommunications filed Critical Nanjing University of Posts and Telecommunications
Priority to CN202010683866.2A priority Critical patent/CN111951186B/en
Publication of CN111951186A publication Critical patent/CN111951186A/en
Application granted granted Critical
Publication of CN111951186B publication Critical patent/CN111951186B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10032—Satellite or aerial image; Remote sensing
    • G06T2207/10036—Multispectral image; Hyperspectral image
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20024—Filtering details
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20048—Transform domain processing
    • G06T2207/20056—Discrete and fast Fourier transform, [DFT, FFT]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A40/00—Adaptation technologies in agriculture, forestry, livestock or agroalimentary production
    • Y02A40/10—Adaptation technologies in agriculture, forestry, livestock or agroalimentary production in agriculture

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Image Processing (AREA)

Abstract

The invention discloses a hyperspectral image denoising method based on low-rank and total variation constraints. Relates to the field of image processing; the method comprises the steps of firstly extracting a target 3-D image block of a hyperspectral image containing noise, then searching similar image blocks of the target image block in a given pixel area, and guiding low-rank optimization solution of the similar image blocks by using weighted average of the similar image blocks as prior information of the target image block. In addition, a space-spectrum global total variation global constraint is constructed, and the denoising effect of the hyperspectral image is further improved.

Description

Hyperspectral image denoising method based on low-rank and total variation constraint
Technical Field
The invention relates to the field of image processing, in particular to a hyperspectral image denoising algorithm which is mainly used for solving the problem of noise interference brought in the hyperspectral image acquisition process.
Background
With the development of the hyperspectral sensor technology, the number of the wave bands of a hyperspectral image is increased from tens to hundreds, and the spectral characteristics of an object in an observation area can be described more comprehensively. The hyperspectral camera can provide a continuous range of all electromagnetic radiation spectrums ranging from visible light, near infrared to short wave infrared. Therefore, the hyperspectral image plays an important role in the fields of environmental monitoring, agriculture, forestry, weather forecast and the like. However, the hyperspectral image is often interfered by factors such as environmental weather and technical limitations of equipment in the acquisition process, and the acquired hyperspectral image contains various types of noise, so that the image quality is reduced, and the follow-up practical application is not facilitated. The hyperspectral image denoising is an image processing technology which can effectively inhibit noise and improve image quality, and is beneficial to the practical application of hyperspectral images.
The hyperspectral image denoising is always a research hotspot in the field of remote sensing image processing and application, and the traditional denoising algorithm comprises the following steps: wavelet transform algorithm, non-local mean algorithm, principal component analysis algorithm, total variation optimization algorithm and the like. The traditional algorithms mainly aim at the problem of denoising two-dimensional images, neglect the relevance between spectrums when processing hyperspectral images, and cannot well keep rich spectrum information. In recent years, sparse and low-rank models are also widely applied to hyperspectral image denoising. The sparse and low-rank prior information can effectively separate the self structural information and noise of the image, and the denoising performance is superior to that of the traditional denoising algorithm. In order to further improve the representation capability of the three-dimensional space structure of the hyperspectral image, tensor sparsity and a low-rank model are also widely applied to hyperspectral image denoising. However, the existing hyperspectral image sparse (low-rank) denoising algorithm mainly considers the characteristics of the hyperspectral image such as local similarity and space-spectrum similarity, and the spatial-spectrum smooth characteristic and 3-D non-local prior information of the hyperspectral image need to be continuously researched.
Disclosure of Invention
Aiming at the problems, the invention provides a hyperspectral image denoising method based on low rank and total variation constraint, which is used for removing Gaussian noise and sparse noise in a hyperspectral image.
The technical scheme of the invention is as follows: a hyperspectral image denoising method based on low-rank and total variation constraint comprises the following specific operation steps:
step (1.1), obtaining a hyperspectral image Y containing mixed noise from a remote sensing sensor; using extraction matrix R i,j Extracting image block Y therein i,j Calculating Y i,j Non-local filtering of
Figure BDA0002586784100000011
Step (1.2) of using a priori information of non-local filtering
Figure BDA0002586784100000021
Guide image Block Y i,j Performing low-rank optimization solution;
and (1.3) removing noise contained in the hyperspectral image Y by adopting space-spectrum global total variation constraint, thereby improving the denoising effect of the hyperspectral image Y.
Further, in the step (1.1), the size of the hyperspectral image Y containing the mixed noise is mxnxb, where mxn represents a spatial dimension of the noise hyperspectral image, and B represents a number of bands of the noise hyperspectral image.
Further, in step (1.1), an extraction matrix R is utilized i,j Extracting image block Y therein i,j Which calculates Y i,j Non-local filtering of
Figure BDA0002586784100000022
The operation process of (1) is as follows:
for any i, j (i e [1, M-M + 1]]，j∈[1,N-n+1]) Using the extraction matrix R i,j Extracting an image block Y at the (i, j) th position in a hyperspectral image Y containing mixed noise i,j ；
The image block Y i,j The size of (1) is mxnxB, wherein mxn represents the spatial dimension of the selected noise hyperspectral image block, and Y is found through Euclidean distance i,j Non-local similar image block
Figure BDA0002586784100000023
By using
Figure BDA0002586784100000024
And
Figure BDA0002586784100000025
finding non-local similar image blocks
Figure BDA0002586784100000026
And image block Y i,j Weight between
Figure BDA0002586784100000027
Computing
Figure BDA0002586784100000028
Further, in step (1.2), non-local filtering is adopted as the image block Y i,j The specific steps of the prior information and guiding the low-rank optimization solution are as follows:
the non-local filtering based on robust principal component analysis is:
Figure BDA0002586784100000029
wherein the regularization coefficient λ 1 A balance coefficient, λ, representing sparse noise 2 Balance coefficients, rank (L), representing non-local filtering i,j ) Represents L i,j R represents the desired rank constraint, epsilon represents the termination error;
alternate iterative optimization solution L using augmented Lagrange function i,j Sub-optimization problem and S i,j Sub-optimization problem:
L i,j sub-optimization problem:
Figure BDA0002586784100000031
by converting to solving the nuclear norm minimization problem:
Figure BDA0002586784100000032
wherein, A represents:
Figure BDA0002586784100000033
equation (3) is solved by singular value threshold, namely:
Figure BDA0002586784100000034
wherein, U Σ r V * A is singular value decomposition about rank r constraint, and U and V respectively represent left and right orthogonal matrixes; d δ Represents a soft threshold solver, namely:
D δ (Σ r )＝diag{max(η i -δ,0)} (5)
S i,j sub-optimization problem:
Figure BDA0002586784100000035
solving equation (6) using a soft threshold algorithm, i.e.
Figure BDA0002586784100000036
Figure BDA0002586784100000037
The lagrange multiplier is represented by a number of lagrange multipliers,
Figure BDA0002586784100000038
represents a soft threshold operation, namely:
Figure BDA0002586784100000039
updating lagrange multipliers
Figure BDA00025867841000000310
Mu represents penalty coefficient, calculating error
Figure BDA00025867841000000311
If satisfied, outputting the denoised image block L i,j 。
Further, in step (1.3), the specific generation process of the space-spectrum global total variation constraint is as follows:
initialization parameter X ═ O ═ 0, F ═ 0, lagrange multiplier
Figure BDA0002586784100000041
μ＝0.01；
The global space-spectrum inter-total variation constraint solution is as follows:
o sub optimization problem:
Figure BDA0002586784100000042
the optimization solution is as follows:
Figure BDA0002586784100000043
wherein
Figure BDA00025867841000000410
A tensor representing elements all being 1;
the X sub-optimization problem:
Figure BDA0002586784100000044
equation (10) solves the equation:
Figure BDA0002586784100000045
wherein, I represents a unit tensor, D represents a full variation multiplier of a spectral domain and a spatial domain, and is solved through fast Fourier transform:
Figure BDA0002586784100000046
wherein ffn represents the fast Fourier transform, iffn represents the inverse fast Fourier transform, | · calc 2 Which represents the square of the element or elements,
Figure BDA0002586784100000047
and F, sub-optimization problem:
Figure BDA0002586784100000048
wherein,
Figure BDA0002586784100000049
F＝[F 1 ,F 2 ,F 3 ](ii) a Using a soft threshold algorithm to solve, namely:
Figure BDA0002586784100000051
by passing
Figure BDA0002586784100000052
Updating lagrange multipliers
Figure BDA0002586784100000053
M F ,M O The update penalty coefficient μ ═ min (ρ μ, μ) max )，
Calculating error
Figure BDA0002586784100000054
The denoised image L is output.
The beneficial effects of the invention are: the method comprises the steps of firstly extracting a target 3-D image block of a hyperspectral image containing noise, then searching similar image blocks of the target image block in a given pixel area, and guiding low-rank optimization solution of the similar image blocks by using weighted average of the similar image blocks as prior information of the target image block. In addition, a space-spectrum global total variation global constraint is constructed, and the denoising effect of the hyperspectral image is further improved.
Drawings
FIG. 1 is a flow chart of the architecture of the present invention.
Detailed Description
In order to more clearly illustrate the technical solution of the present invention, the following detailed description is made with reference to the accompanying drawings:
as shown in the figure; a hyperspectral image denoising method based on low rank and total variation constraint comprises the following specific operation steps:
step (1.1), obtaining a hyperspectral image Y containing mixed noise from a remote sensing sensor; using extraction matrix R i,j Extracting image block Y therein i,j Calculating Y i,j Non-local filtering of
Figure BDA0002586784100000055
Step (1.2) of using a priori information of non-local filtering
Figure BDA0002586784100000056
Guide image Block Y i,j Performing low-rank optimization solution;
and (1.3) removing noise contained in the hyperspectral image Y by adopting space-spectrum global total variation constraint, thereby improving the denoising effect of the hyperspectral image Y.
Further, in the step (1.1), the size of the hyperspectral image Y containing the mixed noise is mxnxb, where mxn represents a spatial dimension of the noise hyperspectral image, and B represents a number of bands of the noise hyperspectral image.
Further, in step (1.1)Using the extraction matrix R i,j Extracting image block Y therein i,j Which calculates Y i,j Non-local filtering of
Figure BDA0002586784100000061
The operation process of (1) is as follows:
for any i, j (i e [1, M-M + 1]]，j∈[1,N-n+1]) Using the extraction matrix R i,j Extracting an image block Y at the (i, j) th position in a hyperspectral image Y containing mixed noise i,j ；
Said image block Y i,j The size of (1) is mxnxB, wherein mxn represents the spatial dimension of the selected noise hyperspectral image block, and Y is found through Euclidean distance i,j Non-local similar image block
Figure BDA0002586784100000062
By using
Figure BDA0002586784100000063
And
Figure BDA0002586784100000064
finding non-local similar image blocks
Figure BDA0002586784100000065
And image block Y i,j Weight between
Figure BDA0002586784100000066
Computing
Figure BDA0002586784100000067
Further, in step (1.2), non-local filtering is adopted as the image block Y i,j The specific steps of the prior information and guiding the low-rank optimization solution are as follows:
the non-local filtering based on robust principal component analysis is:
Figure BDA0002586784100000068
wherein the regularization coefficient λ 1 A balance coefficient, λ, representing sparse noise 2 Balance coefficients, rank (L), representing non-local filtering i,j ) Represents L i,j R represents the desired rank constraint, epsilon represents the termination error;
alternate iterative optimization solution L using augmented Lagrange function i,j Sub-optimization problem and S i,j Sub-optimization problem:
L i,j sub-optimization problem:
Figure BDA0002586784100000069
by converting to solving the nuclear norm minimization problem:
Figure BDA00025867841000000610
wherein, A represents:
Figure BDA0002586784100000071
equation (3) is solved by singular value threshold, namely:
L i,j ＝UΣ r V * ，Σ r ＝diag({η i } 1≤i≤r ) (4)
wherein, U Σ r V * A is singular value decomposition about rank r constraint, and U and V respectively represent left and right orthogonal matrixes; d δ Represents a soft threshold solver, namely:
D δ (Σ r )＝diag{max(η i -δ,0)} (5)
S i,j sub-optimization problem:
Figure BDA0002586784100000072
solving equation (6) using a soft threshold algorithm, i.e.
Figure BDA0002586784100000073
Figure BDA0002586784100000074
The lagrange multiplier is represented by a number of lagrange multipliers,
Figure BDA0002586784100000075
represents a soft threshold operation, namely:
Figure BDA0002586784100000076
updating lagrange multipliers
Figure BDA0002586784100000077
Mu represents penalty coefficient, calculating error
Figure BDA0002586784100000078
If satisfied, outputting the denoised image block L i,j 。
Further, in step (1.3), the specific generation process of the space-spectrum global total variation constraint is as follows:
initialization parameters X-O-0, F-0, Lagrange multiplier
Figure BDA0002586784100000079
μ＝0.01；
The global space-spectrum inter-total variation constraint is solved as follows:
o sub optimization problem:
Figure BDA00025867841000000710
the optimization solution is as follows:
Figure BDA0002586784100000081
wherein
Figure BDA00025867841000000811
A tensor representing elements all being 1;
the X sub-optimization problem:
Figure BDA0002586784100000082
equation (10) solves the equation:
Figure BDA0002586784100000083
wherein, I represents a unit tensor, D represents a full variation multiplier of a spectral domain and a spatial domain, and is solved through fast Fourier transform:
Figure BDA0002586784100000084
wherein ffn denotes the fast Fourier transform, iffn denotes the inverse fast Fourier transform, | · calness 2 Which represents the square of the element or elements,
Figure BDA0002586784100000085
and F, sub-optimization problem:
Figure BDA0002586784100000086
wherein,
Figure BDA0002586784100000087
F＝[F 1 ,F 2 ,F 3 ](ii) a Using a soft threshold algorithm to solve, namely:
Figure BDA0002586784100000088
by passing
Figure BDA0002586784100000089
Updating lagrange multipliers
Figure BDA00025867841000000810
M F ,M O The update penalty coefficient μ ═ min (ρ μ, μ) max ) Calculating the error max (| | O) l+1 -X l+1 || ∞ ,||F l+1 -DX l+1 || ∞ ) And E is less than or equal to epsilon, so that the output of the denoised image L is met.
The specific operation process of the invention is as follows:
firstly, a noise model:
because the hyperspectral sensor is influenced by the physical limitation of equipment, weather environment and other factors, the hyperspectral image often contains different types of noise, such as Gaussian noise, dead line noise, stripe noise, impulse noise and the like, and the invention considers a mixed noise model, namely:
Y≡L+S+N (15)
wherein
Figure BDA0002586784100000097
Representing a hyperspectral image containing noise,
Figure BDA0002586784100000098
in order to be a clean image,
Figure BDA0002586784100000099
is sparse noise such as dead lines, stripes, pulses and the like,
Figure BDA00025867841000000910
the hyperspectral image is Gaussian noise, M multiplied by N is the space size of the hyperspectral image, and B is the number of wave bands of the hyperspectral image;
secondly, an algorithm model:
the relevance and the similarity of the hyperspectral images in a space domain and a spectrum domain enable the hyperspectral images to have a plurality of low-rank characteristics; robust principal component analysis can effectively reveal low-dimensional structural characteristics in high-dimensional data; in some noise bands, highThe gaussian noise and the sparse noise are overlapped, and besides, the gaussian noise with higher intensity also influences the reconstruction result; for any i e [1, M-M +1 ∈]，j∈[1,N-n+1]Defining an extraction matrix R i,j To extract the image block at the (i, j) th position in the hyperspectral image
Figure BDA00025867841000000911
Wherein m × n is the spatial size of the extracted image block; in order to further supplement structural information of a target image block, the method is based on robust principal component analysis, utilizes non-local prior information constraint of spatial self-similarity in a hyperspectral image to guide low-rank model solution, and improves the robustness of low-rank solution, namely:
Figure BDA0002586784100000091
wherein
Figure BDA0002586784100000092
Is defined as
Figure BDA0002586784100000093
Figure BDA0002586784100000094
Represents L i,j The k-th similar block of (2), weight
Figure BDA0002586784100000095
Is defined as:
Figure BDA0002586784100000096
in order to utilize the similarity of space and the continuity of wave bands, the invention adopts a space-spectrum complete variation algorithm to ensure the smooth space and the continuity of spectrums; the anisotropic space-spectrum fully-variant norm for the 3-D hyperspectral image L is defined as:
||L|| SSTV ＝||D 1 L|| 1 +||D 2 L|| 1 +||D 3 L|| 1 (18)
wherein D 1 And D 2 Denotes the forward finite difference, D, of the horizontal and vertical axes of space 3 Represents the forward finite difference between the spectra, which is specifically defined as:
Figure BDA0002586784100000101
based on equations (16) and (19), the final denoising model proposed by the present invention is:
Figure BDA0002586784100000102
wherein
Figure BDA0002586784100000103
And
Figure BDA0002586784100000104
respectively a low rank matrix and a sparse matrix;
thirdly, model optimization solving:
by introducing auxiliary variables, equation (5) can be equivalently transformed into:
Figure BDA0002586784100000105
wherein D ═ τ 1 D 1 ,τ 2 D 2 ,τ 3 D 3 ]Operating operators for full variation on a spatial domain and a spectral domain;
Figure BDA0002586784100000106
is O i,j A reconstructed three-dimensional matrix; the patent adopts an augmented Lagrangian method to solve the formula (21), and the corresponding augmented Lagrangian function is as follows:
Figure BDA0002586784100000107
wherein mu is a penalty parameter, wherein,
Figure BDA0002586784100000108
M F and M X Is a lagrange multiplier; the augmented Lagrange function minimum optimization problem can be solved through alternative iterative optimization by the following sub-problems;
1. non-local constraint solution of low-rank sparse matrix:
1)、L i,j sub-optimization problem:
Figure BDA0002586784100000111
equation (23) solves the nuclear norm minimization problem by transforming:
Figure BDA0002586784100000112
wherein A is defined as:
Figure BDA0002586784100000113
equation (24) can be solved by singular value thresholding, i.e.:
L i,j ＝UΣ r V * ，Σ r ＝diag({η i } 1≤i≤r ) (25)
wherein U Σ r V * A is singular value decomposition about rank r constraint, and U and V are left and right orthogonal matrixes respectively; d δ Represents a soft threshold solver, namely:
D δ (Σ r )＝diag{max(η i -δ,0)} (26)
2)、S i,j sub-optimization problem:
Figure BDA0002586784100000114
formula (25) may beUsing soft threshold algorithms for solution, i.e.
Figure BDA0002586784100000115
Figure BDA0002586784100000116
Represents a soft threshold operation, namely:
Figure BDA0002586784100000117
2. solving global space-spectrum full variation constraint:
1) and O sub optimization problem:
Figure BDA0002586784100000121
if the objective function of equation (29) is a strictly convex function, the optimal solution is:
Figure BDA0002586784100000122
wherein
Figure BDA00025867841000001211
Is a tensor with elements all 1;
2) and the optimization problem of the X sub-unit:
Figure BDA0002586784100000123
equation (31) can be solved by:
Figure BDA0002586784100000124
wherein I represents a unit tensor, which takes into account the periodic boundary condition of X, D T D, obtaining a block circulation matrix with a circulation block structure; the formula (17) can be obtained bySolving Fourier transform:
Figure BDA0002586784100000125
wherein ffn is the fast Fourier transform, iffn is the inverse fast Fourier transform, | · calness 2 Which represents the square of the element(s),
Figure BDA0002586784100000126
3) and F, optimizing the problem:
Figure BDA0002586784100000127
wherein
Figure BDA0002586784100000128
F＝[F 1 ,F 2 ,F 3 ](ii) a Equation (34) is the same as equation (27), and can be solved using a soft threshold algorithm, that is:
Figure BDA0002586784100000129
3. and (3) updating multipliers:
after solving the problems (24), (27), (29), (31), and (34), the Lagrangian multiplier
Figure BDA00025867841000001210
Figure BDA0002586784100000131
M F And M O Can be updated by equation (36):
Figure BDA0002586784100000132
the specific embodiment is as follows:
two sets of hyperspectral images were tested by the invention, image 1 and image 2 having dimensions 145 × 145 × 224 and 200 × 200 × 80 respectively. Pixel values for all experimental data were normalized to [0,1 ];
the image block size is set to be m × n of 20 × 20, and the image block step size is extracted to be 10 × 10 (10 pixels are moved each time from the horizontal and vertical directions); parameter lambda 1 、λ 2 And tau is the balance coefficient of sparse noise, non-local constraint and space-spectrum total variation constraint, and is set as lambda 1 ＝1、λ 2 ＝0.05，τ＝[τ 1 ,τ 2 ,τ 3 ]In which τ is 3 ＝0.5，τ 1 ＝τ 2 1 indicates that two spatial dimensions have the same influence on the space-spectrum total variation, and the stop error is set to 10 -6 (ii) a When the experiment is performed for image 1 and image 2, the parameter rank r is set to r-5 and r-3, respectively. Four different types of simulated noise were experimentally tested, defined as:
noise 1: gaussian noise with the noise intensity of 0.05 is added to each wave band;
noise 2: on the basis of the noise 1, adding salt and pepper noise with the intensity of 0.1 on all wave bands;
noise 3: on the basis of noise 1, selecting 20 wave bands and adding stripe noise, and randomly adding the stripe noise with the quantity of 3 to 10 and the pixel width of 1 to 3 on the selected wave bands;
noise 4: on the basis of the noise 2, selecting 20 wave bands and adding dead line noise, and randomly adding the dead line noise with the number of 3 to 10 and the pixel width of 1 to 3 on the selected wave bands;
this patent adopts four kinds of image quality indexes, including space image quality index: average peak signal-to-noise ratio (MPSNR), average structure similarity (MSSIM), Feature Similarity (FSIM), spectral quality evaluation result (ERRETURE relative colloidal analysis rule) synthesis (ERGAS) and average spectral angle mapping (MSAM);
Figure BDA0002586784100000133
Figure BDA0002586784100000141
Figure BDA0002586784100000142
Figure BDA0002586784100000143
wherein u i And
Figure BDA0002586784100000144
a reference image and a reconstructed image respectively representing the ith band;
Figure BDA0002586784100000145
and
Figure BDA0002586784100000146
is defined as an image u i And
Figure BDA0002586784100000147
is determined by the average value of (a) of (b),
Figure BDA0002586784100000148
and
Figure BDA0002586784100000149
denotes the standard deviation, parameter C 1 And C 2 The avoidance result approaches 0; the larger the MPSNR and MSSIM values are, the closer the denoised image is to the reference image, and the better the denoising effect is; the smaller the ERGAS and MSA values are, the better the denoising effect is.
The denoising results of the image 1 and the image 2 under various types of noise are respectively given in table 1 and table 2; experimental results show that the non-local and global space spectrum total variation constraint provided by the invention can effectively remove the composite noise in the hyperspectral image.
Table 1: reconstruction of image 1 under various noise types
Type of noise MPSNR MSSIM ERGAS MSA
Noise
1 40.1737 0.9877 22.9009 0.0107
Noise 2 42.3250 0.9750 18.8526 0.0111
Noise 3 39.8252 0.9837 26.0421 0.0147
Noise 4 37.8537 0.9788 52.1249 0.0247
Table 2: reconstruction of image 2 under various noise types
Type of noise MPSNR MSSIM ERGAS MSA
Noise
1 38.6984 0.9793 43.2519 0.0678
Noise 2 38.3227 0.9758 45.4125 0.0699
Noise 3 38.3109 0.9783 45.2553 0.0705
Noise 4 37.8177 0.9747 48.6312 0.0741
Finally, it should be understood that the embodiments described herein are merely illustrative of the principles of embodiments of the present invention; other variations are possible within the scope of the invention; thus, by way of example, and not limitation, alternative configurations of embodiments of the invention may be considered consistent with the teachings of the invention; accordingly, the embodiments of the invention are not limited to the embodiments explicitly described and depicted.

Claims (4)

1. A hyperspectral image denoising method based on low rank and total variation constraint is characterized by comprising the following specific operation steps:
step (1.1), a hyperspectral image Y containing mixed noise is obtained from a remote sensing sensor; using extraction matrix R i,j Extracting image block Y therein i,j Calculating Y i,j Non-local filtering of
Figure FDA0003727970390000011
Step (1.2) of using prior information of non-local filtering
Figure FDA0003727970390000012
Guide image Block Y i,j Performing low-rank optimization solution; the method comprises the following specific steps:
the non-local filtering based on robust principal component analysis is:
Figure FDA0003727970390000013
wherein the regularization coefficient λ 1 A balance coefficient, λ, representing sparse noise 2 Balance coefficients, rank (L), representing non-local filtering i,j ) Represents L i,j R represents the desired rank constraint, ε represents the termination error;
alternate iterative optimization solution L using augmented Lagrange function i,j Sub-optimization problem and S i,j Sub-optimization problem:
L i,j sub-optimization problem:
Figure FDA0003727970390000014
by converting to solving the nuclear norm minimization problem:
Figure FDA0003727970390000015
wherein, A represents:
Figure FDA0003727970390000016
equation (3) is solved by singular value threshold, namely:
L i,j ＝UΣ r V * ，Σ r ＝diag({η i } 1≤i≤r ) (4)
wherein, U Σ r V * A is singular value decomposition about rank r constraint, and U and V respectively represent left and right orthogonal matrixes; d δ Represents a soft threshold solver, namely:
D δ (Σ r )＝diag{max(η i -δ,0)} (5)
S i,j sub-optimization problem:
Figure FDA0003727970390000021
solving equation (6) using a soft threshold algorithm, i.e.
Figure FDA0003727970390000022
Figure FDA0003727970390000023
The lagrange multiplier is represented by a number of lagrange multipliers,
Figure FDA0003727970390000024
represents a soft threshold operation, namely:
Figure FDA0003727970390000025
updating lagrange multipliers
Figure FDA0003727970390000026
Mu represents penalty coefficient, calculating error
Figure FDA0003727970390000027
If yes, outputting a denoised image block L i,j ；
And (1.3) removing noise contained in the hyperspectral image Y by adopting space-spectrum global total variation constraint, thereby improving the denoising effect of the hyperspectral image Y.
2. The hyperspectral image denoising method based on low rank and total variation constraint according to claim 1, wherein in step (1.1), the size of the hyperspectral image Y containing mixed noise is mxnxb, wherein mxn represents the spatial dimension of the noise hyperspectral image and B represents the number of wave bands of the noise hyperspectral image.
3. The hyperspectral image denoising method based on low rank and total variation constraint according to claim 1, wherein in step (1.1), extraction matrix R is used i,j Extracting image block Y therein i,j Which calculates Y i,j Non-local filtering of
Figure FDA0003727970390000028
The operation process of (1) is as follows:
for any i, j (i e)[1,M-m+1]，j∈[1,N-n+1]) Using the extraction matrix R i,j Extracting an image block Y at the (i, j) th position in a hyperspectral image Y containing mixed noise i,j ；
Said image block Y i,j The size of (1) is mxnxB, wherein mxn represents the spatial dimension of the selected noise hyperspectral image block, and Y is found through Euclidean distance i,j Non-local similar image block
Figure FDA0003727970390000029
By using
Figure FDA00037279703900000210
And
Figure FDA00037279703900000211
finding non-local similar image blocks
Figure FDA00037279703900000212
And image block Y i,j Weight therebetween
Figure FDA0003727970390000031
Computing
Figure FDA0003727970390000032
4. The hyperspectral image denoising method based on low rank and total variation constraint according to claim 1, wherein in step (1.3), the specific generation process of the spatio-spectral global total variation constraint is as follows:
initialization parameter X ═ O ═ 0, F ═ 0, lagrange multiplier
Figure FDA0003727970390000033
M F ,M O ＝0，μ＝0.01；
The global space-spectrum inter-total variation constraint is solved as follows:
o sub optimization problem:
Figure FDA0003727970390000034
the optimization solution is as follows:
Figure FDA0003727970390000035
wherein
Figure FDA0003727970390000036
A tensor representing elements all being 1;
the X sub-optimization problem:
Figure FDA0003727970390000037
equation (10) solves the equation:
Figure FDA0003727970390000038
wherein, I represents a unit tensor, D represents a full variation multiplier of a spectral domain and a spatial domain, and is solved through fast Fourier transform:
Figure FDA0003727970390000039
wherein ffn denotes the fast Fourier transform, iffn denotes the inverse fast Fourier transform,. C 2 Which represents the square of the element(s),
Figure FDA00037279703900000310
and F, sub-optimization problem:
Figure FDA00037279703900000311
wherein,
Figure FDA00037279703900000312
F＝[F 1 ,F 2 ,F 3 ](ii) a Using a soft threshold algorithm to solve, namely:
Figure FDA0003727970390000041
by passing
Figure FDA0003727970390000042
Updating lagrange multipliers
Figure FDA0003727970390000043
M F ,M O The update penalty coefficient μ ═ min (ρ μ, μ) max )，
Calculate error max (| | O) l+1 -X l+1 || ∞ ,||F l+1 -DX l+1 || ∞ ) And E is less than or equal to epsilon, so that the output of the denoised image L is met.
CN202010683866.2A 2020-07-16 2020-07-16 Hyperspectral image denoising method based on low-rank and total variation constraint Active CN111951186B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010683866.2A CN111951186B (en) 2020-07-16 2020-07-16 Hyperspectral image denoising method based on low-rank and total variation constraint

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010683866.2A CN111951186B (en) 2020-07-16 2020-07-16 Hyperspectral image denoising method based on low-rank and total variation constraint

Publications (2)

Publication Number Publication Date
CN111951186A CN111951186A (en) 2020-11-17
CN111951186B true CN111951186B (en) 2022-08-26

Family

ID=73341324

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010683866.2A Active CN111951186B (en) 2020-07-16 2020-07-16 Hyperspectral image denoising method based on low-rank and total variation constraint

Country Status (1)

Country Link
CN (1) CN111951186B (en)

Families Citing this family (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112596104B (en) * 2020-12-09 2022-04-01 成都理工大学 Seismic data denoising method combining tensor decomposition and total variation
CN112633202B (en) * 2020-12-29 2022-09-16 河南大学 Hyperspectral image classification algorithm based on dual denoising combined multi-scale superpixel dimension reduction
CN112767263A (en) * 2021-01-07 2021-05-07 上饶师范学院 Image mixed noise removing method based on low-rank function and multi-direction total variation
CN112950500B (en) * 2021-02-25 2022-08-26 桂林电子科技大学 Hyperspectral denoising method based on edge detection low-rank total variation model
CN113193855B (en) * 2021-04-25 2022-04-19 西南科技大学 Robust adaptive filtering method for identifying low-rank acoustic system
CN113569905B (en) * 2021-06-10 2024-03-26 西安电子科技大学 Heterogeneous image fusion method based on multi-scale feature extraction and total variation
CN113409261B (en) * 2021-06-13 2024-05-14 西北工业大学 Hyperspectral anomaly detection method based on spatial spectrum feature joint constraint
CN113421198B (en) * 2021-06-17 2023-10-20 南京邮电大学 Hyperspectral image denoising method based on subspace non-local low-rank tensor decomposition
CN113378415B (en) * 2021-08-12 2021-11-02 西南科技大学 Multimedia data self-adaptive recovery method and device based on local and global constraints
CN113706418B (en) * 2021-09-07 2024-07-23 哈尔滨工业大学 Long-wave infrared remote sensing image recovery method based on spectrum separation
CN114022393B (en) * 2021-11-19 2024-05-14 中国科学院长春光学精密机械与物理研究所 Image stripe noise removing method based on total variation and low-rank direction sparse constraint

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105069758A (en) * 2015-08-21 2015-11-18 武汉大学 Hyperspectral image denoising method based on robust low-rank tensor
CN109658351A (en) * 2018-11-26 2019-04-19 浙江工业大学 The high spectrum image denoising method that a kind of combination L0 gradient constraint and local low-rank matrix are restored

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105069758A (en) * 2015-08-21 2015-11-18 武汉大学 Hyperspectral image denoising method based on robust low-rank tensor
CN109658351A (en) * 2018-11-26 2019-04-19 浙江工业大学 The high spectrum image denoising method that a kind of combination L0 gradient constraint and local low-rank matrix are restored

Also Published As

Publication number Publication date
CN111951186A (en) 2020-11-17

Similar Documents

Publication Publication Date Title
CN111951186B (en) Hyperspectral image denoising method based on low-rank and total variation constraint
CN109102477B (en) Hyperspectral remote sensing image recovery method based on non-convex low-rank sparse constraint
Zhong et al. Multiple-spectral-band CRFs for denoising junk bands of hyperspectral imagery
CN105608433B (en) A kind of hyperspectral image classification method based on nuclear coordination expression
CN110533077B (en) Shape adaptive convolution depth neural network method for hyperspectral image classification
CN108197650B (en) Hyperspectral image extreme learning machine clustering method with local similarity maintained
Praveen Kumar et al. Rosette plant segmentation with leaf count using orthogonal transform and deep convolutional neural network
CN110135344B (en) Infrared dim target detection method based on weighted fixed rank representation
CN104463223B (en) Hyperspectral image group sparse unmixing method based on space spectrum information abundance constraint
CN111583230B (en) Low-rank sparse decomposition hyperspectral abnormal target detection method based on local features
Zhao et al. Hyperspectral image denoising using spectral-spatial transform-based sparse and low-rank representations
CN111680579B (en) Remote sensing image classification method for self-adaptive weight multi-view measurement learning
Chen et al. Hyperspectral image denoising with weighted nonlocal low-rank model and adaptive total variation regularization
CN106067165B (en) High spectrum image denoising method based on clustering sparse random field
CN104700379A (en) Remote sensing image fusion method based on multi-dimensional morphologic element analysis
CN103077507B (en) Beta algorithm-based multiscale SAR (Synthetic Aperture Radar) image denoising method
CN113421198B (en) Hyperspectral image denoising method based on subspace non-local low-rank tensor decomposition
Sun et al. Hyperspectral mixed denoising via subspace low rank learning and BM4D filtering
CN112949698A (en) Hyperspectral unmixing method based on non-local low-rank tensor similarity constraint
CN112634167A (en) Hyperspectral image filtering method for total variation collaborative norm constraint iterative projection
CN116051444A (en) Effective infrared and visible light image self-adaptive fusion method
Tong et al. Hyperspectral unmixing via deep matrix factorization
Yufeng et al. Research on SAR image change detection algorithm based on hybrid genetic FCM and image registration
CN115731135A (en) Hyperspectral image denoising method and system based on low-rank tensor decomposition and adaptive graph total variation
Nguyen et al. Deep sparse and low-rank prior for hyperspectral image denoising

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
CB02 Change of applicant information

Address after: 210003, 66 new model street, Gulou District, Jiangsu, Nanjing

Applicant after: NANJING University OF POSTS AND TELECOMMUNICATIONS

Address before: No. 186, software Avenue, Yuhuatai District, Nanjing, Jiangsu Province, 210023

Applicant before: NANJING University OF POSTS AND TELECOMMUNICATIONS

CB02 Change of applicant information
GR01 Patent grant
GR01 Patent grant