CN111598795B - Tensor loop decomposition-based hyperspectral image denoising method and device - Google Patents
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Abstract
The application discloses a hyperspectral image denoising method and device based on tensor ring decomposition, comprising the steps of obtaining hyperspectral image data with noise, and establishing a mathematical model of hyperspectral image noise; combining the total variation and tensor ring decomposition to construct a hyperspectral image denoising model TR-TV based on the total variation regularized tensor ring decomposition; taking the weighted neighborhood mean three-dimensional total variation as the non-convex relaxation of a low-rank term on the basis of the model TR-TV to obtain a hyperspectral image denoising model TR-WDTV based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition; introducing an auxiliary variable; and (3) optimizing a denoising model TR-WDTV, and solving by adopting an ADMM algorithm to obtain a hyperspectral image after denoising. The method has good hyperspectral image denoising effect.
Description
Technical Field
The application belongs to the technical field of hyperspectral image processing, and particularly relates to a hyperspectral image denoising method and device based on tensor loop decomposition.
Background
With the advent of hyperspectral imaging technology and the rapid development of the last thirty years, hyperspectral remote sensing has become a key technology in the field of space remote sensing, and is widely applied to important fields such as geological exploration, agricultural telemetry, hydrologic monitoring, military detection and the like.
Due to various factors such as atmospheric interference, sensor accuracy, etc., hyperspectral Images (HIS) may be affected by gaussian noise, impulse noise, banding noise, etc. during acquisition. Because of the wide range of applications, denoising is an essential pretreatment step prior to subsequent applications of HSI.
Around the problem of denoising hyperspectral images, researchers at home and abroad propose a plurality of denoising methods. Existing hyperspectral image denoising methods are mainly divided into three types: the first is a filtering-based denoising method. The filtering-based hyperspectral image denoising technique typically uses three-dimensional filtering, or filtering denoising in one dimension of the spectrum/space, and denoising in the other dimension using other methods. The second class is methods based on low rank representation. Considering the three-dimensional structure of hyperspectral images, tensors and multiple linear algebra are often used for low-rank approximation of hyperspectral images, classical tensor decomposition methods are CP decomposition, tucker decomposition and tensor loop decomposition (Tensor Ring decomposition, TR). The third class is based on total variation methods. The idea of the Total Variation (TV) image denoising method is that a noise-free image should have smoothness, and noise can be removed by regularizing the noisy image through a Total variation norm. The denoising algorithm based on the TV can be used for processing a smooth hyperspectral image, but is used for hyperspectral images with more details, and detail loss is easy to cause.
Disclosure of Invention
The application aims to provide a hyperspectral image denoising method and device based on tensor ring decomposition, which are called TR-WDTV for short, and further improve the hyperspectral image denoising effect.
In order to achieve the above purpose, the technical scheme of the application is as follows:
a hyperspectral image denoising method based on tensor loop decomposition comprises the following steps:
acquiring hyperspectral image data with noise, and establishing a mathematical model of hyperspectral image noise;
combining the total variation and tensor ring decomposition to construct a hyperspectral image denoising model based on the total variation regularization tensor ring decomposition;
on the basis of a hyperspectral image denoising model based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low-rank term, and constructing a hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition;
introducing auxiliary variables and />Optimizing a hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition;
and solving an optimized hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm to obtain a hyperspectral image after noise reduction.
Further, the mathematical model of the hyperspectral image noise is:
wherein ,representing a noisy hyperspectral image, +.>Representing a clean hyperspectral image, S representing sparse noise,/->Representing high density noise;
the method for constructing the hyperspectral image denoising model based on the total variation regularized tensor ring decomposition by combining the total variation and the tensor ring decomposition comprises the following steps of:
s.t.
wherein ,D v and Dt Representing gradient operators in horizontal and vertical directions, τ is a parameter for adjusting total variation, λ is a sparsity parameter for limiting sparse noise, β is a parameter for limiting gaussian noise, |·|| 1 The L1 norm of the tensor is represented, I.I F The Frobenius norm of tensors, G 1 (i 1 )、G 2 (i 2 )、G 3 (i 3 ) Is tensor loop kernel, i 1 、i 2 、i 3 Is a spatial index parameter.
Further, on the basis of a hyperspectral image denoising model based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low rank term, and constructing the hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition, wherein the method comprises the following steps:
first, a neighborhood mean difference operation of an image is defined:
wherein (i, j, k) represents an imageCorresponding coordinate positions along the directions of the space length, the width and the spectrum,representing the gradient values of the image obtained after differential operation of the positions (i, j, k) in the horizontal, vertical and spectral directions. />Gray value representing the position of the image, +.>Andpixel gray values representing the translation of the corresponding image at a position (i, j, k) along the spatial length, width and spectral length directions by one position;
further construct a neighborhood mean difference operator G s (·)，
G s (·)＝[ρ v G v (·)；ρ t G t (·)；ρ z G z (·)]
wherein ,Gv (·)、G t(·) and Gz (. Cndot.) represents the differential operation in three different directions of horizontal, vertical and spectral, ρ s (s=v, t, z) is a parameter used to control the intensity of the constraint on three dimensions;
thereby obtaining the weighted neighborhood mean three-dimensional total variation:
wherein ,wi,j,k Is the gradient value weight of the image at position (i, j, k);
based on a hyperspectral image denoising model based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low-rank term to obtain the hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition:
further, the introduction of the auxiliary variable and />Optimizing a hyperspectral image denoising model based on weighted neighborhood mean value three-dimensional total variation regularization tensor ring decomposition, wherein the optimized model is expressed as:
further, the solving the optimized hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm to obtain a denoised hyperspectral image comprises the following steps:
step 5.1, solving the optimized hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm, and fixing other variablesUpdating
Where u is a penalty coefficient, Λ 1 ,Λ 2 ,Λ 3 Is the Lagrangian multiplier;
using tensor chain decomposition, pairThe update process of (a) is converted into the update of three tensor ring cores, and the following form can be obtained through conversion:
through updated tensor kernel G 1 (i 1 ) (k+1) ,G 2 (i 2 ) (k+1) ,G 3 (i 3 ) (k+1) Reconstruction of
Step 5.2, fixing other variables and updating
Step 5.3, fixing other variables and updating
Step 5.4, fixing other variables, and updating s (k+1) ：
Step 5.5, fixing other variables and updating
Step 5.6, fixing other variables, and updating Lagrangian multipliers:
step 5.7, judging whether the iteration termination condition is satisfied, if soTerminating the iteration and outputting a noise-free image +.>Otherwise, continuing to update iteratively.
The application also provides a hyperspectral image denoising device based on tensor loop decomposition, which comprises a processor and a memory storing a plurality of computer instructions, and is characterized in that the computer instructions realize the steps of the method when being executed by the processor.
The hyperspectral image denoising method and device based on tensor ring decomposition provided by the application have the following beneficial effects:
(1) The method can effectively remove Gaussian noise, sparse noise and mixed noise;
(2) The low-rank tensor characteristic of the clean hyperspectral image can be effectively utilized;
(3) The consistency between the space dimension and the spectrum dimension is considered, and meanwhile, the smoothness of the space and the spectrum is enhanced;
(4) Spectral information can be effectively utilized, and spectral distortion caused by the spectral information can be avoided while denoising.
Drawings
FIG. 1 is a flow chart of a method for denoising hyperspectral image based on tensor loop decomposition according to the present application.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In one embodiment, as shown in fig. 1, a method for denoising hyperspectral image based on tensor loop decomposition, the method comprising the steps of:
s1, acquiring hyperspectral image data with noise, and establishing a mathematical model of hyperspectral image noise.
The hyperspectral image noise mathematical model established in this embodiment is as follows:
wherein ,representing a noisy hyperspectral image, +.>Representing a clean hyperspectral image (a de-rested hyperspectral image), s representing sparse noise,/->Represents high density noise (Gaussian noise, poisson noise, etc.), and +.>Wherein m and n respectively represent the length and the width of the hyperspectral image in the space dimension, and h represents the band number of the hyperspectral image in the spectrum dimension; />Representing a real number.
And S2, combining the total variation and tensor ring decomposition, and constructing a hyperspectral image denoising model TR-TV based on the total variation regularized tensor ring decomposition.
Specifically, the method comprises the following steps:
considering the low rank and correlation of all dimensions of the image tensor, taking the existing low rank total variation denoising model as a framework,
s.t.
the mathematical expression of the hyperspectral image denoising model TR-TV is obtained by combining tensor loop decomposition as follows:
s.t.
wherein ,D v and Dt Representing the gradient operators in the horizontal and vertical directions, τ being the parameter for adjusting the total variationThe number, lambda, is a sparsity parameter that limits sparse noise, beta is a parameter limiting Gaussian noise, |·||is 1 The L1 norm of the tensor is represented, I.I F The Frobenius norm of tensors, G 1 (i 1 )、G 2 (i 2 )、G 3 (i 3 ) Is tensor loop kernel, i 1 、i 2 、i 3 Is a spatial index parameter.
And S3, based on a hyperspectral image denoising model TR-TV based on total variation regularization tensor ring decomposition, taking the weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low rank term, and constructing a hyperspectral image denoising model TR-WDTV based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition.
First, a neighborhood mean difference operation of an image is defined:
wherein (i, j, k) represents an imageCorresponding coordinate positions along the directions of the space length, the width and the spectrum,representing the gradient values of the image obtained after differential operation of the positions (i, j, k) in the horizontal, vertical and spectral directions. />Gray value representing the position of the image, +.>Andrepresenting the pixel gray values of the corresponding image shifted by one position along the spatial length, width and spectral band directions at position (i, j, k).
Further construct a neighborhood mean difference operator G s (·)，
G s (·)＝[ρ v G v (·)；ρ t G t (·)；ρ z G z (·)]
wherein ,Gv (·)、G t(·) and Gz (. Cndot.) represents the differential operation in three different directions of horizontal, vertical and spectral, ρ s (s=v, t, z) is a parameter used to control the constraint intensity for three dimensions.
Thereby obtaining the weighted neighborhood mean three-dimensional total variation:
wherein ,wi,j,k Is the gradient value weight of the image at position (i, j, k).
The weighted neighborhood mean three-dimensional total variation can be abbreviated as:
wherein, as follows, the outer product operator, W is the weight matrix.
Based on a hyperspectral image denoising model TR-TV based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low-rank term to obtain a hyperspectral image denoising model TR-WDTV based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition:
s4, introducing auxiliary variables for eliminating the correlation between matrix data and />And optimizing a hyperspectral image denoising model TR-WDTV based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition.
Specifically, to eliminate the correlation between matrix data, auxiliary variables are introduced and />The optimized denoising model TR-WDTV is as follows:
s.t.
and S5, solving an optimized hyperspectral image denoising model based on weighted neighborhood mean value three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm to obtain a hyperspectral image after noise reduction.
Specifically, the method comprises the following steps:
(5-1) solving the optimized hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm, fixing other variables, and updating
Where u is a penalty coefficient, Λ 1 ,Λ 2 ,Λ 3 Is the lagrange multiplier.
Using tensor chain decomposition, pairThe update process of (a) is converted into the update of three tensor ring cores, and the following form can be obtained through conversion:
through updated tensor kernel G 1 (i 1 ) (k+1) ,G 2 (i 2 ) (k+1) ,G 3 (i 3 ) (k+1) Reconstruction of
(5-2) fixing other variables, updating
(5-3) fixing other variables, updating
(5-4) fixing other variables, updating
(5-5) fixing other variables, updating
(5-6) fixing other variables, updating the lagrangian multiplier:
(5-7) determining whether the iteration termination condition is satisfied, ifTerminating the iteration and outputting a noise-free image +.>Otherwise, continuing to update iteratively.
In one embodiment, the application further provides a hyperspectral image denoising device based on tensor loop decomposition, which comprises a processor and a memory storing a plurality of computer instructions, wherein the computer instructions realize the steps of the hyperspectral image denoising method based on tensor loop decomposition when being executed by the processor.
For specific limitations on the tensor-loop decomposition-based hyperspectral image denoising apparatus, reference may be made to the above limitation on the tensor-loop decomposition-based hyperspectral image denoising method, and no further description is given here. The above-described tensor loop decomposition-based hyperspectral image denoising apparatus may be implemented in whole or in part by software, hardware, or a combination thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
The memory and the processor are electrically connected directly or indirectly to each other for data transmission or interaction. For example, the components may be electrically connected to each other by one or more communication buses or signal lines. The memory stores a computer program that can be executed on a processor that implements the network topology layout method in the embodiment of the present application by executing the computer program stored in the memory.
The Memory may be, but is not limited to, random access Memory (Random Access Memory, RAM), read Only Memory (ROM), programmable Read Only Memory (Programmable Read-Only Memory, PROM), erasable Read Only Memory (Erasable Programmable Read-Only Memory, EPROM), electrically erasable Read Only Memory (Electric Erasable Programmable Read-Only Memory, EEPROM), etc. The memory is used for storing a program, and the processor executes the program after receiving an execution instruction.
The processor may be an integrated circuit chip having data processing capabilities. The processor may be a general-purpose processor including a central processing unit (Central Processing Unit, CPU), a network processor (Network Processor, NP), and the like. The methods, steps and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (5)
1. The hyperspectral image denoising method based on tensor loop decomposition is characterized by comprising the following steps of:
acquiring hyperspectral image data with noise, and establishing a mathematical model of hyperspectral image noise;
combining the total variation and tensor ring decomposition to construct a hyperspectral image denoising model based on the total variation regularization tensor ring decomposition;
on the basis of a hyperspectral image denoising model based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low-rank term, and constructing a hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition;
introducing auxiliary variables and />Optimizing a hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition;
and solving an optimized hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition by adopting an ADMM algorithm to obtain a hyperspectral image after noise reduction.
2. The tensor loop decomposition based hyperspectral image denoising method of claim 1, wherein the mathematical model of hyperspectral image noise is:
wherein ,representing a noisy hyperspectral image, +.>Representing a clean hyperspectral image, < >>Represents sparse noise->Representing high density noise;
the method for constructing the hyperspectral image denoising model based on the total variation regularized tensor ring decomposition by combining the total variation and the tensor ring decomposition comprises the following steps of:
wherein ,D v and Dt Representing gradient operators in horizontal and vertical directions, τ is a parameter for adjusting total variation, λ is a sparsity parameter for limiting sparse noise, β is a parameter for limiting gaussian noise, |·|| 1 The L1 norm of the tensor is represented, I.I F The Frobenius norm of tensors, G 1 (i 1 )、G 2 (i 2 )、G 3 (i 3 ) Is tensor loop kernel, i 1 、i 2 、i 3 Is a spatial index parameter.
3. The method for denoising a hyperspectral image based on tensor loop decomposition according to claim 2, wherein the constructing a hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularized tensor loop decomposition based on a hyperspectral image denoising model based on total variation regularized tensor loop decomposition by taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of low rank terms comprises:
first, a neighborhood mean difference operation of an image is defined:
wherein (i, j, k) represents an imageCorresponding coordinate positions along the directions of the space length, the width and the spectrum,representing the gradient values of the image obtained after differential operation of the position (i, j, k) in horizontal, vertical and spectral directions,/->Gray value representing the position of the image, +.>Andpixel gray values representing the translation of the corresponding image at a position (i, j, k) along the spatial length, width and spectral length directions by one position;
further construct a neighborhood mean difference operator G s (·)，
G s (·)＝[ρ v G v (·)；ρ t G t (·)；ρ z G z (·)]
wherein ,Gv (·)、G t(·) and Gz (. Cndot.) represents the differential operation in three different directions of horizontal, vertical and spectral, ρ s (s=v, t, z) is a parameter used to control the intensity of the constraint on three dimensions;
thereby obtaining the weighted neighborhood mean three-dimensional total variation:
wherein ,wi,j,k Is the gradient value weight of the image at position (i, j, k);
the weighted neighborhood mean three-dimensional total variation is abbreviated as
Based on a hyperspectral image denoising model based on total variation regularization tensor ring decomposition, taking weighted neighborhood mean three-dimensional total variation as non-convex relaxation of a low-rank term to obtain the hyperspectral image denoising model based on weighted neighborhood mean three-dimensional total variation regularization tensor ring decomposition:
4. a tensor loop decomposition based hyperspectral image denoising method as claimed in claim 3 wherein the introducing auxiliary variable and />Optimizing a hyperspectral image denoising model based on weighted neighborhood mean value three-dimensional total variation regularization tensor ring decomposition, wherein the optimized model is expressed as:
5. a hyperspectral image denoising apparatus based on tensor loop decomposition, comprising a processor and a memory storing a number of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the method of any one of claims 1 to 4.
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