CN112084847B - Hyperspectral image denoising method based on multichannel truncated nuclear norm and total variation regularization - Google Patents

Abstract

A hyperspectral image denoising method based on multichannel truncated nuclear norms and total variation regularization comprises the following steps: 1) Acquiring a hyperspectral data image with to-be-denoised, wherein N is Additive White Gaussian Noise (AWGN), X is a recovered clean image, m and N are respectively the length and the width of the space dimension of the hyperspectral image, and p is the number of spectral bands; 2) Constructing a multi-channel truncated nuclear norm and a full-variation regularized hyperspectral image denoising model; 3) Optimizing the model using an alternating direction multiplier algorithm (ALTERNATING DIRECTION METHOD OF MULTIPLIERS, ADMM); 4) And outputting the hyperspectral image after noise removal. The invention has the advantages that: the segmentation smoothing prior is better reserved, the edge information is effectively kept, and meanwhile, the denoising effect of Gaussian noise is enhanced.

Description

Hyperspectral image denoising method based on multichannel truncated nuclear norm and total variation regularization

Technical Field

The invention relates to the field of remote sensing image processing, in particular to a hyperspectral image denoising method.

Technical Field

Hyperspectral remote sensing images are widely focused in various application fields due to the fact that hyperspectral remote sensing images contain abundant spatial information and spectral information, for example: urban planning, mapping, agriculture, forestry, monitoring and other fields. But hyperspectral images (HYPERSPECTRAL IMAGE, HSI) acquired by multiple detectors are often corrupted by different types of noise, which severely degrades the quality of the image and limits the accuracy of subsequent task processing such as classification, recognition, unmixing, etc. Therefore, hyperspectral image denoising has very important value and significance in current academic research.

In recent years, hyperspectral image denoising has gained attention from many domestic and foreign scholars. To date, many different denoising methods have been proposed for hyperspectral images. The conventional method regards each channel of the hyperspectral image as a gray scale image and processes it one by one, such as K-SVD, block-matched three-dimensional filtering (Block-MATCHING AND 3D filtering,BM3D), etc. However, these approaches ignore the correlation between different spectral bands, which results in poor noise reduction. The most recent denoising method improves denoising performance by combining spatial low rank with spectral low rank, and a representative method is principal component analysis (PRINCIPAL COMPONENT ANALYSIS, PCA) that converts a hyperspectral image into a set of linearly uncorrelated variables, called Principal Components (PCs), using orthogonal transformation. Assuming that the high-dimensional hyperspectral data is located in the low-dimensional eigenspace, the first few PCs contain the main information and the remaining PCs contain noise information, so that the hyperspectral data can be denoised by inverse transforming the preceding PCs. The hyperspectral image denoising problem is further complicated by the fact that the noise variances in the different spectral bands are unequal due to the characteristics of the sensor in the acquisition process, and artifacts can occur if each channel is processed identically in the joint denoising process.

Disclosure of Invention

The invention aims to overcome the defects of the prior art, and provides a hyperspectral image denoising method based on multichannel truncated nuclear norm and total variation regularization aiming at different noise characteristics in different channels and combining with the internal correlation of hyperspectral image channels.

The technical scheme adopted for solving the technical problems is as follows:

a hyperspectral image denoising method based on multichannel truncated nuclear norms and total variation regularization comprises the following steps:

Step 1) obtaining an image y=x+n with hyperspectral data to be denoised, wherein Y, X, N is Additive White Gaussian Noise (AWGN), X is the recovered clean image, where m and N are the length and width of the hyperspectral image space dimension, respectively, and p is the number of spectral bands;

step 2) constructing a multi-channel truncated nuclear norm and a full-variation regularized hyperspectral image denoising model;

Step 3) optimizing a hyperspectral image denoising model by adopting an alternate direction multiplier algorithm (ALTERNATING DIRECTION METHOD OF MULTIPLIERS, ADMM);

And 4) outputting the denoised hyperspectral image.

The invention provides a novel multichannel denoising model aiming at noise values with different variances in different bands. Introducing a weight matrix into data items in different channel cascade truncated nuclear norms; considering the property that the nuclear norms cannot well utilize the characteristic values in the spectrum low-rank prior model, the invention introduces the truncated nuclear norms, and the prior information of the observed data is better utilized by intercepting the first r large singular values, so that the denoising work is better completed; the full variation regularization method utilizes the sparsity of the hyperspectral image, can better reserve the piecewise smoothing prior and effectively keep the edge information, and simultaneously enhances the denoising effect of Gaussian noise; for a multi-channel truncated nuclear norm and total variation regularized hyperspectral image denoising model, the model is solved by utilizing an efficient and simple ADMM algorithm; through verification of a plurality of groups of comparison experiments, the multichannel truncated nuclear norm total variation regularization method is obviously superior to other competitive noise reduction algorithms.

The invention has the advantages that: the segmentation smoothing prior is better reserved, the edge information is effectively kept, and meanwhile, the denoising effect of Gaussian noise is enhanced.

Drawings

Fig. 1 is a hyperspectral image containing noise.

Fig. 2 is a hyperspectral image after noise removal using the present invention.

Fig. 3 is a flow chart of the present invention.

Detailed Description

The technical scheme of the invention is further described below with reference to the accompanying drawings.

The invention relates to a multi-channel truncated nuclear norm and total variation regularized hyperspectral image denoising model, which comprises the following steps:

Step 1) obtaining an image y=x+n with hyperspectral data to be denoised, wherein Y, X, N is Additive White Gaussian Noise (AWGN), X is the recovered clean image, where m and N are the length and width of the hyperspectral image space dimension, respectively, and p is the number of spectral bands;

step 2) constructing a multi-channel truncated nuclear norm and a full-variation regularized hyperspectral image denoising model;

further, definition of the multi-channel truncated kernel norm total variation regularization model in step 2):

Wherein W is a weight matrix and wherein, Is the Frobenius norm, beta, lambda is the regularized term balance parameter,For a given matrix/>Q=min (m, n),Is a finite difference operator with periodic boundary conditions.

Weight matrixIs an identity matrix, the weight matrix W is a diagonal matrix, and is determined by the noise variance of each band, σ ₁,σ₂,…,σ_p corresponds to the noise variance of the channel, respectively.

The optimizing and solving of the hyperspectral image denoising model in the step 3) specifically comprises the following steps:

because of the addition of the weight matrix W and the finite difference operator, a variable splitting method is adopted to solve the new model, and the hyperspectral image denoising model can be reconstructed into the following constraint problems such as linearity and the like by introducing the augmentation variables Q and Z:

(3-1) equation (2) may be optimized using an alternating direction multiplier algorithm, corresponding to an augmented lagrangian function of:

Where Λ ₁,Λ₂ is the augmented Lagrangian multiplier and ρ ₁,ρ₂ > 0 is the penalty parameter, where <. The initial values of matrix variables X, Z, Q, Λ ₁,Λ₂ are set to 0, and the optimal variables for k iterations are denoted by X ^k,Z^k,Λ₁ ^k,Λ₂ ^k, respectively, with k being 0.

(3-2) Solving for the augmented Lagrangian function, one of the variables may be fixed, and the other variables may be alternately minimized. The update process of variable X is as follows:

The solution is as follows:

X^k+1＝(2W^TW+ρ₁ ^k-ρ₂ ^kD^TD)^-1(2W^TWY+ρ₁ ^kZ+D^TQρ₂ ^k+D^TΛ₂ ^k) (5)

Where D ^T is the inverse of D and W ^T is the inverse of W.

(3-3) Update of variable Z:

the solution can be obtained by Partial Singular Value Thresholding (PSVT) algorithm:

(3-4) update of variable Q:

the solution can be obtained by a kringing algorithm:

(3-5) updating penalty parameters:

Λ₁ ^k+1＝Λ₁ ^k+ρ₁(X^k+1-Z^k+1) (10)

Λ₂ ^k+1＝Λ₂ ^k+ρ₂(Q^k+1-DX^k+1) (11)

(3-6) update of ρ ₁,ρ₂:

ρ₁ ^k：ρ₁ ^k+1＝μ*ρ₁ ^k (12)

ρ₂ ^k：ρ₂ ^k+1＝μ*ρ₂ ^k (13)

(3-7) terminating the iteration when the iteration termination condition X ^k+1-Z^k+1||_F≤10^-6,||DX^k+1-Q^k+1||_F≤10^-6 is satisfied.

And 4) outputting the denoised hyperspectral image.

The embodiments described in the present specification are merely examples of implementation forms of the inventive concept, and the scope of protection of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, and the scope of protection of the present invention and equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims (1)

1. A hyperspectral image denoising method based on multichannel truncated nuclear norms and total variation regularization comprises the following steps:

step 1) obtaining a hyperspectral data image y=x+n with the noise to be removed, wherein N is additive white gaussian noise AWGN, X is a recovered clean image, where m and N are the length and width of the hyperspectral image space dimension, respectively, and p is the number of spectral bands;

step 2) constructing a multi-channel truncated nuclear norm and a full-variation regularized hyperspectral image denoising model;

Step 3) optimizing a hyperspectral image denoising model by adopting an alternating direction multiplier algorithm ADMM;

step 4) outputting the denoised hyperspectral image;

The expression formula of the multi-channel truncated nuclear norm and the total variation regularized hyperspectral image denoising model in the step (2) is as follows:

Wherein W is a weight matrix and wherein, Is the Frobenius norm, beta, lambda is the regularized term balance parameter,/>For a given matrix/>Q=min (m, n),

Is a finite difference operator with periodic boundary conditions;

Weight matrix Is an identity matrix, the weight matrix W is a diagonal matrix and is determined by the noise variance of each wave band, and sigma ₁,σ₂,…,σ_p corresponds to the noise variance of the channel respectively;

the optimizing and solving of the hyperspectral image denoising model in the step 3) specifically comprises the following steps:

because of the addition of the weight matrix W and the finite difference operator, a variable splitting method is adopted to solve the new model, and the hyperspectral image denoising model can be reconstructed into the following constraint problems such as linearity and the like by introducing the augmentation variables Q and Z:

(3-1) equation (2) may be optimized using an alternating direction multiplier algorithm, corresponding to an augmented lagrangian function of:

Wherein Λ ₁,Λ₂ is an augmented Lagrangian multiplier, ρ ₁,ρ₂ > 0 is a penalty parameter, and </SUB > represents the trace of the matrix; setting initial values of matrix variables X, Z, Q and lambda ₁,Λ₂ to 0, respectively using X ^k,Z^k,Λ₁ ^k,Λ₂ ^k to represent optimization variables of iterating k times, wherein the initial value of k is 0;

(3-2) solving an augmented lagrangian function, one of the variables being fixed, the other variables being alternately minimized; the update process of variable X is as follows:

The solution is as follows:

X^k+1＝(2W^TW+ρ₁ ^k-ρ₂ ^kD^TD)^-1(2W^TWY+ρ₁ ^kZ+D^TQρ₂ ^k+D^TΛ₂ ^k) (5)

Wherein D ^T is the inverse of D, W ^T is the inverse of W;

(3-3) update of variable Z:

The solution can be obtained by PSVT algorithm:

(3-4) update of variable Q:

the solution can be obtained by a kringing algorithm:

(3-5) updating penalty parameters:

Λ₁ ^k+1＝Λ₁ ^k+ρ₁(X^k+1-Z^k+1) (10)

Λ₂ ^k+1＝Λ₂ ^k+ρ₂(Q^k+1-DX^k+1) (11)

(3-6) update of ρ ₁,ρ₂:

ρ₁ ^k：ρ₁ ^k+1＝μ*ρ₁ ^k (12)

ρ₂ ^k：ρ₂ ^k+1＝μ*ρ₂ ^k (13)

(3-7) terminating the iteration when the iteration termination condition X ^k+1-Z^k+1||_F≤10^-6,||DX^k+1-Q^k+1||_F≤10^-6 is satisfied.