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

Abstract

A hyperspectral image denoising method based on multi-channel truncated nuclear norm and total variation regularization includes the following steps: 1) obtaining a hyperspectral data image to be denoised, wherein N is additive white Gaussian noise (AWGN), X is a restored clean image, wherein m and n are respectively the length and width of the hyperspectral image spatial dimension, and p is the number of spectral bands; 2) constructing a hyperspectral image denoising model based on multi-channel truncated nuclear norm and total variation regularization; 3) optimizing the model using an alternating direction multiplier algorithm (ADMM); 4) outputting a hyperspectral image after denoising. The advantages of the present invention are: better retaining the piecewise smoothing prior and effectively maintaining edge information, while enhancing the denoising effect of Gaussian noise.

Description

Hyperspectral image denoising based on multi-channel truncated nuclear norm and total variation regularization Method

Technical Field

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

technical background

Hyperspectral remote sensing images contain rich spatial and spectral information, and have attracted widespread attention in various application fields, such as urban planning, mapping, agriculture, forestry, and monitoring. However, hyperspectral images (HSI) acquired by multiple detectors are usually damaged by different types of noise, which seriously reduces the quality of the image and limits the accuracy of subsequent tasks such as classification, recognition, and unmixing. Therefore, hyperspectral image denoising has very important value and significance in current academic research.

In recent years, hyperspectral image denoising has attracted the attention of many scholars at home and abroad. So far, many different denoising methods have been proposed for hyperspectral images. Traditional methods treat each channel of the hyperspectral image as a grayscale image and process it one by one, such as K-SVD, Block-matching and 3D filtering (BM3D), etc. However, these methods ignore the correlation between different spectral bands, which will lead to poor denoising effect. The latest denoising methods improve the denoising performance by combining spatial low rank with spectral low rank. The representative method is principal component analysis (PCA), which uses orthogonal transformation to convert the hyperspectral image into a set of linearly uncorrelated variables, called principal components (PCs). 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. Therefore, the first PCs can be inversely transformed to denoise the hyperspectral data. The characteristics of the sensor will cause unequal noise variances in different spectral bands during the acquisition process, making the hyperspectral image denoising problem more complicated. If each channel is processed the same way during the joint denoising process, artifacts will appear.

Summary of the invention

The present invention aims to overcome the above-mentioned shortcomings of the prior art, and proposes a hyperspectral image denoising method based on multi-channel truncated nuclear norm and total variation regularization according to different noise characteristics in different channels and combined with the internal correlation of hyperspectral image channels.

The technical solution adopted by the present invention to solve the technical problem is:

A hyperspectral image denoising method based on multi-channel truncated nuclear norm and total variation regularization comprises the following steps:

Step 1) Obtain the hyperspectral data image Y=X+N with noise to be removed, where Y, X, N is additive white Gaussian noise (AWGN), X is the restored clean image, where m and n are the length and width of the spatial dimension of the hyperspectral image, respectively, and p is the number of spectral bands;

Step 2) constructing a hyperspectral image denoising model with multi-channel truncated nuclear norm and total variation regularization;

Step 3) Using the Alternating Direction Method of Multipliers (ADMM) algorithm to optimize the hyperspectral image denoising model;

Step 4) Output the denoised hyperspectral image.

The present invention proposes a novel multi-channel denoising model for noise values with different variances in different spectral bands. A weight matrix is introduced for data items in the cascaded truncated nuclear norms of different channels; considering that the nuclear norm cannot make good use of the properties of eigenvalues in the spectral low-rank prior model, the present invention introduces the truncated nuclear norm, which better utilizes the prior information of the observed data by intercepting the first r large singular values, thereby better completing the denoising work; the total variation regularization method utilizes the sparsity of the hyperspectral image, can better retain the piecewise smoothing prior and effectively maintain the edge information, and at the same time enhances the denoising effect of Gaussian noise; for the hyperspectral image denoising model of multi-channel truncated nuclear norm and total variation regularization, the present invention uses the efficient and simple ADMM algorithm to solve this model; through multiple groups of comparative experiments, it is verified that the multi-channel truncated nuclear norm total variation regularization method is significantly better than other competitive denoising algorithms.

The advantages of the present invention are: better retaining the piecewise smoothness prior and effectively maintaining edge information, while enhancing the denoising effect of Gaussian noise.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a hyperspectral image containing noise.

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

FIG3 is a flow chart of the present invention.

Detailed ways

The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

The multi-channel truncated nuclear norm and total variation regularized hyperspectral image denoising model of the present invention comprises the following steps:

Step 1) Obtain the hyperspectral data image Y=X+N with noise to be removed, where Y, X, N is additive white Gaussian noise (AWGN), X is the restored clean image, where m and n are the length and width of the spatial dimension of the hyperspectral image, respectively, and p is the number of spectral bands;

Step 2) constructing a hyperspectral image denoising model with multi-channel truncated nuclear norm and total variation regularization;

Further, the definition of the multi-channel truncated nuclear norm total variation regularization model described in step 2) is:

Where W is the weight matrix, is the Frobenius norm, β, λ are the regularization term balance parameters, For a given matrix/> The truncated nuclear norm of , q = min(m,n), is a finite difference operator with periodic boundary conditions.

Weight Matrix is the identity matrix, the weight matrix W is a diagonal matrix and is determined by the noise variance of each band, σ ₁ , σ ₂ , …, σ _p correspond to the noise variance of the channel respectively.

The optimization solution of the hyperspectral image denoising model described in step 3) specifically includes:

Due to the addition of the weight matrix W and the finite difference operator, the variable splitting method is used to solve the new model. By introducing augmented variables Q and Z, the hyperspectral image denoising model can be reconstructed into the following linear equiconstrained problem:

(3-1) Formula (2) can be optimized using the alternating direction multiplier algorithm, and the corresponding augmented Lagrangian function is:

Where Λ ₁ , Λ ₂ are augmented Lagrange multipliers, ρ ₁ , ρ ₂ > 0 are penalty parameters, and <·> represents the trace of the matrix. The initial values of the matrix variables X, Z, Q, Λ ₁ , Λ ₂ are set to 0, and X ^k , Z ^k , Λ ₁ ^k , Λ ₂ ^k are used to represent the optimization variables of iteration k, respectively, and the initial value of k is 0.

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

The solution is:

X ^k+1 ＝(2W ^T W+ρ ₁ ^k −ρ ₂ ^k D ^T D) ⁻¹ (2W ^T WY+ρ ₁ ^k Z+D ^T Qρ ₂ ^k +D ^T Λ ₂ ^k ) (5)

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

(3-3) Update of variable Z:

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

(3-4) Update of variable Q:

The solution can be obtained by the shrinkage algorithm:

(3-5) Update of penalty parameters:

Λ ₁ ^k+1 ＝Λ ₁ ^k +ρ ₁ (X ^k+1 -Z ^k+1 ) (10)

Λ ₂ ^k+1 ＝Λ ₂ ^k +ρ ₂ (Q ^k+1 -DX ^k+1 ) (11)

(3-6) Update of ρ ₁ , ρ ₂ :

ρ ₁ ^k ：ρ ₁ ^k+1 ＝μ*ρ ₁ ^k (12)

ρ ₂ ^k ：ρ ₂ ^k+1 ＝μ*ρ ₂ ^k (13)

(3-7) When the iteration termination conditions ||X ^k+1 -Z ^k+1 || _F ≤10 ^-6 , ||DX ^k+1 -Q ^k+1 || _F ≤10 ^-6 are met, the iteration is terminated.

Step 4) Output the denoised hyperspectral image.

The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to 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.