CN109658340A - The SAR image rapid denoising method saved based on RSVD and histogram - Google Patents

Abstract

The invention discloses a kind of SAR image rapid denoising methods saved based on RSVD and histogram, this method carries out logarithmic transformation to SAR image first, multiplicative noise is converted to additive noise, then non local similar image Block- matching is carried out, then low-rank matrix is carried out to the low-rank matrix that non local similar image block forms using random singular value decomposition to approach, texture enhancing is carried out to image using the method that histogram of gradients saves again, finally by image block reset, the quick denoising to SAR image is realized.It is on MSTAR database the experimental results showed that, compared with the conventional method, method proposed by the present invention be obviously improved edge keep index while, denoising speed accelerate three times.

Description

Fast denoising method of SAR image based on RSVD and histogram preservation

technical field

The invention belongs to the technical field of radar image processing, and in particular relates to a fast denoising method for SAR images based on RSVD and histogram preservation.

Background technique

Synthetic Aperture Radar (SAR) images provide useful information for remote sensing mapping, ground monitoring, automatic target recognition, and other fields. However, due to the difference in the distances of many scattering points reaching the radar in a resolution unit of the radar radiation area, their echo phases are also different. The coherent superposition of echoes inevitably produces speckle noise in SAR images. Affected by speckle noise, the visual quality of the observed SAR image is degraded, and its edge information is also weakened. Therefore, speckle noise removal is a critical task before subsequent image segmentation, detection, and classification. SAR image denoising has traditional filtering algorithms based on spatial domain, such as Lee, Kuan, Frost, GammaMAP and enhanced Lee filter, enhanced Frost filter, etc., which basically use the local small block information of the image for denoising, which is easy to over-smooth. And the problem of losing texture details. With the improvement of signal processing methods, wavelet transform has been applied to SAR image denoising, but this method cannot effectively express the edge information of the image; then multi-scale analysis methods such as Contourlet transform appeared. In recent years, Markov random field, Gibbs random field, BLS-GSM (Bayes Least Squares-Gaussian Scale Mixtures) and other models of SAR image denoising have achieved good denoising results. In addition, Buades et al. applied the non-local model to image denoising, and designed a non-local means (NL-means) denoising method, which has poor denoising effect in the image edge region. K.Dabov proposed a three-dimensional block matching (Block Matching and 3D filtering, BM3D) algorithm, this method has good denoising effect, but the algorithm complexity is high.

In 2006, Terrence Tao et al. proposed Low Rank Matrix Approximation (LRMA), which was introduced into image denoising, that is, the original low-rank matrix was recovered from the noise-contaminated matrix. The methods of low-rank matrix approximation can generally be divided into two categories: low-rank matrix factorization (LRMF) and nuclear norm minimization (NNM). Since there are many similar image blocks in SAR images, and similar blocks have similar structural and data characteristics, the matrix they consist of can be considered to be approximately low-rank, so NNM can be applied to SAR image denoising.

The disadvantage of the NNM algorithm is that the singular values are treated equally in the calculation process, resulting in a large deviation. In the literature to improve this method, a spatially adaptive iterative singular value thresholding (SAIST) method combining non-local image similarity and low-rank model is proposed. Since the real information of the signal is mainly concentrated in the larger singular values, and the noise is mainly reflected in the small singular values, the Weighted Nuclear Norm Minimization (WNNM) method is proposed, that is, for large singular values value, use small weights, and use large weights for small singular values, the algorithm can better approximate low-rank matrices. However, the disadvantage of the WNNM algorithm is that it needs to perform singular value decomposition in each iteration, which consumes a lot of computing time. Also, WNNM will over-smooth texture details. Therefore, consider replacing the singular value decomposition with RSVD (stochastic singular value decomposition) with fewer iterations to improve the denoising efficiency, and use GHP (gradient histogram preservation) to enhance the image texture in the denoising process.

SUMMARY OF THE INVENTION

In view of the above-mentioned deficiencies of the prior art, the purpose of the present invention is to provide a fast denoising method for SAR images based on RSVD and histogram preservation, so as to solve the problems existing in the denoising algorithms in the prior art; Perform logarithmic transformation, convert multiplicative noise into additive noise, and then perform non-locally similar image block matching, and then use random singular value decomposition to perform low-rank matrix approximation on the low-rank matrix composed of non-locally similar image blocks, and then use gradient. The histogram preservation method enhances the texture of the image, and finally resets the image block to achieve fast denoising of the SAR image. The experimental results on the MSTAR database show that, compared with the existing methods, the method proposed in the present invention can significantly improve the edge retention index, and at the same time, the denoising speed is accelerated by three times.

For achieving the above object, the technical scheme adopted in the present invention is as follows:

A method for fast denoising of SAR images based on RSVD and histogram preservation of the present invention includes the following steps:

(1) Establish the speckle noise model of the SAR image, that is, convert the multiplicative noise into additive noise through logarithmic transformation;

(2) Use non-local similarity to perform block matching on the transformed image;

(3) RSVD is used to decompose the low-rank matrix composed of non-locally similar image blocks to achieve low-rank matrix approximation;

(4) Using the gradient histogram preservation method to enhance the texture of the SAR image;

(5) Reset the image block to obtain the denoised SAR image.

Further, the step (1) specifically includes: establishing a multiplicative noise model of the SAR image, that is, Y(x,y)=X(x,y)N(x,,y) where Y(x,y) is The SAR image with speckle noise added is the final observation image; X(x,y) is the original SAR image; N(x,y) is the coherent speckle noise; X(x,y) and N(x,y) are independent random processes. The speckle noise N(x,y) obeys a Gamma distribution with a mean of 1 and a variance of 1/L. Its probability density function is: Among them, L is the equivalent apparent number, and e is the natural base; taking the logarithm of both sides of Y(x,y)=X(x,y)N(x,y) at the same time, the multiplicative noise is converted into a common additive Sexual noise: lg(Y(x,y))=lg(X(x,y))+lg(N(x,y)).

Further, the step (2) specifically includes:

(21) dividing the original image into several image blocks of the same size, and searching for its non-locally similar image blocks according to the designated image blocks;

(22) Integrate non-locally similar image blocks into a matrix to form a low-rank matrix.

Further, the step (3) specifically includes:

(31) Generate an n×l-dimensional Gaussian random matrix Ω;

(32) Multiply the Gaussian random matrix Ω by the m×n-dimensional original matrix A to be decomposed to construct an m×l-dimensional sample matrix Y=AΩ;

(33) QR decomposition is performed on the matrix Y to obtain an m×l-dimensional orthogonal matrix Q;

(34) Construct an 1×n-dimensional matrix B=Q ^T ×A, and finally perform singular value decomposition on matrix B, that is, B=SΛV ^T ;

(35) make QS=U obtain the singular value decomposition of A, namely A=UΛV ^T ;

Among them, l is much smaller than the smaller value of m and n, S is a square matrix of l × l, Λ is a diagonal matrix of l × n, the elements on the diagonal are called singular values, and V ^T is the value of V Transpose, is an n×n square matrix.

Further, the step (4) specifically includes:

(41) First estimate the gradient histogram h _r of the original image x, and use it as the reference gradient, and take the updated image as close to the reference gradient histogram as the constraint condition to obtain the result image; among them, the gradient histogram h The formula for solving _r is as follows:

where d is a constant, R(h _x ) is the regularization term based on the prior information of the natural image gradient histogram, is the gradient of the noise n, h _y , h _x and h _g are the histograms of the noise image, the original image and the gradient g, respectively;

(42) To make the denoised image The gradient histogram of is approximated by the reference histogram h _r , and the denoising model saved based on the gradient histogram is as follows:

sth _f = h _r

in, For the gradient operation, F is an odd function monotonically increasing on (0, +∞), and h _f is the transformed gradient image Histogram, hr is the histogram of the original image, _R (x) is the regularization term, λ is a normal constant, σ _n ² is the noise variance, and μ is a constant.

Beneficial effects of the present invention:

1. The present invention can improve the denoising efficiency of the SAR image and reduce the denoising time;

2. The present invention improves the peak signal-to-noise ratio of the denoised image;

3. The present invention improves the edge retention capability of the denoised image;

4. The present invention improves the equivalent view count of the denoised image.

Description of drawings

Fig. 1 is the principle block diagram of the SAR image denoising method of the present invention;

Figure 2a is a schematic diagram of the original 128×128 SAR image;

Figure 2b is the original 128×128 SAR image after denoising by SAIST;

Figure 2c is the original 128×128 SAR image after denoising by WNNM;

FIG. 2d is the effect diagram of the original 128×128 SAR image after denoising by the method of the present invention.

Detailed ways

In order to facilitate the understanding of those skilled in the art, the present invention will be further described below with reference to the embodiments and the accompanying drawings, and the contents mentioned in the embodiments are not intended to limit the present invention.

Referring to Figure 1, a method for fast denoising of SAR images based on RSVD and histogram preservation of the present invention includes the following steps:

(1) Establish the speckle noise model of the SAR image, that is, convert the multiplicative noise into additive noise through logarithmic transformation;

(2) Use non-local similarity to perform block matching on the transformed image;

(3) RSVD is used to decompose the low-rank matrix composed of non-locally similar image blocks to achieve low-rank matrix approximation;

(4) The method of gradient histogram preservation is introduced into the iterative regular term of SAR image denoising to achieve texture enhancement of SAR images;

(5) Finally, reset the image block to obtain the denoised SAR image.

The invention adopts the SAR images of T72_SN132 (main battle tank), BMP_SN9563 (armored vehicle) and BTR70_SNC71 (armored vehicle) in the data set disclosed by the MSTAR project jointly funded by the US Defense Advanced Research Projects Agency and the US Air Force Research Laboratory as experimental data.

First, add Gaussian white noise with a variance of 70 to the original SAR image in Fig. 2a, and then use the WNNM method, the SAIST method and the fast SAR image denoising algorithm proposed by the present invention to denoise, and compare the denoising results. Figure 2b, Figure 2c, Figure 2d are the denoising results of the SAR image of T72_SN132 after denoising by three algorithms.

It can be seen from Figure 2b, Figure 2c and Figure 2d that, compared with the WNNM algorithm and the SAIST algorithm, the method of the present invention better retains the edge and texture details of the target while denoising, and has better visual effects.

In order to describe the performance of the denoising algorithm more accurately, the Equivalent Number of Looks (ENL), the Edge Preserve Index (EPI), and the Peak Signal to Noise Ratio (PSNR) are selected for these three The denoising performance of this algorithm is analyzed. The larger the ENL, the better the visual effect of the denoised image; the larger the EPI, the stronger the edge preservation ability of the algorithm; the larger the PSNR, the stronger the denoising ability of the algorithm. Table 1 lists the results of the three objective evaluation indicators after the SAR images of the three targets are denoised by the above three denoising algorithms. Table 1 is as follows:

Table 1

From the evaluation indicators in Table 1, the PSNR of the image denoised by the method of the present invention is slightly improved compared with the other two algorithms, which shows that the denoising ability of the method of the present invention is relatively strong; The ENL of the image denoised by the method has a certain degree of improvement compared with the other two algorithms, which shows that the visual effect of the image denoised by the method of the present invention is better than that of the other two algorithms; the EPI of the image denoised by the method of the present invention is higher than that of other algorithms. two algorithms, which shows that the edge-preserving ability of the method of the present invention is significantly better than the other two algorithms.

In order to accurately compare the denoising efficiency of the three algorithms, Table 2 lists the denoising consumption of the SAR images of the above three targets by the SAIST algorithm, the WNNM algorithm and the SAR image fast denoising algorithm with minimum kernel norm proposed by the present invention. time t. Table 2 is as follows:

Table 2

It can be seen from Table 2 that for the same target, the denoising speed of the method of the present invention is 3 times faster than that of the SAIST algorithm, and 4 times faster than that of the WNNM algorithm, and the denoising efficiency is significantly improved. From the above analysis, it can be seen that, compared with the SAIST algorithm and the WNNM algorithm, the method of the present invention can greatly improve the denoising efficiency while having better edge retention capability, and has improved both the peak signal-to-noise ratio and the equivalent view count. .

There are many specific application ways of the present invention, and the above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, several improvements can be made. These Improvements should also be considered as the protection scope of the present invention.

Claims (5)

1. a SAR image fast denoising method based on RSVD and histogram preservation, is characterized in that, comprises the steps: (1) Establish the speckle noise model of the SAR image, that is, convert the multiplicative noise logarithmically into additive noise; (2) Use non-local similarity to perform block matching on the transformed image; (3) RSVD is used to decompose the low-rank matrix composed of non-locally similar image blocks to achieve low-rank matrix approximation; (4) Using the gradient histogram preservation method to enhance the texture of the SAR image and realize the denoising of the SAR image; (5) Reset the image block to obtain the denoised SAR image. 2. the SAR image fast denoising method based on RSVD and histogram preservation according to claim 1, is characterized in that, described step (1) specifically comprises: establish SAR image multiplicative noise model, namely Y(x,y )=X(x,y)N(x,y), where Y(x,y) is the SAR image with speckle noise added, that is, the final observation image; X(x,y) is the original SAR image; N(x,y) is speckle noise; X(x,y) and N(x,y) are independent random processes, the speckle noise N(x,y) obeys the mean of 1 and the variance is 1/L The Gamma distribution of , and its probability density function is: Among them, L is the equivalent apparent number, and e is the natural base; taking the logarithm of both sides of Y(x,y)=X(x,y)N(x,y) at the same time, the multiplicative noise is converted into a common additive Sexual noise: lg(Y(x,y))=lg(X(x,y))+lg(N(x,y)). 3. the SAR image fast denoising method based on RSVD and histogram preservation according to claim 1, is characterized in that, described step (2) specifically comprises: (21) dividing the original image into several image blocks of the same size, and searching for its non-locally similar image blocks according to the designated image blocks; (22) Integrate non-locally similar image blocks into a matrix to form a low-rank matrix. 4. the SAR image fast denoising method based on RSVD and histogram preservation according to claim 1, is characterized in that, described step (3) specifically comprises: (31) Generate an n×l-dimensional Gaussian random matrix Ω; (32) Multiply the Gaussian random matrix Ω by the m×n-dimensional original matrix A to be decomposed to construct an m×l-dimensional sample matrix Y=AΩ; (33) QR decomposition is performed on the original matrix Y to obtain an m×l-dimensional orthogonal matrix Q; (34) Construct an 1×n-dimensional matrix B=Q ^T ×A, and finally perform singular value decomposition on matrix B, that is, B=SΛV ^T ; (35) make QS=U obtain the singular value decomposition of A, namely A=UΛV ^T ; Among them, l is much smaller than the smaller of m and n, Q ^T is the transpose of Q, S is a square matrix of l × l, Λ is a diagonal matrix of l × n, and the elements on the diagonal are called Singular values, V ^T is the transpose of V and is an n×n square matrix. 5. the SAR image fast denoising method based on RSVD and histogram preservation according to claim 1, is characterized in that, described step (4) specifically comprises: (41) First estimate the gradient histogram h _r of the original image x, and use it as the reference gradient, and take the updated image as close to the reference gradient histogram as the constraint condition to obtain the result image; among them, the gradient histogram h The formula for solving _r is as follows: where d is a constant, R(h _x ) is the regularization term based on the prior information of the natural image gradient histogram, is the gradient of the noise n, h _y , h _x and h _g are the histograms of the noise image, the original image and the gradient g, respectively; (42) To make the denoised image The gradient histogram of is approximated by the reference histogram h _r , and the denoising model saved based on the gradient histogram is as follows: sth _f = h _r Among them, ▽ is the gradient operation, F is a monotonically increasing odd function on (0, +∞), h _f is the transformed gradient image |F(▽x)| histogram, h _r is the histogram of the original image , R(x) is the regularization term, λ is a constant, σ _n ² is the noise variance, and μ is a constant.