CN112927169A - Remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization - Google Patents
Remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization Download PDFInfo
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Abstract
The invention discloses a remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization, which comprises the following steps: the method comprises the steps of firstly estimating the noise variance of a noise image by using a wavelet transform method, then searching similar image blocks by using the pixel similarity of neighborhood image blocks, carrying out singular value decomposition and singular value soft thresholding on the similar image blocks, traversing the whole image, and finally carrying out edge enhancement processing by using a canny operator to obtain a denoised image with clear edges. Compared with NLM and a conventional WNNM method for removing noise in remote sensing images, the method is simple to operate, and can obtain higher PSNR value and better visual effect.
Description
Technical Field
The invention belongs to the technical field of remote sensing images, and particularly relates to a remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization.
Background
Non-local self-similarity means that an image block has many similar blocks at other positions in the whole image range where the image block is located, that is, a clean image structure has redundancy, so that the similar blocks of an image block may exist at any position of the whole image. The weighted kernel norm minimization method is an image denoising method provided on the basis of non-local self-similarity, and due to the characteristics of high efficiency and accuracy, the influence degree of different singular values on a model is improved, so that the denoising effect is improved, and the method is generally applied to the field of image processing. The wavelet transform can automatically adapt to the requirement of video signal analysis, so as to achieve the purpose of focusing on any details of signals, overcome the difficult problems of incapability of processing non-stationary signals and inconvenience caused by fixed window shapes, and is known as a 'mathematical microscope' in the field of signal transform. Therefore, the method for decomposing the image signal by using the wavelet transform and denoising by combining the weighted nuclear norm minimization has important significance for denoising the remote sensing image. However, the conventional application of wavelet transform does not involve the separate application of scale 1 information in multi-scale decomposition, and in the process of processing images by the weighted nuclear norm minimization method, the searching for image similar blocks becomes more difficult as the amount of image information increases.
Some organizations have developed directions for non-local self-similarity based applications, and a low rank matrix recovery algorithm is one of them. The optimization methods for low rank matrix recovery can be divided into two categories: low rank matrix decomposition methods and nuclear norm minimization. For example, the low-rank matrix recovery model adopted by Zhang et al has a good effect of removing various model noises in the remote sensing image. Dabov K. et al utilize 3D data arrays in the transform domain to achieve sparsity enhancement, which effectively filters out noise in the remote sensing images.
However, in any method, the information of the image is lost to some extent, which results in smoothing of some pixels and accuracy of image denoising.
The image noise variance is an important information essential in the denoising process of the weighted nuclear norm minimization method, so that the estimation of the noise variance is necessary for an image with unknown noise variance. In the original weighted nuclear norm minimization method process, when the Euclidean distance is adopted to search for the image similar blocks, relatively more errors and image denoising precision are caused due to position information, and pixel information can be utilized to the maximum extent by using the gray value of a pixel to search for the image similar blocks, so that the similar blocks are searched more accurately, and the denoising precision is improved. Wavelet transformation is typically used to pre-process the transformation of a signal from the spatial domain to the frequency domain without separately using information on the diagonal of scale 1 in a multi-scale two-dimensional wavelet decomposition process to estimate the noise variance.
Disclosure of Invention
The invention aims to provide a remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization, so as to improve the precision of remote sensing denoising and improve the visual effect.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
in order to achieve the purpose, the invention adopts the following technical scheme:
the remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization comprises the following steps:
s1, carrying out two-dimensional multi-scale wavelet decomposition on the image
Calculating variance in the diagonal component coefficient of the decomposed first scale, and estimating a noise variance value of the image;
s2, denoising by using improved weighted nuclear norm minimization method
s2.1. search of similar image blocks
S2.1.1, determining similarity and gray value of an image block by using each pixel and adjacent pixels in the image block, and determining a feature vector of the image block;
s2.1.2, determining a small image block set by uniformly sampling pixels of the positive image;
s2.1.3, constructing a k-dimensional tree representing the image block set by using the image block set;
s2.1.4, dividing the image into several sub-images without overlapping;
s2.1.5 constructing a k-dimensional tree of the image from the subgraph, and searching similar image blocks in the k-dimensional tree;
s2.1.6, determining the k-dimensional tree containing the most similar image blocks and searching out similar image blocks, namely similar image blocks to be searched;
s2.2 singular value decomposition of similar blocks
s2.3 singular value soft thresholding operation
Traversing the whole image in the step of S2, and resetting the images in sequence after the step is finished;
s3, calculating the peak signal-to-noise ratio of the image, setting the peak signal-to-noise ratio as a limiting condition, and iterating the steps S1 and S2;
s4, performing edge enhancement on the denoised image by using a Canny algorithm, wherein the final output image is the required image.
Preferably, in step S1, the noise variance value of the image is estimated by using the variance of the diagonal component coefficient of the first scale obtained by wavelet decomposition, which is as follows:
after the multi-scale two-dimensional wavelet decomposition is completed, low-frequency coefficients in the horizontal, vertical and diagonal directions under corresponding scales can be obtained, and are expressed as follows:
wherein ,
、
、
respectively representing low frequency coefficients in the horizontal, vertical and diagonal directions,k，mrespectively representing the coordinates corresponding to the pixels of the image after decomposition,zrepresenting the entire image. Since the decomposition in the diagonal direction is a low-frequency signal in the wavelet decomposition process, and the image information included in the multi-scale signal decomposition gradually decreases as the decomposition proceeds, the noise signal included in the diagonal decomposition information of the scale 1 is the most, and therefore, the variance is calculated for the diagonal component of the first scale, as follows:
wherein ,
the diagonal decomposition information representing the scale 1,
the average of the diagonal decomposition information representing scale 1,
i.e. the estimated noise variance of the noisy image.
Preferably, the method for determining the s2.1 image block feature vector specifically includes:
firstly, determining that each image block contains 25 pixel values which are respectively marked as p1, p2, … … and p25, calculating the similarity between the image block and 8 surrounding image blocks by using the following formula (5), respectively marked as s1, s2, … … and s8, combining the 25 pixel values and the 8 similarity values into a vector, and performing normalization processing to obtain the required feature vector EV = [ p1, p2, … …, p25, s1, s2, … … and s8 ].
in the formula aIn order to control the parameters of the device,
for the image blocks to be processed,
is the first of the surroundingsiAnd each image block.
Preferably, the k-dimensional tree of s2.1.3 is determined as follows:
calculating the standard deviation of each dimension of the feature vector by formula (6) for the feature vectors of all image blocks in the corresponding set of image blocks,
wherein ,
is the value of the characteristic of the image,
is the mean of the corresponding feature vectors,mand (3) selecting the one-dimensional features with the largest standard deviation for the number of the image blocks, solving the median of the dimension-changing features, wherein the median is the root node of the k-dimensional tree, dividing the image block set into two parts by utilizing the root node, wherein the image blocks smaller than the root node are positioned on the left side of the tree and the image blocks larger than the root node are positioned on the right side of the tree, and repeating the operation on the image blocks on the left side and the image blocks on the right side until the image blocks cannot be divided.
Preferably, the S3 sets the peak signal-to-noise ratio as a limiting condition, specifically as follows:
the peak signal-to-noise ratio value is used as a judgment standard for stopping iteration, namely, in the image iteration operation process, the iteration is stopped immediately when the peak signal-to-noise ratio value is judged to be larger than or equal to the peak signal-to-noise ratio result of the next iteration.
The invention has the following advantages:
(1) the image noise method is more convenient and faster to estimate:
the noise variance of the image is estimated by using the diagonal component coefficient of the first scale of wavelet decomposition, so that the operation is simpler and more convenient, and the efficiency can be improved;
(2) the precision is higher after denoising:
after the remote sensing image is denoised, compared with NLM, BM3D and a traditional weighted nuclear norm minimization method, the peak signal-to-noise ratio is higher, and partial edge information can be recovered.
Drawings
FIG. 1 is a flow chart of a remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization according to the present invention;
FIG. 2 is a comparison graph of denoising results of a house dense area with a noise variance of 0.001;
FIG. 3 is a comparison graph of denoising results of a house dense area with a noise variance of 0.005;
FIG. 4 is a comparison graph of denoising results of a house dense area with a noise variance of 0.01;
FIG. 5 is a comparison graph of the denoising result of a farmland region with a noise variance of 0.001;
FIG. 6 is a comparison graph of the denoising result of the farmland region with a noise variance of 0.005;
FIG. 7 is a comparison graph of the denoising result of the farmland region with a noise variance of 0.01.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
as shown in fig. 1-7, the present invention mainly solves two problems:
(1) the image noise variance estimation method comprises the following steps:
high-frequency information and low-frequency information of the image can be extracted after multi-scale two-dimensional wavelet decomposition, information in the diagonal direction of the low-frequency information is decomposed, the information comprises the most noise information, and almost all the noise information is contained in the scale 1.
(2) Finding image similar blocks by using pixel similarity:
the searching of the image similar block by using the pixel similarity can utilize the pixel information to the maximum extent, so that the similar block is more accurately searched, and the denoising precision is improved.
The specific idea for solving the problems is as follows:
through research, after the image is subjected to the scale two-dimensional wavelet decomposition, the information in the diagonal direction of the scale 1 contains almost all noise information because the information has low frequency and the noise is almost all low-frequency.
Therefore, an idea of performing noise estimation of a video by calculating a variance of diagonal direction information in the scale 1 is proposed.
Low-frequency coefficient in diagonal direction:
，k，mrespectively representing the coordinates corresponding to the pixels of the image after decomposition,zrepresenting the entire image. The variance is calculated for the diagonal component of the first scale:
At 25 pixelsTaking the value as an example, first determine that each image block contains 25 pixel values, denoted as p1, p2, … …, and p25, and calculate the similarity between the image block and its surrounding 8 image blocks:
s1, s2, … … and s8 respectively, and then combining 25 pixel values and 8 values of similarity into a vector, and performing normalization processing to obtain a feature vector: EV = [ p1, p2, … …, p25, s1, s2, … …, s8]Calculating the standard deviation of each dimension of the feature vector for the feature vectors of all the image blocks in the corresponding image block set
Then, selecting the one-dimensional feature with the largest standard deviation, solving the median of the dimension-changing features, wherein the median is the root node of the k-dimensional tree, dividing the image block set into two parts by using the root node, wherein the image block smaller than the root node is positioned on the left side of the tree, and the image block larger than the root node is positioned on the right side, repeating the operation on the image blocks on the left side and the right side until the image blocks can not be divided, constructing the k-dimensional tree representing the image block set, and finally determining the k-dimensional tree containing the most similar image blocks and searching the image blocks similar to the k-dimensional tree, namely the similar image blocks to be searched.
The invention is described in further detail below with reference to the accompanying drawings and the detailed description;
the embodiment of the invention carries out denoising processing on the images with different noise levels in the dense house area and the farmland area of the multispectral image of the high-resolution second-order satellite.
With reference to fig. 1, a remote sensing image denoising method based on wavelet transform and improved weighted nuclear norm minimization includes the following steps:
s1 performing two-dimensional multi-scale wavelet decomposition on the image
Calculating variance in the diagonal component coefficient of the decomposed first scale, and estimating a noise variance value of the image;
s2, denoising by using improved weighted nuclear norm minimization method
s2.1. search of similar image blocks
S2.1.1, determining similarity and gray value of an image block by using each pixel and adjacent pixels in the image block, and determining a feature vector of the image block;
s2.1.2 determining a small image block set by uniformly sampling pixels of the whole image;
s2.1.3, constructing a k-dimensional tree representing the image block set by using the image block set;
s2.1.4, dividing the image into several sub-images without overlapping;
s2.1.5 constructing a k-dimensional tree of the image from the subgraph, and searching similar image blocks in the k-dimensional tree;
s2.1.6, determining the k-dimensional tree containing the most similar image blocks and searching out similar image blocks, namely similar image blocks to be searched;
s2.2 singular value decomposition of similar blocks
s2.3 singular value soft thresholding operation
Traversing the whole image in the step s2, and resetting the images in sequence after the step s2 is finished;
s3, calculating the peak signal-to-noise ratio of the image, setting the peak signal-to-noise ratio as a limiting condition, and iterating the steps s1 and s 2;
and s4, performing edge enhancement on the denoised image by using a canny algorithm, wherein the finally output image is the required image.
From fig. 2 to fig. 7, which are the results of denoising images with different noise levels in different regions, it can be seen that all the denoised images have different smoothing phenomena, wherein the smoothing phenomenon of the image of the NLM method is severe and some noise points still exist, and the images processed by the original WNNM and the improved method of the present invention have better visual effect, but in contrast, the edge smoothing phenomenon of the original WNNM method is still slightly severe.
It can be seen from the PSNR of table 1 that all denoising methods gradually weaken the denoising effect with noise emphasis, the PSNR values of the WNNM and the text method are the highest under different conditions compared to other contrast methods, and the PSNR after denoising in the text method is slightly higher than the original WNNM, when the noise variance is smaller than 0.001, the PSNR of the denoised image in two different scenes can both reach more than 35dB, which is respectively improved by 6.5% and 5.6% compared to the original WNNM. Meanwhile, as can be seen from comparison of the structural similarity data in table 2, the structural similarity of the noise images in different regions is kept best under different noise conditions, and both can reach about 99%, and when the noise variance is 0.001, the structural similarity can reach more than 99%.
TABLE 1 PSNR comparison table for denoising by different methods
TABLE 2 denoise SSIM comparison table by different methods
The above description is the preferred embodiment of the present invention, and it is within the scope of the appended claims to cover all modifications of the invention which may occur to those skilled in the art without departing from the spirit and scope of the invention.
Claims (6)
1. The remote sensing image denoising method based on wavelet transformation and improved weighted nuclear norm minimization is characterized by comprising the following steps of: the method comprises the following steps:
s1, performing two-dimensional multi-scale wavelet decomposition on images
Calculating variance in the diagonal component coefficient of the decomposed first scale, and estimating a noise variance value of the image;
s2 improved weighted kernel norm minimization method denoising
Step 1: search for similar image blocks
Determining similarity and gray value of the image block by using the pixels in the image block and the neighborhood pixels thereof, and determining the feature vector of the image block;
determining a small image block set by uniformly sampling pixels of the correctness image;
constructing a k-dimensional tree representing the image block set by using the image block set;
dividing the image into several sub-images without overlapping;
constructing a k-dimensional tree of the image from the subgraph, and searching similar image blocks in the k-dimensional tree;
determining a k-dimensional tree containing the most similar image blocks and searching out similar image blocks, namely the similar image blocks to be searched;
step 2: singular value decomposition of similar blocks
And step 3: singular value soft thresholding operation
Traversing the whole image in the step of S2, and resetting the images in sequence after the step is finished;
s3, calculating the peak signal-to-noise ratio of the image, setting the peak signal-to-noise ratio as a limiting condition, and iterating the steps S1 and S2;
and S4, performing edge enhancement on the denoised image by using a canny algorithm, wherein the finally output image is the required image.
2. The denoising method for remote sensing images based on wavelet transform and improved weighted nuclear norm minimization according to claim 1, wherein: in step S1, the variance of the diagonal component coefficient of the first scale obtained by wavelet decomposition is used to estimate the noise variance value of the image.
3. The denoising method for remote sensing images based on wavelet transform and improved weighted nuclear norm minimization according to claim 2, wherein: the noise variance value of the image is estimated as follows:
after the multi-scale two-dimensional wavelet decomposition is completed, low-frequency coefficients in the horizontal, vertical and diagonal directions under corresponding scales can be obtained, and are expressed as follows:
wherein ,
、
、
respectively representing low frequency coefficients in the horizontal, vertical and diagonal directions,k，mrespectively representing the coordinates corresponding to the pixels of the image after decomposition,zrepresenting the entire image;
since the decomposition in the diagonal direction is a low-frequency signal in the wavelet decomposition process, and the image information included in the multi-scale signal decomposition gradually decreases as the decomposition proceeds, the noise signal included in the diagonal decomposition information of the scale 1 is the most, and therefore, the variance is calculated for the diagonal component of the first scale, as follows:
wherein ,
the diagonal decomposition information representing the scale 1,
the average of the diagonal decomposition information representing scale 1,
i.e. estimated noise contentNoise variance of acoustic images.
4. The denoising method for remote sensing images based on wavelet transform and improved weighted nuclear norm minimization according to claim 1, wherein: the method for determining the feature vector of the image block in step S2 specifically includes the following steps:
firstly, determining that each image block contains 25 pixel values which are respectively marked as p1, p2, … … and p25, calculating the similarity between the image block and 8 surrounding image blocks by using the following formula (5), respectively marked as s1, s2, … … and s8, combining the 25 pixel values and the 8 similarity values into a vector, and performing normalization processing to obtain a required feature vector EV = [ p1, p2, … …, p25, s1, s2, … … and s8 ];
in the formula aIn order to control the parameters of the device,
for the image blocks to be processed,
is the first of the surroundingsiAnd each image block.
5. The denoising method for remote sensing images based on wavelet transform and improved weighted nuclear norm minimization according to claim 1, wherein: the determination of the k-dimensional tree in step S2 is specifically as follows:
calculating the standard deviation of each dimension of the feature vector by formula (6) for the feature vectors of all image blocks in the corresponding set of image blocks,
wherein ,
is the value of the characteristic of the image,
is the mean of the corresponding feature vectors,mand (3) selecting the one-dimensional features with the largest standard deviation for the number of the image blocks, solving the median of the dimension-changing features, wherein the median is the root node of the k-dimensional tree, dividing the image block set into two parts by utilizing the root node, wherein the image blocks smaller than the root node are positioned on the left side of the tree and the image blocks larger than the root node are positioned on the right side of the tree, and repeating the operation on the image blocks on the left side and the image blocks on the right side until the image blocks cannot be divided.
6. The denoising method for remote sensing images based on wavelet transform and improved weighted nuclear norm minimization according to claim 1, wherein: in step S3, the peak snr is set as a limiting condition, specifically as follows:
the peak signal-to-noise ratio value is used as a judgment standard for stopping iteration, namely, in the image iteration operation process, the iteration is stopped immediately when the peak signal-to-noise ratio value is judged to be larger than or equal to the peak signal-to-noise ratio result of the next iteration.
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