CN112927169B - Remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization - Google Patents
Remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization Download PDFInfo
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Abstract
The application discloses a remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization, which comprises the following steps: firstly, estimating the noise variance of a noise image by using a wavelet transformation method, then searching similar image blocks by using the pixel similarity of a neighborhood image block, performing singular value decomposition and singular value soft thresholding operation on the similar image blocks, traversing the whole image, and finally performing edge enhancement processing by using a canny operator to obtain the image with denoising and clear edges. Compared with NLM and conventional WNNM methods, the method for removing noise in the remote sensing image is simple in operation, and can obtain a higher PSNR value and a better visual effect.
Description
Technical Field
The application 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 kernel norm minimization.
Background
Non-local self-similarity means that an image block has many similar blocks at other locations within the entire image where it is located, i.e., a clean image structure is redundant, so that a similar block of an image block may exist anywhere in the entire image. The weighted kernel norm minimization method is an image denoising method based on non-local self-similarity, and due to the high-efficiency and accurate characteristics, the influence degree of different singular values on a model is improved, so that the denoising effect is improved, and the method is widely applied to the field of image processing. The wavelet transformation can automatically adapt to the requirement of video signal analysis, achieves the aim of focusing on any details of signals, overcomes the difficult problem that the non-stationary signals cannot be processed and the window shape is fixed to bring inconvenience, and is known as a mathematical microscope in the field of signal transformation. Therefore, the method of decomposing the image signal by using wavelet transformation and denoising by combining weighted kernel norm minimization is of great significance to 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 searching for similar blocks of an image becomes more and more difficult as the amount of image information increases in the process of processing images by a weighted kernel norm minimization method.
Some organizations have proposed a direction of development for applications based on non-local self-similarity, one of which is the low rank matrix recovery algorithm. Optimization methods for low rank matrix recovery can be divided into two categories: low rank matrix decomposition methods and kernel norms 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. The Dabov K and the like realize sparsity enhancement by using the 3D data array in a transformation domain, and the method effectively filters noise in the remote sensing image.
However, in either method, there is a certain loss of information of the image, which results in smoothing of some pixels and accuracy of denoising the image.
The image noise variance is an essential information in the denoising process by the weighted kernel norm minimization method, so that the estimation of the noise variance is necessary for an image with unknown noise variance. In the original weighted kernel norm minimization method, relatively more errors are caused by position information when the Euclidean distance is adopted to search the image similar blocks, the image denoising precision is improved, and the gray value of the pixel is used to search the image similar blocks so as to utilize the pixel information to the greatest extent, so that the similar blocks are searched more accurately, and the denoising precision is improved. Wavelet transforms are typically used to pre-process the transformation of signals from the spatial domain to the frequency domain, without using the information in the diagonal direction of scale 1 in the multi-scale two-dimensional wavelet decomposition process alone to estimate the noise variance.
Disclosure of Invention
The application aims to provide a remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization, so as to improve the accuracy of remote sensing denoising and the visual effect.
In order to achieve the above purpose, the technical scheme adopted by the application is as follows:
in order to achieve the above purpose, the application adopts the following technical scheme:
the remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization comprises the following steps:
s1, performing two-dimensional multi-scale wavelet decomposition on an image
Calculating variance in the diagonal component coefficient of the first scale, and estimating the noise variance value of the image;
s2, denoising by using improved weighted kernel norm minimization method
s2.1 search for similar image blocks
s2.1.1, determining the similarity and the gray value of the image block by utilizing pixels in the image block and neighbor pixels thereof, and determining the feature vector of the image block;
s2.1.2 determining a small set of image blocks by uniformly sampling pixels of the sharpness 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 the subgraph into a k-dimensional tree of the image, and searching similar image blocks therein;
s2.1.6, determining the k-dimensional tree with the most similar image blocks, and searching out the image blocks similar to the k-dimensional tree, namely the similar image blocks to be searched;
s2.2 similarly blocky singular value decomposition
s2.3 singular value soft thresholding operations
Traversing the whole image in the step S2, and resetting the images according to the sequence after finishing;
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, carrying out edge enhancement on the denoised image by using a Canny algorithm, and finally obtaining the output image as the required image.
Preferably, in the 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, which is specifically as follows:
after the multi-scale two-dimensional wavelet decomposition is completed, the low-frequency coefficients in the horizontal, vertical and diagonal directions under the corresponding scale can be obtained, and the low-frequency coefficients are expressed as follows:
（1）
（2）
（3）
wherein ,、/>、/>representing the low frequency coefficients in the horizontal, vertical and diagonal directions respectively,k，mrespectively represent the divisionsCoordinates corresponding to the pixels of the image after the solution,zrepresenting the entire image. Since the decomposition in the diagonal direction is a low-frequency signal during the wavelet decomposition and the image information contained in the multi-scale signal decomposition gradually decreases as the decomposition proceeds, the noise signal contained in the diagonal decomposition information of scale 1 is the largest, and therefore the variance is calculated for the diagonal component of the first scale, as follows:
（4）
wherein ,diagonal decomposition information representing scale 1, +.>Mean value of diagonal decomposition information representing scale 1, < >>I.e. the estimated noise variance of the noisy image.
Preferably, the method for determining the feature vector of the s2.1 image block specifically includes the following steps:
firstly, determining that each image block contains 25 pixel values, namely p1, p2, … … and p25, calculating the similarity between the image block and 8 image blocks around the image block by using the following formula (5), namely s1, s2, … … and s8, combining the 25 pixel values and the 8 similarity values into a vector, and carrying out normalization processing, namely the feature vector which is obtained by EV= [ p1, p2, … …, p25, s1, s2, … … and s8].
（5）
in the formula aIn order to control the parameters of the device,for the image block to be processed, < > for>Is the surrounding firstiImage blocks.
Preferably, the determination of the k-dimensional tree of s2.1.3 is specifically as follows:
for the feature vectors of all image blocks in the corresponding image block set, the standard deviation of each dimension feature vector is calculated by the formula (6),
（6）
wherein ,is a characteristic value->Is the mean value of the corresponding feature vector,mselecting one-dimensional characteristics with the largest standard deviation for the number of image blocks, and solving a median value of the dimension-changing characteristics, wherein the median value is a root node of a k-dimensional tree, the image block set is divided into two parts by using the root node, the image blocks smaller than the root node are positioned on the left side of the tree and larger than the root node and are positioned on the right side of the tree, and the operation is repeated on the image blocks on the left side and the right side until the image blocks cannot be divided any more.
Preferably, the S3 sets the peak signal-to-noise ratio as a limiting condition, specifically as follows:
and the value of the peak signal-to-noise ratio is used as a judgment standard for stopping iteration, namely, when the value of the peak signal-to-noise ratio is judged to be larger than or equal to the peak signal-to-noise ratio result of the next iteration in the image iteration operation process, the iteration is stopped immediately.
The application has the following advantages:
(1) The image noise method is simpler and quicker 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 after denoising is higher:
after denoising the remote sensing image, compared with NLM, BM3D and the traditional weighted kernel norm minimization method, the peak signal-to-noise ratio is higher, and part of edge information can be recovered.
Drawings
FIG. 1 is a flow chart of a remote sensing image denoising method based on wavelet transform and improved weighted kernel norm minimization in the present application;
FIG. 2 is a graph comparing denoising results in a dense house area with a noise variance of 0.001;
FIG. 3 is a graph comparing denoising results in a dense house area with a noise variance of 0.005;
FIG. 4 is a graph showing the comparison of denoising results in a dense house area with a noise variance of 0.01;
FIG. 5 is a graph showing the comparison of the denoising results in a farmland area with a noise variance of 0.001;
FIG. 6 is a graph showing the comparison of the denoising results of a farmland area with a noise variance of 0.005;
FIG. 7 is a graph showing the comparison of the denoising results in a farmland area with a noise variance of 0.01.
Detailed Description
The application is further described with reference to the accompanying drawings:
as shown in fig. 1-7, the present application mainly solves two problems:
(1) The image noise variance estimation method comprises the following steps:
the high-frequency information and the low-frequency information of the image can be extracted after the multi-scale two-dimensional wavelet decomposition, the information of the low-frequency information in the diagonal direction is decomposed, the maximum noise information is contained, and almost all the noise information is contained in scale 1.
(2) Searching for image similarity blocks using pixel similarity:
the pixel information can be utilized to the greatest extent by searching the image similar blocks by using the pixel similarity, so that the similar blocks are searched more accurately, and the denoising precision is improved.
The specific thinking of the application to solve the above problems is:
it was found through research that after the image is subjected to scale two-dimensional wavelet decomposition, the information in the diagonal direction of scale 1 contains almost all noise information because it has low frequency and noise is almost all low frequency.
Therefore, an idea of estimating the noise method of the video by calculating the variance of the diagonal direction information of the scale 1 is proposed.
Low frequency coefficients in the diagonal direction:，k，mrespectively representing the coordinates corresponding to the decomposed image pixels,zrepresenting the entire image. Computing variance for the diagonal component of the first scale:
, wherein ,/>Diagonal decomposition information representing scale 1, +.>Mean value of diagonal decomposition information representing scale 1, < >>I.e. the estimated noise variance of the noisy image.
Taking 25 pixel values as an example, it is first determined that each image block contains 25 pixel values, denoted as p1, p2, … …, and p25, respectively, and similarity between the image block and 8 image blocks around the image block is calculated:respectively denoted as s1, s2, … …, s8, and then combining the 25 pixel values and the 8 similarity values into a vector, and performing normalization processing to obtain a feature vector: ev= [ p1, p2, … …, p25, s1, s2, … …, s8]For all images in the corresponding image block setFeature vectors of the block, calculating standard deviation +.>And then selecting a one-dimensional feature with the largest standard deviation, solving a median value of the feature, namely a root node of the k-dimensional tree, dividing the image block set into two parts by using the root node, wherein the image blocks smaller than the root node are positioned at the left side of the tree and the image blocks larger than the root node are positioned at the right side of the tree, repeating the operation on the image blocks at the left side and the right side until the image blocks can not be divided any more, constructing a k-dimensional tree representing the image block set, finally determining the k-dimensional tree with the largest number of similar image blocks, and searching the image blocks similar to the k-dimensional tree, namely the similar image blocks to be searched.
The application will be described in further detail with reference to the accompanying drawings and detailed description;
the embodiment of the application carries out denoising processing on images with different noise levels in a house dense area and a farmland area of multispectral images of the high-resolution second satellite.
Referring to fig. 1, the remote sensing image denoising method based on wavelet transformation and improved weighted kernel norm minimization comprises the following steps:
s1, performing two-dimensional multi-scale wavelet decomposition on an image
Calculating variance in the diagonal component coefficient of the first scale, and estimating the noise variance value of the image;
s2. improved weighted kernel norm minimization method denoising
s2.1 search for similar image blocks
s2.1.1, determining the similarity and the gray value of the image block by utilizing pixels in the image block and neighbor pixels thereof, and determining the feature vector of the image block;
s2.1.2 determining a small set of image blocks by uniformly sampling the 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 the subgraph into a k-dimensional tree of the image, and searching similar image blocks therein;
s2.1.6, determining the k-dimensional tree with the most similar image blocks, and searching out the image blocks similar to the k-dimensional tree, namely the similar image blocks to be searched;
s2.2 similarly blocky singular value decomposition
s2.3 singular value soft thresholding operations
Traversing the whole image in the step s2, and resetting the image according to the sequence after finishing;
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, carrying out edge enhancement on the denoised image by using a canny algorithm, and finally obtaining the output image as the required image.
From fig. 2 to fig. 7, the results of denoising the images with different noise levels in different regions respectively, it can be seen that the smoothing phenomenon of the images with different degrees appears in all the images after denoising, wherein the smoothing phenomenon of the images with the NLM method is serious, some noise points exist, the original WNNM and the images processed with the improved method of the present application have better visual effects, but the edge smoothing phenomenon of the original WNNM method is slightly serious.
As can be seen from PSNR in Table 1, all denoising methods gradually weaken along with noise aggravation denoising effect, PSNR values of WNNM and the method are highest compared with other control methods under different conditions, PSNR after denoising by the method is slightly higher than that of the original WNNM, when noise variance is smaller than 0.001, PSNR of images after denoising under two different scenes can reach more than 35dB, and compared with the original WNNM, PSNR is respectively improved by 6.5% and 5.6%. Meanwhile, as can be seen from comparing the structural similarity data in table 2, the structural similarity of the noise images of different areas treated by the method can be maintained to be best under different noise conditions, and can reach about 99%, and when the noise variance is 0.001, the structural similarity can reach more than 99%.
Table 1 different methods denoising PSNR comparison table
Table 2 different methods denoising SSIM comparison table
The foregoing is a preferred embodiment of the present application, and modifications, obvious to those skilled in the art, of the various equivalent forms of the present application can be made without departing from the principles of the present application, are intended to be within the scope of the appended claims.
Claims (4)
1. The remote sensing image denoising method based on wavelet transformation and improved weighted kernel 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 an image
Calculating variance in the diagonal component coefficient of the first scale, and estimating the noise variance value of the image;
s2, denoising by using improved weighted kernel norm minimization method
Step 1: searching of similar image blocks
Determining the similarity and the gray value of the image block by utilizing 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 alignment 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 the k-dimensional tree with the most similar image blocks, and searching out the image blocks similar to the k-dimensional tree, namely the similar image blocks to be searched;
step 2: similar block singular value decomposition
Step 3: singular value soft thresholding operations
Traversing the whole image in the step S2, and resetting the images according to the sequence after finishing;
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, carrying out edge enhancement on the denoised image by using a canny algorithm, and finally obtaining an output image as the required image;
in the 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;
the noise variance value of the estimated image is specifically as follows:
after the multi-scale two-dimensional wavelet decomposition is completed, the low-frequency coefficients in the horizontal, vertical and diagonal directions under the corresponding scale can be obtained, and the low-frequency coefficients are expressed as follows:
wherein ,cj,1 、c j,2 、c j,3 Respectively representing low-frequency coefficients in horizontal, vertical and diagonal directions, k, m respectively representing coordinates corresponding to the decomposed image pixels, and z representing the whole image;
since the decomposition in the diagonal direction is a low-frequency signal during the wavelet decomposition and the image information contained in the multi-scale signal decomposition gradually decreases as the decomposition proceeds, the noise signal contained in the diagonal decomposition information of scale 1 is the largest, and therefore the variance is calculated for the diagonal component of the first scale, as follows:
wherein ,diagonal decomposition information representing scale 1, +.>Mean value, sigma, of diagonal decomposition information representing scale 1 2 I.e. the estimated noise variance of the noisy image.
2. The remote sensing image denoising method based on wavelet transform and improved weighted kernel norm minimization according to claim 1, wherein: the method for determining the feature vector of the image block in the step S2 specifically includes the following steps:
firstly, determining that each image block contains 25 pixel values, namely p1, p2, … … and p25, calculating the similarity between the image block and 8 image blocks around the image block by using the following formula (5), respectively marking the similarity as s1, s2, … … and s8, combining the 25 pixel values and the 8 similarity values into a vector, and carrying out normalization processing, namely, obtaining the feature vector, namely EV= [ p1, p2, … …, p25, s1, s2, … … and s8];
wherein a is a control parameter, P is an image block to be processed, P i Is the ith image block of the surroundings.
3. The remote sensing image denoising method based on wavelet transform and improved weighted kernel norm minimization according to claim 1, wherein: the determination of the k-dimensional tree in the step S2 is specifically as follows:
for the feature vectors of all image blocks in the corresponding image block set, the standard deviation of each dimension feature vector is calculated by the formula (6),
wherein ,vi Is a characteristic value of the characteristic,the method comprises the steps that the average value of corresponding feature vectors is m, the number of image blocks is m, then, one-dimensional features with the largest standard deviation are selected, the median value of the dimension changing features is obtained, the median value is the root node of a k-dimensional tree, the image block set is divided into two parts by the root node, the image blocks smaller than the root node are positioned on the left side of the tree and larger than the root node, and the operation is repeated on the image blocks on the left side and the right side until the image blocks cannot be divided any more.
4. The remote sensing image denoising method based on wavelet transform and improved weighted kernel norm minimization according to claim 1, wherein: the step S3 sets the peak signal-to-noise ratio as a limiting condition, specifically as follows:
and the value of the peak signal-to-noise ratio is used as a judgment standard for stopping iteration, namely, when the value of the peak signal-to-noise ratio is judged to be larger than or equal to the peak signal-to-noise ratio result of the next iteration in the image iteration operation process, the iteration is stopped immediately.
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