CN116109519B - Image denoising method - Google Patents

Image denoising method Download PDF

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CN116109519B
CN116109519B CN202310348593.XA CN202310348593A CN116109519B CN 116109519 B CN116109519 B CN 116109519B CN 202310348593 A CN202310348593 A CN 202310348593A CN 116109519 B CN116109519 B CN 116109519B
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CN116109519A (en
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王晓雯
赵君喜
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Nanjing University of Posts and Telecommunications
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Abstract

The invention provides an image denoising method, which comprises the steps of decomposing high-frequency information and low-frequency information of a noisy image by adopting a Haar wavelet basis of wavelet transformation; local pixel grouping processing is carried out on the pixel points of the low-frequency information, and a sample set of similar local pixel blocks is obtained; traversing each acquired sample set to obtain an orthogonal transformation matrix, and removing the dimension containing a small amount of information in the sample set by combining the eigenvalue matrix to obtain a reconstructed low-frequency component; decomposing the high-frequency information into overlapping blocks with the same size, and reconstructing high-frequency components by using sparse coding and an adaptive learning dictionary; the wavelet inverse transformation aggregates the high-frequency component and the low-frequency component to obtain a denoised image. The invention effectively removes noise and better retains image details, and meanwhile, the high-frequency part adopts group sparsity, so that high sparsity and high recovery quality can be realized, and the visual performance, peak signal-to-noise ratio and structural similarity of the image are improved.

Description

Image denoising method
Technical Field
The invention relates to an image denoising method, belonging to the technical field of image processing and computer vision detection.
Background
Image processing is an important research part of computer vision. Image color distortion, edge blurring, noise, etc. can have unpredictable effects on image information extraction. The recognition effect of the image can be seriously affected, so that the problems of wrong recognition, failure in classification and the like of the image are caused. In the process of image acquisition and transmission, the acquired image often contains a certain noise pollution due to the influence of image equipment or external factors. The noisy image will directly affect the performance of the vision system in terms of image processing and understanding. The purpose of image denoising is to recover a clean image from a distorted image while preserving the details of the original image. Image denoising has become an indispensable important step in the field of computer vision processing.
In view of the foregoing, it is necessary to propose an image denoising method to solve the above problems.
Disclosure of Invention
The invention aims to provide an image denoising method which can improve the visual performance of a reconstructed image, peak signal-to-noise ratio and structural similarity.
In order to achieve the above object, the present invention provides an image denoising method, which mainly includes the following steps:
step 1, decomposing high-frequency information and low-frequency information of a noise-containing image by adopting a Haar wavelet basis of wavelet transformation;
step 2, carrying out local pixel grouping processing on the pixel points of the low-frequency information, adopting unbiased estimation of errors to approximately represent the similarity between a local pixel block and a target pixel block, and obtaining a sample set of similar local pixel blocks;
step 3, traversing each acquired sample set, sequentially denoising by using a principal component analysis algorithm, obtaining an orthogonal transformation matrix by calculating a covariance matrix, and removing the dimension containing a small amount of information in the sample set by combining a characteristic value matrix to obtain a reconstructed low-frequency component;
step 4, decomposing the high-frequency information into overlapping blocks with the same size, calculating Euclidean distance, constructing similar blocks into groups, utilizing singular value decomposition to learn the self-adaptive learning dictionary of each group, calculating sparse coding by combining a split Bregman iterative algorithm with a convex optimization algorithm, and utilizing the sparse coding and the self-adaptive learning dictionary to reconstruct high-frequency components;
and 5, carrying out wavelet inverse transformation to aggregate the high-frequency component and the low-frequency component to obtain a denoised image.
As a further improvement of the present invention, step 1 specifically comprises the steps of: and performing wavelet transformation on the image by using a dwt2 function, selecting a Haar function as a wavelet basis, decomposing the image information into a high-frequency part and a low-frequency part, and then processing the high-frequency information and the low-frequency information respectively.
As a further improvement of the present invention, step 2 specifically comprises the steps of:
step 21, selecting a target pixel block for the low-frequency part of the image, taking an L multiplied by L size matrix taking the pixel block as a center as a training window, selecting a pixel block with K multiplied by K size from the training window as a local pixel block, and using unbiased estimation of errors to approximately represent the similarity between the local pixel block and the target pixel block;
step 22, calculating the mean square error between the ith local pixel block and the target pixel block in the L multiplied by L size matrix window;
step 23, setting a threshold value T, when the mean square error between the noiseless local pixel blocks is smaller than or equal toSelecting a local pixel block sample set y when the threshold value T is set i Is a vector meeting the condition.
As a further improvement of the present invention, in step 22, the mean square error is
Wherein m=k×k, y 0 For the central target pixel block, y i For other noisy local pixel blocks, x 0 、x i For a corresponding noise-free local pixel block,is a sample vector of pixels in the noisy target pixel block,/for the block of pixels>Is the sample vector of the other block, +.>And->Are respectively->And->Is used for the correlation of the noise-free sample vector.
As a further improvement of the present invention, step 3 specifically includes the steps of:
step 31, for a sample set of size m×nWherein-> Mean>Normalized to obtain->Calculating a sample covariance matrix +.>Performing eigenvalue decomposition on the covariance matrix to obtain an eigenvalue matrix lambda and an eigenvector matrix phi corresponding to the eigenvalue matrix lambda, and calculating an orthogonal transformation matrix P=phi T Sample set +.>And is present in
Step 32, calculating a sample set by using the eigenvalue matrix ΛLine k->Removing dimensions containing a small amount of information.
As a further improvement of the present invention, in step 32, the estimated value is
Wherein lambda is k Is the characteristic value delta in the corresponding dimension sample set 2 Is the diagonal component of the noise covariance matrix.
As a further improvement of the present invention, step 4 specifically includes the steps of:
step 41, dividing the image high frequency component into sizesSearching for c best matching blocks in the L x L training window with Euclidean distance as similarity criterion between different blocks to form a set->Will->All blocks in (a) are stacked as columns to a size B s X c matrix, these block matrices with similar structure +.>Is arranged as a group;
step 42, repeating step 3 to obtain a predicted valueFrom the predicted value using singular value decomposition>Each group is learnedIs->
Step 43, pairingEach group->Sparse coding is carried out, and corresponding sparse vectors are searched for +.> Make->The high frequency components of the image are represented by sparse coding in the group domain.
As a further improvement of the present invention, the predicted valueIs that
Wherein,,is a diagonal matrix>Are respectively->And->Is a column of (c).
As a further improvement of the present invention, the sparse coding is
Wherein D is G Representing allAlpha, alpha G Indicating all->Is/represents the element split of two vectors,/is +.>Is an identity matrix with the size of 64 x 60, ">Is a group extracted from image x +.>The operator, whose transpose replaces the group back to the kth position in the reconstructed image and fills in zeros at other positions.
As a further improvement of the present invention, step 5 specifically includes the steps of: and performing wavelet inverse transformation on the image by using the idwt2 function, selecting a Haar function as a wavelet basis, and polymerizing the high-frequency component and the low-frequency component of the image to obtain the whole denoising image.
The beneficial effects of the invention are as follows: the invention effectively removes noise and better retains image details, and meanwhile, the high-frequency part adopts group sparsity, so that high sparsity and high recovery quality can be realized, and the visual performance, peak signal-to-noise ratio and structural similarity of the image are improved.
Drawings
Fig. 1 is a schematic diagram of an image denoising process in an image denoising method according to the present invention.
Fig. 2 is a set of images tested Lena, barbara, cameraman, peppers, goldhill in the present invention.
Fig. 3 is a graph of the high frequency and low frequency components of the Lena image of the present invention after wavelet decomposition on a Haar wavelet basis.
Fig. 4 is a packet diagram of a partial pixel packet in the present invention.
FIG. 5 is a schematic diagram of GSR group structure according to the invention.
Fig. 6 is a visual comparison of the denoising results of the image Lena at a noise level of 25 in the present invention.
FIG. 7 is a visual comparison of the denoising results of the image Peppers at a noise level of 25 in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
In this case, in order to avoid obscuring the present invention due to unnecessary details, only the structures and/or processing steps closely related to the aspects of the present invention are shown in the drawings, and other details not greatly related to the present invention are omitted.
In addition, it should be further noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1 to 7, the present invention discloses an image denoising method, which mainly comprises the following steps:
step 1, decomposing high-frequency information and low-frequency information of a noise-containing image by adopting a Haar wavelet basis of wavelet transformation;
step 2, carrying out local pixel grouping processing on the pixel points of the low-frequency information, adopting unbiased estimation of errors to approximately represent the similarity between a local pixel block and a target pixel block, and obtaining a sample set of similar local pixel blocks;
step 3, traversing each acquired sample set, sequentially denoising by using a principal component analysis algorithm, obtaining an orthogonal transformation matrix by calculating a covariance matrix, and removing the dimension containing a small amount of information in the sample set by combining a characteristic value matrix to obtain a reconstructed low-frequency component;
step 4, decomposing the high-frequency information into overlapping blocks with the same size, calculating Euclidean distance, constructing similar blocks into groups, utilizing singular value decomposition to learn the self-adaptive learning dictionary of each group, calculating sparse coding by combining a split Bregman iterative algorithm with a convex optimization algorithm, and utilizing the sparse coding and the self-adaptive learning dictionary to reconstruct high-frequency components;
and 5, carrying out wavelet inverse transformation to aggregate the high-frequency component and the low-frequency component to obtain a denoised image.
Steps 1-5 will be described in detail below.
In step 1, decomposing the high-frequency component and the low-frequency component of the noise-containing image by wavelet transform means: and performing wavelet transformation on the image by using a dwt2 function, selecting a Haar function as a wavelet basis, decomposing the image information into a high-frequency part and a low-frequency part, and then processing the high-frequency information and the low-frequency information respectively.
As shown in fig. 2, the high frequency component and the low frequency component of the image are restored separately and then aggregated, which has a better denoising effect than the direct restoration of the entire image. In the experiment, five images Barbara, lena, cameraman, peppers, goldhill with the sizes of 512 x 512 and 256 x 256 are respectively adopted as a standard test image set, and a dwt2 function is utilized to carry out wavelet transformation on a noisy image, wherein a Haar function is selected by a wavelet basis, so that image information is decomposed into a low-frequency component and three high-frequency components.
As shown in fig. 3, wherein the high frequency components are horizontal, vertical and diagonal components, respectively.
It can be seen that the first image is an approximation of the image, corresponding to the low frequency part of the image, while the other three images are contours of the image, i.e. details in the three directions horizontal, vertical and diagonal, are the high frequency parts of the image. The dimension of each variable thus far becomes 256 x 256.
In step 2, local pixel grouping processing is performed on the pixel points of the low-frequency information, and a sample set of similar local pixel blocks is obtained. To better preserve the local structure of the image, modeling the pixels and their neighboring pixels as vector variables, training samples are selected from the local window using LPG based on block matching, ensuring that only sample blocks with similar content are used in the local statistical computation of PCA transform estimation, so that the local features of the image can be well preserved after coefficient contraction in the PCA domain to remove noise. The process of carrying out local pixel grouping processing on the low-frequency information comprises the following steps:
and 21, selecting a target pixel block for the low-frequency part of the image, taking an L multiplied by L size matrix taking the pixel block as a center as a training window, selecting a pixel block with K multiplied by K size from the training window as a local pixel block, and using unbiased estimation of errors to approximately represent the similarity between the local pixel block and the target pixel block.
As shown in fig. 4, pixels are grouped, where l=41, k=5.
Step 22, calculating the mean square error between the ith local pixel block and the target pixel block in the L×L size matrix window, which is defined as:
wherein m=k×k, y 0 For the central target pixel block, y i For other noisy local pixel blocks, x 0 、x i For a corresponding noise-free local pixel block,is a sample vector of pixels in the noisy target pixel block,/for the block of pixels>Is the sample vector of the other block, +.>Andare respectively->And->Is used for the correlation of the noise-free sample vector.
Step 23, setting a proper threshold T, when the mean square error between the noiseless local pixel blocks is less than or equal to the threshold TAnd mean square error e i ≤T+2δ 2 Selecting a local pixel block sample set y i Is a vector meeting the condition. If the number of vectors meeting the condition is less than cm, taking cm with the minimum mean square error, and obtaining a sample set Y with the number not less than cm. Where c is typically 8 to ζ10, and t is manually adjustable, preferably t=25, and δ represents the estimated standard deviation of gaussian noise of the image.
The center vector represents the pixel point to be denoised, and the vectors selected in the sample set are all as close as possible to the center vector and are sufficiently similar to the center vector. Information about the pixel point can thus be obtained from these vectors, and the local structure is preserved at the time of dimension reduction.
In step 3, a method of combining Local Pixel Grouping (LPG) with principal component analysis is provided, normalization processing is performed on each row of the sample set after grouping processing, a sample covariance matrix is calculated, eigenvalue decomposition is performed, an eigenvalue matrix and an eigenvector matrix corresponding to the eigenvalue matrix are obtained, an orthogonal transformation matrix is calculated, and a sample set under a new space is obtained through orthogonal linear transformation. And calculating an estimated value of each row in the sample set under the new space by using the eigenvalue matrix, removing the dimension with less information content, and restoring the data by using the orthogonal transformation matrix to obtain a reconstructed low-frequency component. Denoising each acquired sample set by using a principal component analysis algorithm, wherein the denoising method comprises the following steps of:
step 31, for a sample set of size m×nWherein-> Mean>Normalized to obtain->Calculating a sample covariance matrix +.>Performing eigenvalue decomposition on the covariance matrix to obtain an eigenvalue matrix lambda and an eigenvector matrix phi corresponding to the eigenvalue matrix lambda, and calculating an orthogonal transformation matrix P=phi T Sample set +.>And is present in
Step 32, calculating a sample set by using the eigenvalue matrix ΛLine k->Removing dimensions containing a small amount of information, the estimated value being
Wherein lambda is k Is corresponding toCharacteristic values in a dimensional sample set, delta 2 Is the diagonal component of the noise covariance matrix, when λ k -δ 2 When the dimension tends to 0, the dimension contains little information, the data is removed, and the data is restored by using an orthogonal transformation matrix, so that a reconstructed low-frequency component is obtained.
In step 4, for the high-frequency component, a sparse representation model based on groups is provided, the high-frequency component is decomposed into overlapping blocks with the same size, the Euclidean distance is calculated to construct similar blocks into groups, the self-adaptive learning dictionary of each group is learned by singular value decomposition, the sparse coding is calculated by combining a split Bregman iterative algorithm with a convex optimization algorithm, and the high-frequency component is reconstructed by using the sparse coding and the self-adaptive learning dictionary. The natural image is sparsely represented in the group domain using sparse representation (GSR) of the group, enhancing the inherent local sparsity and non-local self-similarity of the image. The method comprises the following steps:
step 41, as shown in FIG. 3, dividing the image high frequency component into sizesSearching c best matching blocks in an L x L training window by taking Euclidean distance as a similarity criterion between different blocks to form a setWill->All blocks in (a) are stacked as columns to a size B s X c matrix, these block matrices with similar structure +.>Is arranged as a group;
step 42, obtaining the predicted value by the method in step 3Then, using singular value decomposition from the predicted value +.>Study of each group->Is->Namely:
wherein,,is a diagonal matrix>Are respectively->And->Is a column of (c). Computing representation group->Is->Each atom of->Constitution->Is->
For the followingSelf-adaptive learning dictionaryHas the following components
Wherein each atomAnd group->Equal in size, m is +.>The number of atoms in (a) is used.
Step 43, pairingEach group->Sparse coding is carried out, and corresponding sparse vectors are searched for +.> Make->The high frequency components of the image are sparsely represented by sparse coding in the group domain:
wherein D is G Representing allAlpha, alpha G Indicating all->Is/represents the element split of two vectors,/is +.>Is an identity matrix with a size of 64 x 60. />Is a group extracted from image x +.>The operator, whose transpose replaces the group back to the kth position in the reconstructed image and fills in zeros at other positions. Recovering images by averaging all groups and optimizing/using split Bregman iterative algorithm 0 Problem of norm minimization, use ∈ ->An image is reconstructed.
In step 5, the high-frequency component and the low-frequency component are aggregated by utilizing wavelet inverse transformation to obtain a denoised image, the wavelet inverse transformation is conducted on the image by utilizing idwt2 function, a Haar function is selected as a wavelet basis, and the high-frequency component and the low-frequency component of the image are aggregated to obtain the whole denoised image.
The effects of the present invention can be further illustrated by the following simulations and results:
in the experimental result part, as shown in fig. 6 and 7, the image denoising method based on LPG-PCA and GSR provided by the invention is a representative method for denoising five images by non-parametric bayesian dictionary learning algorithm (BPFA), hybrid sparse representation algorithm (HSR), space adaptive iterative singular value thresholding (SAIST), group sparse residual algorithm (GSR-NLS) and low rank approximate singular value decomposition algorithm LRA-singular value decomposition.
The present invention compares the proposed LPG-PCA and GSR based approach with the representative approach of denoising the last five images: BPFA, HSR, SAIST, GSR-NLS and LRA-singular value decomposition.
The invention selects 5 gray image data sets with 512 x 512 and 256 x 256 for experiment. Adding additive Gaussian white noise with different intensities into the test image to generate a noise-containing image, wherein the noise level values are 15/25/35/50 respectively, and the intensity value of each pixel of the data set is 0-255.
As shown in fig. 6, in visual representation, the present invention has good denoising effect on the texture of the hat in the Lena diagram and the edge portions of the face and the hat, and some classical contrast algorithms exemplified above have an overcomplete phenomenon on the texture portion of the hat, and the contrast algorithm loses part of the detail on the edge portion, so that the transition of the image area is not obvious enough.
As shown in fig. 7, compared with the result of the comparison algorithm, the present invention has clearer distinction of different vegetables in the Peppers graph, more focus of the high-light portion halo, and more excellent performance in terms of preservation of details.
Table 1 compares the PSNR and SSIM values for six methods at different noise levels
The quality of the restored image is evaluated by calculating a peak signal-to-noise ratio (PSNR) and a Structural Similarity Index (SSIM), and the denoising effect of the invention on the noise condition of the image is checked. As shown in table 1 above, the performance of the six methods on test images with different noise levels is shown by PSNR and SSIM values, with the highest value of each measurement highlighted in bold.
The average PSNR value of the invention is 0.2-0.75 higher than other methods, and the SSIM value is 0.01-0.03 higher than other methods. According to objective quantitative result analysis, the method is generally superior to a comparison algorithm under the condition of low-intensity noise or high-intensity noise, and can achieve advantages in PSNR and SSIM performance evaluation. In particular, the method of the invention shows better denoising results in images with more texture areas and edge areas. In the test image, the invention has better visual quality for the image with complex details.
In summary, the image denoising method based on the principal component analysis and group sparsity of the local pixel grouping provided by the invention processes the high-frequency information and the low-frequency information of the image respectively through wavelet transformation, recovers the low-frequency component by using the LPG-PCA method, sparsely represents the natural image in the group domain in the process of recovering the high-frequency component, clearly and effectively simultaneously represents the inherent local sparsity and the non-local self-similarity of the natural image in a unified manner, and extracts the high-frequency part from the image without being influenced by noise. The method has the advantages that the noise is effectively removed, meanwhile, the image details are reserved, high sparsity and high recovery quality are achieved, and the visual performance, peak signal-to-noise ratio and structural similarity of the image are improved.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention.

Claims (7)

1. An image denoising method, comprising the steps of:
step 1, decomposing high-frequency information and low-frequency information of a noise-containing image by adopting a Haar wavelet basis of wavelet transformation;
step 2, carrying out local pixel grouping processing on the pixel points of the low-frequency information, adopting unbiased estimation of errors to approximately represent the similarity between a local pixel block and a target pixel block, and obtaining a sample set of similar local pixel blocks;
step 3, traversing each acquired sample set, sequentially denoising by using a principal component analysis algorithm, obtaining an orthogonal transformation matrix by calculating a covariance matrix, and removing the dimension containing a small amount of information in the sample set by combining a characteristic value matrix to obtain a reconstructed low-frequency component;
step 4, decomposing the high-frequency information into overlapping blocks with the same size, calculating Euclidean distance, constructing similar blocks into groups, utilizing singular value decomposition to learn the self-adaptive learning dictionary of each group, calculating sparse coding by combining a split Bregman iterative algorithm with a convex optimization algorithm, and utilizing the sparse coding and the self-adaptive learning dictionary to reconstruct high-frequency components;
the step 4 specifically comprises the following steps:
step 41, dividing the image high frequency component into sizesN overlapping blocks of (2), in->In the training window, searching c best matched blocks by taking Euclidean distance as similarity criterion between different blocks to form a set +.>Will->All blocks of (1) are stacked as columns to be +.>These block matrices having a similar structure are +.>Is arranged as a group;
step 42, repeating step 3 to obtain a predicted valueFrom the predicted value using singular value decomposition +.>Study of each group->Is->The method comprises the steps of carrying out a first treatment on the surface of the For adaptive learning dictionary->There is
，
，
Wherein each atomAnd group->Equal in size, m is +.>The number of atoms in (a);
step 43, pairingEach group->Sparse coding is carried out, and corresponding sparse vectors are searched forSo that->The high frequency components of the image are represented by sparse coding in the group domain;
the predicted valueIs that
，
Wherein,,，/>is a diagonal matrix>，/>Are respectively->And->Is a column of (2);
the sparse coding is as follows
，
，
Wherein,,indicating all->Is cascade of->Indicating all->Is a concatenation of/representing the element segmentation of two vectors,is an identity matrix with the size of 64 x 60, ">Is a group extracted from image x +.>An operator whose transpose replaces the group to the kth position in the reconstructed image and fills zeros in other positions;
and 5, carrying out wavelet inverse transformation to aggregate the high-frequency component and the low-frequency component to obtain a denoised image.
2. The image denoising method according to claim 1, wherein: the step 1 specifically comprises the following steps: and performing wavelet transformation on the image by using a dwt2 function, selecting a Haar function as a wavelet basis, decomposing the image information into a high-frequency part and a low-frequency part, and then processing the high-frequency information and the low-frequency information respectively.
3. The image denoising method according to claim 1, wherein step 2 specifically comprises the steps of:
step 21, selecting a target pixel block for the low frequency part of the image, and centering on the pixel blockThe size matrix is used as a training window, and the +.>The pixel blocks with the sizes are used as local pixel blocks, and the similarity between the local pixel blocks and the target pixel blocks is approximately represented by using unbiased estimation of errors;
step 22, calculatingSize matrix window +.>Mean square error between the local pixel blocks and the target pixel block;
step 23, setting a threshold valueWhen the mean square error between the noiseless local pixel blocks is less than or equal to the threshold value T, selecting a local pixel block sample set +.>Is a vector meeting the condition.
4. The image denoising method according to claim 3, wherein: in step 22, the mean square error is
，
Wherein,,，/>for the central target pixel block +.>For other noisy local pixel blocks, +.>、/>For the corresponding noiseless local pixel block, < >>Is a sample vector of pixels in the noisy target pixel block,/for the block of pixels>Is a vector of samples of the other block,and->Are respectively->And->Is used for the correlation of the noise-free sample vector.
5. The image denoising method according to claim 1, wherein step 3 specifically comprises the steps of:
step 31, for a size ofSample set of->Wherein->Each row is filled with the average value->Normalized to obtain->Calculating a sample covariance matrix +.>Performing eigenvalue decomposition on the covariance matrix to obtain an eigenvalue matrix +.>Feature vector matrix corresponding thereto>Calculate orthogonal transformation matrix->Sample set +.>And is coexisted with
、/>，
；
Step 32, utilizing the eigenvalue matrixCalculate sample set->Line k->Removing dimensions containing a small amount of information.
6. The method according to claim 5, wherein in step 32, the estimated value is
，
Wherein,,is the eigenvalue in the corresponding dimension sample set, +.>Is the diagonal component of the noise covariance matrix.
7. The image denoising method according to claim 1, wherein step 5 specifically comprises the steps of: and performing wavelet inverse transformation on the image by using the idwt2 function, selecting a Haar function as a wavelet basis, and polymerizing the high-frequency component and the low-frequency component of the image to obtain the whole denoising image.
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