CN110264429B - Image enhancement method based on sparsity and similarity priori - Google Patents
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Abstract
The invention relates to an image enhancement method based on sparse and similar priori, comprising the following steps of (1) carrying out discrete shear wave transformation on an image to obtain a shear wave coefficient; (2) Using a hard threshold function T τ Processing a shear wave coefficient obtained after discrete shear wave conversion; (3) And (3) carrying out artifact removal processing on the image processed in the step (2). The invention adopts discrete shear wave transformation, thereby ensuring the quick realization of the algorithm; the shear wave coefficient of the image is processed by using the hard threshold function, so that image noise is effectively removed, and the edge and detail part of the image are enhanced; the shear wave transformation is combined with the non-local mean value, the advantages are complementary, the problem that the non-local mean value has poor treatment effect on the high noise level is solved, meanwhile, artifacts in an image of a shear wave transformation band are avoided, and the whole algorithm has a better denoising enhancement effect.
Description
Technical Field
The invention relates to an image enhancement method based on sparsity and similar priori, and belongs to the technical field of image processing.
Background
At present, the image acquisition and transmission process is affected by various interferences, so that the image definition is reduced and the detail information is lost. In image processing, image denoising is an important preprocessing technology, which is the basis and premise of other technologies in image processing, namely, the purpose of image denoising is to extract an original image from a damaged image, provide clear and complete image information which is as close to the original image as possible for other stages of image processing, and the position of an efficient and high-quality image denoising method in image processing is important, so that image denoising is always a very hot research subject in image processing. A number of very efficient denoising methods have been proposed to date for image denoising.
Numerous denoising methods can be broadly divided into two main categories, one is a method based on spatial domain processing, and one is a method based on transform domain processing.
For the spatial domain processing method, the non-local mean method proposed by Baudes et al is an effective denoising algorithm capable of protecting detail information, and has been widely applied to many digital image processing fields. The algorithm fully utilizes the information redundancy in the image, and the main idea is that the gray value of the current pixel to be processed is replaced by the weighted average of a plurality of pixels taking the point to be processed as the center, so that the denoised image is obtained, when the weight is calculated, the image blocks with the same size are selected by taking a single pixel as the center, the similarity between the pixels is measured by utilizing the difference between the image blocks, and the weight of a certain pixel to the pixel to be processed is further determined. However, the non-local mean algorithm has the defect that the denoising effect is greatly influenced by parameters such as the neighborhood size, the image block size, the distance measurement and the like, and in addition, the accuracy of weight calculation is reduced under the condition of strong image noise. Although there are many modifications and optimization algorithms for their shortcomings, such as modifying neighborhood shapes, improving weight calculation methods, etc., these algorithms inevitably increase algorithm complexity.
In the transform domain processing method, the image is subjected to multi-scale transformation, and then the transformed coefficients are processed by using different methods and models to obtain a denoising image, for example, the image is transformed into a frequency domain by widely applied Fourier transformation, so that image frequency information can be embodied, and the wavelet transformation can simultaneously contain time information and frequency information. However, due to the lack of directionality of wavelet transformation, many detail features of an image cannot be well approximated, so that the denoising effect of the image tends to be blurred visually. In order to overcome the defect of the lack of wavelet transformation directions, a plurality of multi-scale transformations based on wavelet are proposed, wherein the shear wave transformation can perform random direction transformation, meanwhile, the direction number of each scale can be different, and the multi-scale transformation has very good effects on edge detection and denoising enhancement of an image, but the Gibbs effect of a final image can be caused when the scale transformation and the direction transformation are performed, and the multi-scale transformation visually represents a few artifacts.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an image enhancement method based on sparsity and similar priori.
The invention provides a natural image sharpening enhancement method based on sparse and similar priori without artifacts, which comprises the steps of firstly, applying shear wave transformation to a noisy image; secondly, enhancing the transformed image by adopting a hard threshold function; finally, the artifact is removed by using a non-local mean value method, and the generation of the artifact caused by excessive enhancement is effectively avoided while important details are highlighted.
Term interpretation:
1. discrete shear wave transformation, wherein the shear wave transformation is to expand a certain function into a linear combination of certain base functions, the coefficients of the base functions are the inner products of the expanded functions and the base functions, and under the condition of a given group of base functions, the result of the shear wave transformation is a group of coefficients corresponding to the base functions; the discrete shear wave transform is a case where the spread function is considered as a discrete function, and the result of the transform is also a set of coefficients corresponding to the respective basis functions.
2. The hard threshold function may be expressed by the following equation:
DST-Hard discrete shearlet transform with Hard thresholding, discrete shear wave transform Hard thresholding.
The technical scheme of the invention is as follows:
an image enhancement method based on sparsity and similarity prior comprises the following steps:
(1) Performing discrete shear wave transformation on the image to obtain a shear wave coefficient; the shear wave coefficients can be seen as projections of the image onto different basis functions of anisotropy, the basis functions of the shear wave transform having anisotropy compared to the wavelet transform of the basis functions of isotropy, the coefficients of the image corresponding to the different shear wave basis functions comprising information on the direction of texture in the image, so that useful information in the image can be better preserved with the shear wave transform. In addition, the shear wave basis function uses a shear process, which makes it consistent for processing in the case of continuous and discrete functions, ensuring an efficient implementation of the algorithm.
(2) Using a hard threshold function T τ Processing a shear wave coefficient obtained after discrete shear wave conversion, wherein the processing process is as follows:if a certain shear wave coefficient is greater than or equal to a first selected threshold value tau, retaining the shear wave coefficient; if a certain shear wave coefficient is smaller than a first selected threshold value tau, setting the shear wave coefficient to be zero; using a hard threshold function T τ The shear wave coefficient obtained after discrete shear wave conversion is processed, so that details can be enhanced, and if the direction of the singular point is the same as the direction of a certain basis function, the corresponding shear wave coefficient can be larger; if the direction of the singular point is different from a certain basis function, the shear wave coefficient is smaller, however, the projection of noise on the basis function direction is the same large, so that useful information in the image can be separated from the noise by utilizing the property, and the purpose of enhancing the details of the image is achieved.
(3) Performing artifact removal treatment on the image processed in the step (2); due to the adoption of the hard threshold function T in the step (2) τ Some small coefficient errors containing image information are set to be zero, and some claw-shaped artifacts appear on the processed result image, and the phenomenon is particularly obvious in a smooth area; these artifacts can be regarded as a special form of noise, and the non-local mean algorithm can effectively remove noise on the premise of preserving image details, so that we use the non-local mean algorithm to remove the artifacts.
In the step (1), the discrete shear wave transformation is performed on the image to obtain a shear wave coefficient, and the calculation method is shown as a formula (I):
in the formula (I), g represents a function which needs discrete shear wave conversion;
representing the mapping relation, and mapping the function g into a shear wave coefficient; psi represents a shear wave mother function; psi phi type j,k,m Representing a basis function generated by a shear wave mother function ψ; j, k, m represent scale, direction and translation, respectively, g (j, k, m) represent shear wave coefficients of different scale, direction and translation; psi phi type j,k,m Representing a basis function generated by a shear wave mother function ψ; />
Representing the mapping symbols, representing the mapping of the function g to be phi j,k,m Corresponding coefficients;<g,ψ j,k,m >represents g and ψ j,k,m Making an inner product, namely a shear wave coefficient; />
SH (ψ) represents the entire shear wave basis function ψ generated from the shear wave mother function ψ j,k,m As shown in formula (II):
in the formula (II),
representing a basis function obtained by performing scale transformation and translational transformation on the shear wave mother function psi; 2 j Is a scale factor, S k Represents a shear factor->
Representing the scale matrix, representing the function argument.
According to a preferred embodiment of the present invention, in step (2), a hard threshold function T is used τ Processing shear wave coefficients obtained after discrete shear wave conversion, wherein the calculation method is shown in a formula (III):
in the formula (III), DST-Hard (g) represents the discrete shear wave transformation Hard thresholding of g, and the processed result is recorded as
Representing a preliminary denoising image obtained after the discrete shear wave transformation hard threshold processing; t (T) τ Is a threshold value tau>0 (0)A hard threshold function; t (T) τ (<g,ψ j,k,m >) Representing shear wave coefficients<g,ψ j,k,m >Performing hard threshold operation; s is S c And S is equal to f Is two index sets, S c Representing coarse scale coefficients, s, associated with the smooth regions of the image f Representing the fine scale factors associated with the edges and detail regions of the image.
According to the invention, in the step (3), artifact removal processing is performed by using a non-local mean algorithm, and the calculation method is shown in a formula (IV):
in formula (IV), SSF (u) ij ) Representing gray values of pixel points (i, j) obtained by a non-local mean algorithm; u represents the whole image; u (u) mn Representing gray values at the pixel points (m, n); omega represents a search area of a certain fixed size in the calculation process; (m, n) ∈Ω denotes that the pixel point (m, n) is localized in Ω, SSF (u ij ) When the gray value of the pixel point (i, j) is carried out in a neighborhood, not the pixels of the whole image participate in the weighted average calculation, but the calculation is limited to be carried out in a search area omega taking the pixel point (i, j) as the center, and the area omega is smaller than the whole image, so that the calculation load can be reduced, and the calculation efficiency of the self-similarity filtering is improved; SSF (u) ij ) The denominator in the calculation formula of (a) is a normalization factor;
ω ij (m, n) represents a weighted average function measuring the similarity of two pixel points (i, j) and (m, n), and the calculation formula (V) is shown as follows:
in the formula (V), N ij Representing a neighborhood centered on pixel (i, j), N mn Represents a neighborhood centered on a pixel (m, N), u (N) ij ) Representing an image block centered on a pixel (i, j); u (N) mn ) Representing an image block centered on a pixel point (m, n),
representing a gaussian weighted distance between two image blocks; h is a smoothing factor used to control the smoothing ability of the exponential function in the similarity measure. />
According to the invention, the threshold value τ is preferably the noise standard deviation σ and the parameter t j Product of t j 2.5 or 3.8.
The beneficial effects of the invention are as follows:
1. the invention provides an image enhancement method based on sparse and similar priori, which adopts discrete shear wave transformation, thereby ensuring the quick realization of algorithm; the shear wave coefficient of the image is processed by the hard threshold function, so that image noise is effectively removed, and the edge and detail parts of the image are enhanced.
2. The non-local mean value is used for carrying out post-processing, so that noise amplification and excessive enhancement common in an image enhancement method are avoided, and the effect of carrying out artifact-free enhancement on noise-removed and blurred retina image data is realized; experimental results show that the algorithm can effectively strengthen important details of image data, avoid excessive enhancement and noise amplification, and bring assistance to image interpretation and subsequent processing.
3. The shear wave is combined with the non-local mean value, the advantages are complementary, the problem that the non-local mean value has poor high noise level processing effect is solved, meanwhile, artifacts in images of the shear wave transformation band are avoided, and the whole algorithm has a better denoising and enhancing effect.
Drawings
Fig. 1 is a flow chart of an image enhancement method based on sparsity and similar priors provided by the present invention.
Fig. 2 shows the raw image without processing.
Fig. 3 is an image processed by the hard threshold function of step (2).
Fig. 4 is an image after the artifact removal processing performed by the non-local mean algorithm in step (3).
Fig. 5 is a denoised image using only a non-local mean algorithm.
Detailed Description
The invention is further illustrated, but not limited, by the following examples and figures of the specification.
Example 1
An image enhancement method based on sparsity and similarity prior, as shown in fig. 1, comprises the following steps:
(1) Inputting a natural image containing noise, and performing discrete shear wave transformation on the image to obtain a shear wave coefficient as shown in fig. 2; the shear wave coefficients can be seen as projections of the image onto different basis functions of anisotropy, the basis functions of the shear wave transform having anisotropy compared to the wavelet transform of the basis functions of isotropy, the coefficients of the image corresponding to the different shear wave basis functions comprising information on the direction of texture in the image, so that useful information in the image can be better preserved with the shear wave transform. In addition, the shear wave basis function uses a shear process, which makes it consistent for processing in the case of continuous and discrete functions, ensuring an efficient implementation of the algorithm.
The calculation method is shown in formula (I):
in the formula (I), g represents a function which needs discrete shear wave conversion;
representing the mapping relation, and mapping the function g into a shear wave coefficient; psi represents a shear wave mother function; psi phi type j,k,m Representing a basis function generated by a shear wave mother function ψ; j, k, m represent scale, direction and translation, respectively, g (j, k, m) represent shear wave coefficients of different scale, direction and translation; psi phi type j,k,m Representing a basis function generated by a shear wave mother function ψ; />
Representing the mapping symbols, representing the mapping of the function g to be phi j,k,m Corresponding coefficients;<g,ψ j,k,m >represents g and ψ j,k,m Making an inner product, namely a shear wave coefficient;
the basis functions satisfying equation (II) form a set SH (ψ), SH (ψ) representing the entire shear wave basis functions ψ generated by the shear wave mother function ψ j,k,m As shown in formula (II):
in the formula (II),
representing a basis function obtained by performing scale transformation and translational transformation on the shear wave mother function psi; 2 j Is a scale factor, S k Represents a shear factor->
Representing the scale matrix, representing the function argument.
(2) Using a hard threshold function T τ Processing a shear wave coefficient obtained after discrete shear wave conversion, wherein the processing process is as follows: if a certain shear wave coefficient is greater than or equal to a first selected threshold value tau, retaining the shear wave coefficient; if a certain shear wave coefficient is smaller than a first selected threshold value tau, setting the shear wave coefficient to be zero;
wherein the threshold τ is selected by: noise standard deviation sigma and parameter t j Is multiplied by (t) to obtain a selected threshold value j Is a parameter whose value is related to j, when j is 0,1,2,3, t j The values of (2) are 2.5,2.5,2.5,3.8 respectively. For the noise standard deviation sigma, a plurality of classical methods are used for estimation, in this patent, an image patch of an image smoothing area is selected, and the variance of the pixel gray value of the patch is calculated as the noise variance, so as to obtain the noise standard deviation. The square root of the noise variance is the noise standard deviation, and many classical methods are used to estimate the noise variance.
Using a hard threshold function T τ For discrete shear wave changesThe shear wave coefficient obtained after the conversion is processed, and the calculation method is shown as a formula (III):
in the formula (III), DST-Hard (g) represents the discrete shear wave transformation Hard thresholding of g, and the processed result is recorded as
Representing a preliminary denoising image obtained after the discrete shear wave transformation hard threshold processing;<g,ψ j,k,m >representing shear wave coefficients; t (T) τ Is a threshold value tau>A hard threshold function of 0; t (T) τ (<g,ψ j,k,m >) Representing shear wave coefficients<g,ψ j,k,m >Performing hard threshold operation; s is S c And S is equal to f Is two index sets, S c Representing a coarse scale factor associated with an image smoothing region, wherein the image smoothing region is a region in which a change in an image gray value is small; s is S f Representing fine scale factors related to the edges and detail areas of the image, wherein the detail areas are areas with large changes of gray values of the image, and are usually texture areas and edges; in a specific operation, after all shear wave coefficients are calculated, the maximum value of the absolute values of the coefficients is selected, 30% of the maximum value is used as a definition standard, the fine scale coefficient is larger than the standard, and the coarse scale coefficient is smaller than the standard.
Using a hard threshold function T τ The shear wave coefficient obtained after discrete shear wave conversion is processed, so that details can be enhanced, and if the direction of the singular point is the same as the direction of a certain basis function, the corresponding shear wave coefficient can be larger; if the direction of the singular point is different from a certain basis function, the shear wave coefficient is smaller, however, the projection of noise on the basis function direction is the same large, so that useful information in the image can be separated from the noise by utilizing the property, and the purpose of enhancing the details of the image is achieved.
The left picture of FIG. 3 shows the hard threshold function T after step (2) τ The processed image, the right picture of fig. 3 is a partial enlarged picture of a dotted line frame in the left picture, and as can be seen from the picture, most of noise in the image is removed after the processing, and detailed information of the image is well reserved, but as can be seen from the partial enlarged picture, some claw-shaped artifacts still exist in the image.
(3) Performing artifact removal treatment on the image processed in the step (2); due to the adoption of the hard threshold function T in the step (2) τ Some small coefficient errors containing image information are set to be zero, and some claw-shaped artifacts appear on the processed result image, and the phenomenon is particularly obvious in a smooth area; these artifacts can be regarded as a special form of noise, and the non-local mean algorithm can effectively remove noise on the premise of preserving image details, so that we use the non-local mean algorithm to remove the artifacts.
The artifact removal processing is carried out by utilizing a non-local mean value algorithm, and the specific calculation method is shown in a formula (IV):
in formula (IV), SSF (u) ij ) Representing gray values of pixel points (i, j) obtained by a non-local mean algorithm; u represents the whole image; u (u) mn Representing gray values at the pixel points (m, n); omega represents a search area of a certain fixed size in the calculation process; (m, n) ∈Ω denotes that the pixel point (m, n) is localized in Ω, SSF (u ij ) When the gray value of the pixel point (i, j) is carried out in a neighborhood, not the pixels of the whole image participate in the weighted average calculation, but the calculation is limited to be carried out in a search area omega taking the pixel point (i, j) as the center, and the area omega is smaller than the whole image, so that the calculation load can be reduced, and the calculation efficiency of the self-similarity filtering is improved; SSF (u) ij ) The denominator in the calculation formula of (a) is a normalization factor;
ω ij (m, n) represents a weighted average function measuring the similarity of two pixel points (i, j) and (m, n), and the calculation formula (V) is shown as follows:
in the formula (V), N ij Representing a neighborhood centered on pixel (i, j), N mn Represents a neighborhood centered on a pixel (m, N), u (N) ij ) Representing an image block centered on a pixel (i, j); u (N) mn ) Representing an image block centered on a pixel point (m, n),
representing a gaussian weighted distance between two image blocks; h is a smoothing factor used to control the smoothing ability of the exponential function in the similarity measure.
After the processing of the step (3), the left picture in fig. 4 is the image after the artifact removal processing of the step (3), the right picture is a partial enlarged picture of a dotted line frame of the left picture in fig. 4, after the processing of the step (3), the detail information of the image can still be well reserved, and as can be seen from the partial enlarged picture, compared with the result of the last step, almost all artifacts are removed.
Comparative example 1
In comparative example 1, only classical non-local mean processing is used, a noisy natural image is input, the non-local mean algorithm is used for artifact removal processing, and the calculation method is shown as a formula (IV):
in formula (IV), SSF (u) ij ) Representing gray values of pixel points (i, j) obtained by a non-local mean algorithm; u represents the whole image; u (u) mn Representing gray values at the pixel points (m, n); Ω denotes that the calculation process is limited to a search area Ω of a certain fixed size, SSF (u ij ) When gray values of pixel points (i, j) are performed in a neighborhood, pixels of the whole image are not involved in weighted average calculation, but are limited to a search area omega centered on the pixel points (i, j), and the area omega is smaller thanThe whole image can reduce the calculation load and improve the calculation efficiency of the self-similar filtering; SSF (u) ij ) The denominator in the calculation formula of (a) is a normalization factor;
ω ij (m, n) represents a weighted average function measuring the similarity of two pixel points (i, j) and (m, n), and the calculation formula (V) is shown as follows:
in the formula (V), N ij Representing a neighborhood centered on pixel (i, j), N mn Represents a neighborhood centered on a pixel (m, N), u (N) ij ) Representing an image block centered on a pixel (i, j); u (N) mn ) Representing an image block centered on a pixel point (m, n),
representing a gaussian weighted distance between two image blocks; h is a smoothing factor used to control the smoothing ability of the exponential function in the similarity measure;
the image after classical non-local mean processing is shown in fig. 5, because the noise level is high, the image becomes blurred while the noise is removed, and much detail information is lost. In summary, the image contrast after processing by the image enhancement method based on shear waves provided by the invention is obviously higher than the processing result of the classical non-local mean value algorithm.
Claims (3)
1. The image enhancement method based on sparse and similar priori is characterized by comprising the following steps:
(1) Performing discrete shear wave transformation on the image to obtain a shear wave coefficient, wherein the calculation method is shown in a formula (I):
in formula (I), g represents the function required to perform discrete shear wave conversionA number;
representing the mapping relation, and mapping the function g into a shear wave coefficient; psi represents a shear wave mother function; psi phi type j，k，m Representing a basis function generated by a shear wave mother function ψ; j, k, m represent scale, direction and translation, respectively, g (j, k, m) represent shear wave coefficients of different scale, direction and translation; psi phi type j，k，m Representing a basis function generated by a shear wave mother function ψ; />
Representing the mapping symbols, representing the mapping of the function g to be phi j，k，m Corresponding coefficients;<g，ψ j，k，m >represents g and ψ j，k，m Making an inner product, namely a shear wave coefficient;
SH (ψ) represents the entire shear wave basis function ψ generated from the shear wave mother function ψ j，k，m As shown in formula (II):
in the formula (II) of the present invention,
representing a basis function obtained by performing scale transformation and translational transformation on the shear wave mother function psi; 2 j Is a scale factor, S k Represents a shear factor->
Representing a scale matrix, representing function arguments;
(2) Using a hard threshold function T τ Processing a shear wave coefficient obtained after discrete shear wave conversion, wherein the processing process is as follows: if a certain shear wave coefficient is greater than or equal to a first selected threshold value tau, retaining the shear wave coefficient; if a certain shear wave coefficient is smaller than a first selected threshold value tau, setting the shear wave coefficient to be zero;
(3) And (3) carrying out artifact removal treatment on the image processed in the step (2) by using a non-local mean algorithm, wherein the calculation method is shown in a formula (IV):
in formula (IV), SSF (u) ij ) Representing gray values of pixel points (i, j) obtained by a non-local mean algorithm; u represents the whole image; u (u) m Representing gray values at the pixel points (m, n); omega represents a search area of a certain fixed size in the calculation process; (m, n) ∈Ω denotes that the pixel point (m, n) is localized in Ω;
ω ij (m, n) represents a weighted average function measuring the similarity of two pixel points (i, j) and (m, n), and the calculation formula (V) is shown as follows:
in the formula (V), N ij Representing a neighborhood centered on pixel (i, j), N mn Represents a neighborhood centered on a pixel (m, N), u (N) ij ) Representing an image block centered on a pixel (i, j); u (N) mn ) Representing an image block centered on a pixel (m, n),
representing a gaussian weighted distance between two image blocks; h is a smoothing factor.
2. The sparse and similar prior based image enhancement method of claim 1, wherein in step (2), a hard threshold function T is employed τ Processing shear wave coefficients obtained after discrete shear wave conversion, wherein the calculation method is shown in a formula (III):
in formula (III), DST-Hard (g) represents performing discrete shear wave transformation on gHard thresholding, the result of which is noted as
Representing a preliminary denoising image obtained after the discrete shear wave transformation hard threshold processing; t (T) τ A hard threshold function for a threshold τ > 0; t (T) τ (<g，ψ j，k，m >) Representing shear wave coefficients<g，ψ j，k，m >Performing hard threshold operation; s is(s) c And s f Is two index sets, s c Representing coarse scale coefficients, s, associated with the smooth regions of the image f Representing the fine scale factors associated with the edges and detail regions of the image.
3. An image enhancement method based on sparsity and similarity priors according to any of claims 1 or 2 wherein the threshold τ is the noise standard deviation σ and the parameter t j Product of t j 2.5 or 3.8.
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