CN114255182B - CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation - Google Patents

CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation Download PDF

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CN114255182B
CN114255182B CN202111515665.2A CN202111515665A CN114255182B CN 114255182 B CN114255182 B CN 114255182B CN 202111515665 A CN202111515665 A CN 202111515665A CN 114255182 B CN114255182 B CN 114255182B
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张�杰
王凤仙
李林伟
齐企业
张焕龙
张建伟
陈宜滨
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Zhengzhou University of Light Industry
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Abstract

The invention provides a CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation, which comprises the following steps: initializing a reconstructed image and an initial noisy observed value; performing iterative updating on the obtained reconstructed image to obtain an estimated value; performing profile wave transformation based on an optimized threshold soft threshold operator to obtain a denoising estimated value profile wave sparse coefficient; inputting the obtained denoising estimated value profile wave sparse coefficient into a space-based self-adaptive total variation CS reconstruction model to obtain a reconstructed image profile wave coefficient; filtering by using a wiener filtering operator based on the profile wave to obtain a profile wave coefficient of the reconstructed image; and carrying out inverse contour wave transformation on the contour wave coefficient of the reconstructed image to obtain the reconstructed image. According to the invention, the profile wave transformation based on the optimized threshold soft threshold operator is adopted for sparse transformation, so that not only can the image data and the noise information be effectively separated, but also the noise information hidden in each layer of the image can be effectively removed to obtain high-quality image sparse coefficients, and the denoising reconstruction capability is improved.

Description

CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation
Technical Field
The invention relates to the technical field of image denoising, in particular to a CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation, which is suitable for denoising reconstruction of high-resolution high-noise images, and particularly relates to denoising reconstruction of high-resolution images under the condition of high noise at night.
Background
At present, the use of computer vision technology to promote all-weather real-time monitoring and effective personnel management in important national security areas and urban sensitive public places has become a highly valued research topic around the world. Especially in the environment with poor night illumination conditions, the image information obtained in the night environment usually contains a large amount of noise information due to the working characteristics of the camera sensor, and thus the quality of the night image acquisition is affected. How to realize effective tracking and monitoring of important personnel and personnel identification and access management of important areas from images or videos with high random noise has become an important development direction in the current image processing field, and has important significance for current epidemic prevention and control. In addition, with the rapid development of image sensor technology, the resolution of the obtained image is higher and higher, and the processing of mass data brings a certain pressure to the existing image processing technology although the high-resolution image can expand our field of view. Therefore, the high-resolution high-noise image denoising reconstruction method, in particular to a high-resolution high-noise denoising reconstruction technology under night environment, is a direction of struggling among scholars of all countries at present, and provides powerful technical support for processing big data.
In order to effectively solve the reconstruction problem of the high-resolution image, foreign scholars propose a well-known compressed sensing (Compressed Sensing, CS) theory, and design a corresponding image reconstruction algorithm based on the theory so as to improve the reconstruction speed and reconstruction quality of the high-resolution image and achieve a certain achievement. CS theory mainly consists of three main parts: sparse transformation process, measurement matrix design, and design process of reconstruction algorithm. The innovation part of the invention is mainly in two aspects of sparse transformation process and design of reconstruction algorithm.
At present, the common sparse transformation mainly adopts wavelet transformation, but the wavelet transformation is difficult to perform the most sparse representation on the high-dimensional image data. In addition, in the design of CS denoising reconstruction algorithm, the sparse transformation process is not fully and effectively utilized, and the denoising reconstruction quality of the image is further affected. For the denoising reconstruction of the high-resolution high-noise image, how to introduce a noise removal mechanism in the CS sparse transformation process has a certain influence on the denoising performance of the subsequent CS high-resolution high-noise image denoising reconstruction method.
Therefore, a sparse transformation method of a high-performance high-noise high-resolution image must be designed, and effective data information of the image and noise information can be separated to the greatest extent in the process of performing image sparse transformation; on the basis, the CS high-noise high-resolution image denoising reconstruction method with high reconstruction speed and high reconstruction precision is designed, so that the denoising reconstruction problem of the high-resolution image under the high-noise condition is effectively solved, and the method has important significance for epidemic prevention and control at present.
Disclosure of Invention
Aiming at the technical problem that the existing CS denoising reconstruction algorithm does not fully utilize sparse transformation information to influence the denoising reconstruction quality of an image, the invention provides a CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation (Spatial Adaptive Total Variation, SATV), which improves the denoising capacity of sparse transformation, improves the denoising reconstruction quality of a high-noise high-resolution image and can effectively remove the high-quality reconstruction of the high-resolution image under the high-noise condition.
In order to achieve the above purpose, the technical scheme of the invention is realized as follows: a CS iteration threshold image denoising reconstruction method based on space self-adaptive total variation comprises the following steps:
step 1: initializing a reconstructed image f 0 =0, iterative index value
Figure SMS_1
Obtaining an initial noise-containing observed value y according to an input original clear image f;
step 2: iteratively updating the obtained reconstructed image by using the initial noisy observed value y to obtain an estimated value
Figure SMS_2
Step 3: the estimated value to be obtained
Figure SMS_3
Inputting to the soft threshold operator χ (x) based on the optimized threshold to perform profile wave transformation to obtain the noise-removed estimated value profile wave sparse coefficient +.>
Figure SMS_4
Step 4: the obtained denoising estimated value profile wave sparse coefficient
Figure SMS_5
Inputting the reconstructed image into a CS reconstruction model based on space self-adaptive total variation to obtain a reconstructed image profile wave coefficient +.>
Figure SMS_6
Step 5: reconstructed image contourlet coefficients obtained using pairs of contourlet-based wiener filter operators gamma (x)
Figure SMS_7
Filtering to remove noise information hidden in the reconstructed image contour wave coefficient to obtain a filtered reconstructed image contour wave coefficient +.>
Figure SMS_8
Step 6: the filtered reconstructed image contour wave coefficient
Figure SMS_9
Performing inverse transformation of the contour wave to obtain a reconstructed image
Figure SMS_10
Step 7: judging whether the iteration stop condition is met, if so, stopping the iteration process, and outputting the obtained reconstructed image
Figure SMS_11
If not, iterate index value->
Figure SMS_12
Returning to the step 2, and repeating the processes from the step 2 to the step 7.
In the step 2, an initial noise-containing observed value y=pf+epsilon=pbω+epsilon, wherein P is a compressed sensing measurement matrix, epsilon is white gaussian noise, and B is a profile wave transformation matrix; ω=b T f is the obtained sparse coefficient, f is N×N original clear image, x 1 The original noisy image after adding gaussian white noise epsilon to the image f.
The iterative updating method in the step 2 is as follows:
Figure SMS_13
wherein P is a compressed sensing measurement matrix, < >>
Figure SMS_14
and />
Figure SMS_15
Respectively +.>
Figure SMS_16
Secondary and->
Figure SMS_17
And the estimated value obtained by the iteration is T which is the transpose of the matrix.
The soft threshold operator χ (x) based on the optimized threshold is:
Figure SMS_18
wherein ,
Figure SMS_19
represents the optimization threshold, the variable k e (1, 2,., β), β represents the total number of layers of the decomposition, L q Represents the length of the q-th layer subband, σ represents the noise standard deviation, and N represents the length and width of the original high noise image.
Reconstructing image contour wave coefficients in the step 4
Figure SMS_20
The method of (1) is as follows:
Figure SMS_21
wherein κ is an adjustable parameter; p is the compressed sensing measurement matrix,
Figure SMS_22
is a space self-adaptive full-variance model, and +.>
Figure SMS_23
Wherein r and s are as followsIllustrating reconstructed image contourlet coefficients
Figure SMS_24
Spatial location of the pixel of (2),>
Figure SMS_25
represents the spatial weight, θ represents the contrast factor, +.>
Figure SMS_26
Representing a differential eigenvalue edge indicator, wherein +_>
Figure SMS_27
The weight factors are represented and calculated by a gray variance estimation method:
Figure SMS_28
wherein max (ζ) and min (ζ) respectively represent the reconstructed image contourlet coefficients
Figure SMS_29
Maximum gray level variance and minimum gray level variance of (2); lambda (lambda) 1 and λ2 A maximum local area and a minimum local area at a certain pixel, respectively.
The gray variance ζ r,s Calculation by its 3×3 neighborhood:
Figure SMS_30
the solving method of the maximum local area and the minimum local area comprises the following steps:
Figure SMS_31
wherein ,
Figure SMS_32
represents the standard deviation of noise, G α A gaussian kernel of size 5 x 5 and with the parameter α=0.8 is represented.
In the step 5, the wiener filtering operator gamma (x) based on the profile wave is as follows:
Figure SMS_33
wherein ,
Figure SMS_34
representing the variance of the contourlet coefficients, +.>
Figure SMS_35
Representing an original high noise image x 1 The standard deviation of the contour wave coefficient of the medium noise.
The variance of the contourlet coefficients is:
Figure SMS_36
wherein N (x) is represented by
Figure SMS_37
A 5×5 neighborhood for the center, M being the number of coefficients in the neighborhood N (k), λ being the set parameter;
standard deviation of the contour wave coefficient
Figure SMS_38
The calculation method of (1) is as follows: for original noise-containing image x by median method 1 Noise standard deviation>
Figure SMS_39
And (3) performing estimation: />
Figure SMS_40
wherein ,fD For the original high noise image x 1 Diagonal subband coefficients of a layer 1 haar wavelet decomposition;
using the obtained noise standard deviation
Figure SMS_41
Generating a noise-free image I n For pure noise image I n Performing contourlet decomposition to obtain->
Figure SMS_42
Denoising estimated value profile wave sparse coefficient
Figure SMS_43
Wherein B represents a contourlet transformation matrix; the filtered reconstructed image contour coefficients +.>
Figure SMS_44
The method comprises the following steps: />
Figure SMS_45
The inverse transformation of the profile wave in the step 6 is as follows:
Figure SMS_46
the iteration stop condition of the step 7 is as follows:
Figure SMS_47
wherein ,
Figure SMS_48
for a set small value, +.>
Figure SMS_49
and />
Figure SMS_50
Are respectively->
Figure SMS_51
Secondary and->
Figure SMS_52
Reconstructed image from multiple iterations, < >>
Figure SMS_53
Is l 1 Norms.
The invention has the beneficial effects that: the high-noise high-resolution image is subjected to sparse transformation by adopting the profile wave transformation based on the optimized threshold soft threshold operator, in the process of sparse transformation, the image data and the noise information can be effectively separated, meanwhile, the noise information hidden in each layer of the image can be effectively removed, the high-quality image sparse coefficient is obtained, and powerful support is provided for effective extraction and reconstruction of the subsequent high-resolution image data.
In order to obtain a high-quality reconstructed image, a CS reconstruction model based on space self-adaptive total variation is established, a CS high-noise high-resolution image denoising reconstruction method is designed, the reconstructed image data inevitably contains certain noise information in the process of contour wave transformation based on an optimized threshold soft threshold operator, and in order to improve the denoising quality of the reconstructed image, a contour wave wiener filter operator is used for screening high-resolution image reconstruction coefficients in the iterative process, so that the denoising reconstruction capability of the reconstructed image is improved. The invention can quickly reconstruct a high-quality high-resolution image from the high-noise high-resolution image, has important meaning for effective analysis and feature extraction of high-resolution image data and high-noise image processing in night environment, and has extremely important reference meaning for the design of big data algorithm.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the present invention.
Fig. 2 shows a high-resolution reconstructed image obtained with different compression sampling ratios (Compression Sampling Ratio, CSR) under the condition of noise standard deviation σ=35, wherein (a) is an original moon image, (b) is an original window image, (c) is an original building image, (d) is a noisy moon image, (e) is a noisy window image, (f) is a noisy building image, (g) is a reconstructed image of a noisy moon image when CSR is 0.1, (h) is a reconstructed image of a noisy window image when CSR is 0.1, (i) is a reconstructed image of a noisy building image when CSR is 0.1, (j) is a reconstructed image of a noisy window image when CSR is 0.3, (k) is a reconstructed image of a noisy building image when CSR is 0.3, (m) is a reconstructed image of a noisy moon image when CSR is 0.4, (n) is a reconstructed image of a noisy window when CSR is 0.4, and (o) is a reconstructed image of a noisy building image when CSR is 0.4.
FIG. 3 is a comparison of the performance of the reconstructed image of the present invention, wherein (a) is the standard deviation in noise
Figure SMS_54
Under the condition, the peak signal-to-noise ratio (Peak Signal to Noise Ratio, PSNR) obtained by reconstructing the night moon image is shown as a result of the change of CSR; (b) The PSNR comparison results obtained under different noise standard deviations are shown in the invention when the compressed sampling ratio is 0.35.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the idea of the invention is that: (1) The method comprises the steps that a contour wave transformation process based on an optimization threshold soft threshold operator is innovatively designed in a CS sparse transformation process, and noise information hidden in each layer of an image can be removed to the greatest extent in the contour wave transformation process; (2) The acquired reconstructed image coefficients are iteratively updated by using the proposed space-based adaptive full-variance CS model, so that more accurate image data information can be acquired; (3) And the contour wave wiener filter operator is adopted, so that the obtained reconstructed image contour wave coefficients are effectively screened in the iterative process, and the quality of the reconstructed image is improved.
The hardware environment for implementation of the invention is as follows: intel (R) Core (TM) i7 CPU Core2 computer, 16G memory, running software environment: MATLAB2016b, operating system Windows10. The image data were high resolution image data obtained with a SPARK series of black and white industrial cameras from JAI.
As shown in fig. 1, a CS iterative threshold high noise image denoising reconstruction method based on spatial adaptive total variation includes the following steps:
first) initialization procedure
Initializing reconstructed image x 0 =0, iteration index
Figure SMS_55
Initial noisy observations y=pf+epsilon=pbω+epsilon; p is a compressed sensing measurement matrix, here a random measurement matrix, f is an input N x N original clear image, ε represents Gaussian white noise, x 1 The original noise-containing image after the Gaussian white noise epsilon is added for f, and B is a profile wave transformation matrix; ω=b T f is the obtained sparse coefficient, and T is the transpose of the matrix. A high noise image is generally considered to be an image having a noise standard deviation of 20 or more.
And secondly), carrying out iterative updating on the obtained reconstructed image by utilizing the initial noisy observed value y, and further obtaining an estimated value.
Figure SMS_56
wherein ,
Figure SMS_57
and />
Figure SMS_58
Respectively +.>
Figure SMS_59
Secondary and->
Figure SMS_60
And (5) obtaining an estimated value through multiple iterations.
Thirdly), inputting the obtained estimated value into a soft threshold operator χ (x) based on an optimized threshold to perform contour wave transformation to obtain a noise-removed estimated value contour wave sparse coefficient
Figure SMS_61
Wherein, soft threshold operator χ (x) calculation process based on optimization threshold ζ is:
Figure SMS_62
wherein ,
Figure SMS_63
to optimize the threshold, the variable k e (1, 2,., β), β represents the total number of layers decomposed, L q Represents the length of the k-th layer subband and σ represents the noise standard deviation. In the specific example, σ=35, the value of k varies with the number of layers of the image decomposition, and β=6.
Noise-removed estimated value profile wave sparse coefficient
Figure SMS_64
In the process of carrying out the multi-scale decomposition of the profile wave on the image, after each layer of image coefficient is obtained by decomposition, filtering and denoising the layer of coefficient by using a soft threshold operator based on an optimized threshold value xi, and so on until the total layer beta number is decomposed and then the process is finished. That is, after each layer of decomposition coefficients is obtained, the soft threshold operator filter is used to denoise once.
Fourth), the obtained denoising estimated value profile wave sparse coefficient
Figure SMS_65
Inputting the reconstructed image into a CS reconstruction model based on space self-adaptive total variation to obtain a reconstructed image profile wave coefficient +.>
Figure SMS_66
And is also provided with
Figure SMS_67
Wherein, kappa is an adjustable parameter,
Figure SMS_68
is 2 norms. The calculation method of the space self-adaptive total variation model comprises the following steps:
Figure SMS_69
wherein r and s represent reconstructed image contour wave coefficients
Figure SMS_70
The value range of the spatial position of the pixel is 1-r, s-N and +.>
Figure SMS_71
Represents spatial weight, θ represents contrast factor, +.>
Figure SMS_72
Representing a differential eigenvalue edge indicator, wherein +_>
Figure SMS_73
The weight factor is represented to balance the enhancement of image details and noise suppression, and can be calculated by a gray variance estimation method:
Figure SMS_74
wherein max (ζ) and min (ζ) respectively represent the reconstructed image contourlet coefficients
Figure SMS_75
And a minimum gray level variance. Gray level variance ζ r,s Can be calculated by its 3 x 3 neighborhood and: />
Figure SMS_76
a. b is the neighborhoodAnd (5) taking a value. Lambda (lambda) 1 and λ2 The solution process is as follows for the maximum local area and the minimum local area at a certain pixel respectively:
Figure SMS_77
wherein ,
Figure SMS_78
sigma represents the standard deviation of noise, G α A gaussian kernel of size 5 x 5 and with the parameter α=0.8 is represented.
Solving a space-based self-adaptive total variation CS reconstruction model by adopting an iteration method, wherein the calculation process is as follows:
Figure SMS_79
wherein, τ represents the iteration number, and the value range is: τ is more than or equal to 0 and less than or equal to 15.
Fifth), the reconstructed image contour wave coefficient obtained by utilizing the gamma (x) pair based on the contour wave wiener filtering operator
Figure SMS_80
Filtering to remove noise information hidden in the reconstructed image contour wave coefficient to obtain a filtered reconstructed image contour wave coefficient
Figure SMS_81
/>
And is also provided with
Figure SMS_82
The calculation process based on the contour wave wiener filter operator gamma (x) is as follows:
Figure SMS_83
wherein ,
Figure SMS_84
the variance representing the profile wave sparseness is estimated by:
Figure SMS_85
wherein N (x) is represented by
Figure SMS_86
Is a central 5×5 neighborhood, M is the number of coefficients in neighborhood N (k). λ is a setting parameter, in the example set to λ=3.5.
Figure SMS_87
Representing an original high noise image x 1 The standard deviation of the contour wave coefficient of the medium noise in order to obtain the variance +.>
Figure SMS_88
First, the original noise-containing image x is obtained by median method 1 Noise standard deviation>
Figure SMS_89
And (3) performing estimation:
Figure SMS_90
wherein ,xD Diagonal subband coefficients for layer 1 haar wavelet decomposition of the original high noise image x 1. Then, the obtained noise standard deviation is utilized
Figure SMS_91
Generating a noise-free image I n Then for pure noise image I n Performing contour decomposition to obtain a standard deviation of the contour coefficients +.>
Figure SMS_92
In the present invention
Figure SMS_93
Sixth) filtering the reconstructed image contour coefficients
Figure SMS_94
Performing inverse contourlet transform to obtain reconstructed image +.>
Figure SMS_95
Figure SMS_96
Seventh) judging whether the iteration stop condition is satisfied:
Figure SMS_97
wherein ,
Figure SMS_98
is a set small value. If reconstruct image +>
Figure SMS_99
And the previous reconstructed image->
Figure SMS_100
L of difference 1 Stopping the iterative process when the norm is greater than or equal to the set parameter, and outputting the obtained reconstructed image +.>
Figure SMS_101
Otherwise, returning to the second step), and repeating the iterative processes of the second to seventh steps).
The implementation steps of the invention are as follows: initializing a reconstructed image, an iteration index value and an initial noisy observed value; carrying out iterative updating on the obtained reconstructed image by utilizing the initial noisy observed value, thereby obtaining an estimated value; inputting the obtained estimated value into a soft threshold operator profile wave transformation process based on an optimized threshold value to obtain a denoising estimated value profile wave sparse coefficient; inputting the obtained denoising estimated value profile wave sparse coefficient into a CS reconstruction model based on space self-adaption total variation to obtainObtaining a reconstructed image contour wave coefficient; the method comprises the steps of performing a filtering process on an obtained reconstructed image contour wave coefficient by using a contour wave wiener-based filtering operator, removing noise information hidden in the reconstructed image contour wave coefficient, and obtaining a filtered reconstructed image contour wave coefficient; and carrying out a contour wave inverse transformation process on the filtered reconstructed image contour wave coefficient to obtain a reconstructed image. Judging whether the iteration stop condition is met, if so, determining that the reconstructed image and the last reconstructed image are l 1 Stopping the iterative process when the norm is greater than or equal to the set parameter, and outputting the obtained reconstructed image; and otherwise repeating the above process.
The invention adopts subjective and objective evaluation methods to evaluate the effectiveness of the proposed algorithm. The subjective evaluation method mainly evaluates the quality of the reconstructed image directly through a human visual system, as shown in fig. 2. Raw night moon, window and building images of 4096×4096 taken are shown in fig. 2 (a) - (c); fig. 2 (d) - (f) show noisy night moon, noisy windows and noisy architectural images obtained by adding noise of the noise standard difference σ=35 to the original image. CSR is the ratio of the obtained dimension of the reconstructed observation value to the dimension of the original image, and the smaller the value of CSR is, the less measurement data is required for reconstructing the image; the more vice versa. FIGS. 2 (g) - (i) show the reconstruction results obtained by the present invention for noisy night moon, noisy windows and noisy building images, respectively, at CSR of 0.1; it can be seen that the present invention can remove most of noise information in the high noise high resolution image when CSR is 0.1, and reconstruct the high quality high resolution image. FIGS. 2 (j) - (l) show the reconstruction results obtained by the present invention for noisy night moon, noisy windows and noisy architectural images, respectively, at CSR of 0.3; the reconstruction results obtained by the present invention for noisy night moon, noisy windows and noisy building images, respectively, are shown in fig. 2 (m) - (o) with CSR of 0.4. As can be seen from fig. 2 (g) - (o), as CSR increases gradually, the quality of the high resolution reconstructed image obtained by the present invention increases.
The objective evaluation method mainly comprises the steps of completing the evaluation of the quality of the reconstructed image by using a specific formula through an established mathematical model. In fig. 3, (a) shows the PSNR value obtained by reconstructing the noisy night moon image under different CSR conditions by the proposed algorithm when the noise standard deviation is 35; it can be seen that as CSR increases, the PSNR obtained by the proposed algorithm increases gradually. In fig. 3 (b) is shown the PSNR values obtained by the present invention for reconstructing noisy night moon images with different noise standard deviations at CSR of 0.35; it can be seen that as the standard deviation of noise increases, the noise information gradually increases, and the method can obtain a higher PSNR value for denoising reconstruction of a high-noise image. Meanwhile, as noise information increases, the PSNR value of the invention is slower in reduction rate and higher in robustness. As can be seen from fig. 3, when the compressed sampling is relatively low, the present invention can take a relatively short reconstruction time to obtain a high peak signal-to-noise ratio, thereby strongly proving the effectiveness of the present invention.
The above description is only of the preferred embodiments of the present invention, and is not intended to limit the invention, but any modifications, equivalent substitutions, improvements, etc. within the spirit and scope of the present invention should be included in the scope of the present invention.

Claims (9)

1. The CS iteration threshold image denoising reconstruction method based on the space self-adaptive total variation is characterized by comprising the following steps of:
step 1: initializing a reconstructed image f 0 =0, iterative index value
Figure FDA0004182231490000011
Obtaining an initial noise-containing observed value y according to an input original clear image f;
step 2: iteratively updating the obtained reconstructed image by using the initial noisy observed value y to obtain an estimated value
Figure FDA0004182231490000012
Step 3: the estimated value to be obtained
Figure FDA0004182231490000013
Input toPerforming profile wave transformation based on an optimized threshold soft threshold operator χ (x) to obtain a denoising estimated value profile wave sparse coefficient +.>
Figure FDA0004182231490000014
The soft threshold operator χ (x) based on the optimized threshold is:
Figure FDA0004182231490000015
wherein ,
Figure FDA0004182231490000016
represents the optimization threshold, the variable k e (1, 2,., β), β represents the total number of layers of the decomposition, L q Representing the length of the q-th layer sub-band, σ representing the noise standard deviation, and N representing the length and width of the original high noise image;
step 4: the obtained denoising estimated value profile wave sparse coefficient
Figure FDA0004182231490000017
Inputting the reconstructed image into a CS reconstruction model based on space self-adaptive total variation to obtain a reconstructed image profile wave coefficient +.>
Figure FDA0004182231490000018
Reconstructing image contour wave coefficients in the step 4
Figure FDA0004182231490000019
The method of (1) is as follows:
Figure FDA00041822314900000110
wherein κ is an adjustable parameter; p is the compressed sensing measurement matrix,
Figure FDA00041822314900000111
is a space self-adaptive full-variance model, and
Figure FDA00041822314900000112
wherein r and s represent reconstructed image contour wave coefficients
Figure FDA00041822314900000113
Spatial location of the pixel of (2),>
Figure FDA00041822314900000114
represents spatial weight, θ represents contrast factor, +.>
Figure FDA00041822314900000115
Representing a differential eigenvalue edge indicator, wherein,
Figure FDA00041822314900000116
representing the weight factor;
step 5: reconstructed image contourlet coefficients obtained using pairs of contourlet-based wiener filter operators gamma (x)
Figure FDA00041822314900000117
Filtering to remove noise information hidden in the reconstructed image contour wave coefficient to obtain a filtered reconstructed image contour wave coefficient
Figure FDA00041822314900000118
Step 6: the filtered reconstructed image contour wave coefficient
Figure FDA00041822314900000119
Performing inverse contourlet transform to obtain reconstructed image +.>
Figure FDA00041822314900000120
Step 7: judging whether the iteration stop condition is met, if so, stopping the iteration process, and outputting the obtained reconstructed image
Figure FDA0004182231490000021
If not, iterate index value->
Figure FDA0004182231490000022
Returning to the step 2, and repeating the processes from the step 2 to the step 7.
2. The CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 1, wherein in the step 2, an initial noisy observed value y=pf+ε=pBETA ω+ε, where P is a compressed sensing measurement matrix, ε is white gaussian noise, and β is a profile wave transformation matrix; omega = beta T f is the obtained sparse coefficient, f is N×N original clear image, x 1 The original noisy image after adding gaussian white noise epsilon to the image f.
3. The CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 1 or 2, wherein the iterative update method in step 2 is:
Figure FDA0004182231490000023
wherein P is a compressed sensing measurement matrix, < >>
Figure FDA0004182231490000024
and />
Figure FDA0004182231490000025
Respectively +.>
Figure FDA0004182231490000026
Secondary and->
Figure FDA0004182231490000027
And the estimated value obtained by the iteration is T which is the transpose of the matrix.
4. A CS iterative threshold image denoising reconstruction method based on spatially adaptive total variation according to claim 3, wherein the weight factor is calculated by a gray variance estimation method:
Figure FDA0004182231490000028
wherein max (ζ) and min (ζ) respectively represent the reconstructed image contourlet coefficients
Figure FDA0004182231490000029
A maximum gray variance and a minimum gray variance of (2); lambda (lambda) 1 and λ2 A maximum local area and a minimum local area at a certain pixel, respectively.
5. The CS iterative threshold image denoising reconstruction method based on spatially adaptive total variation according to claim 4, wherein the gray variance ζ r,s Calculation by its 3×3 neighborhood:
Figure FDA00041822314900000210
the solving method of the maximum local area and the minimum local area comprises the following steps:
Figure FDA00041822314900000211
wherein ,
Figure FDA00041822314900000212
sigma represents the standard deviation of noise, G α A gaussian kernel of size 5 x 5 and with the parameter α=0.8 is represented.
6. The CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 4 or 5, wherein the contour wave wiener filter operator γ (x) based in step 5 is:
Figure FDA00041822314900000213
wherein ,
Figure FDA0004182231490000031
representing the variance of the contourlet coefficients, +.>
Figure FDA0004182231490000032
Representing an original high noise image x 1 The standard deviation of the contour wave coefficient of the medium noise.
7. The CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 6, wherein the variance of the contourlet coefficient is:
Figure FDA0004182231490000033
wherein N (x) is represented by
Figure FDA0004182231490000034
A 5×5 neighborhood for the center, M being the number of coefficients in the neighborhood N (k), λ being the setting parameter;
standard deviation of the contour wave coefficient
Figure FDA0004182231490000035
The calculation method of (1) is as follows: for original noise-containing image x by median method 1 Noise standard deviation>
Figure FDA00041822314900000319
And (3) performing estimation: />
Figure FDA0004182231490000036
/>
wherein ,fD For the original high noise image x 1 Diagonal subband coefficients of a layer 1 haar wavelet decomposition;
using the obtained noise standard deviation
Figure FDA0004182231490000037
Generating a noise-free image I n For pure noise image I n Performing contourlet decomposition to obtain
Figure FDA0004182231490000038
8. The CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 7, wherein the denoising estimate value contour wave sparse coefficient
Figure FDA0004182231490000039
Wherein, BETA represents a profile wave transformation matrix; the filtered reconstructed image contour coefficients +.>
Figure FDA00041822314900000310
The method comprises the following steps: />
Figure FDA00041822314900000311
The inverse transformation of the profile wave in the step 6 is as follows:
Figure FDA00041822314900000312
9. the CS iterative threshold image denoising reconstruction method based on spatial adaptive total variation according to claim 4, wherein the iteration stop condition of step 7 is:
Figure FDA00041822314900000313
wherein ,
Figure FDA00041822314900000314
for a set small value, +.>
Figure FDA00041822314900000315
and />
Figure FDA00041822314900000316
Are respectively->
Figure FDA00041822314900000317
Secondary and->
Figure FDA00041822314900000318
The reconstructed image obtained from the number of iterations, l1 is l 1 Norms. />
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