CN112233046B - Image restoration method under Cauchy noise and application thereof - Google Patents
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Abstract
The invention belongs to the technical field of image processing, and discloses an image restoration method under Cauchy noise and application thereof. Acquiring a degraded image composed of an original image and Cauchy noise; determining the size of a proportional parameter in Cauchy distribution according to the size of Cauchy noise; determining a corresponding data fidelity term, and establishing a minimization regularization model under Cauchy noise by using a mixed regularization scheme; and (3) solving the model by a rapid algorithm under the framework of an alternative direction multiplier method, such as obtaining a restored image by a stable solution of the model. The method can effectively remove the fuzzy and Cauchy noises in the image, the novel mixed regular scheme can overcome the defects under single regular, reduce or avoid the step effect, keep the smoothness and the detail texture characteristics of the image and greatly reduce the time for restoring the image. Through numerical simulation experiments, the method has advantages in the aspects of peak signal-to-noise ratio, structural similarity and operation time, and can also show good recovery effect in the aspects of visual sense.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image restoration method under Cauchy noise and application thereof.
Background
At present: in the digital age, images are an important aspect of people to know the objective world, and high-quality images can provide more useful information for people. However, the obtained image is often degraded and degraded by interference and influence of objective conditions such as imaging equipment and living environment, accompanied by certain noise and blur. In order to further acquire high-quality images, one on the one hand raises the sensor level of the imaging device from hardware and on the other hand digitally processes degraded images from the software level. In recent years, image restoration techniques have been widely used and studied in the fields of remote sensing satellite imaging, medical imaging, public safety, and the like.
The model of image degradation can be generally expressed as: and f is Hu + n, wherein u, f, n and H respectively represent an ideal image, a degraded image, additive noise and a fuzzy kernel. Obviously, the inverse problem typical of u obtained from f is that of the greatest feature of this problem, namely the ill-qualification. In order to obtain a stable solution, scholars develop a series of research works by applying a regularization method, a statistical inference method, a primal-dual method and the like. Among them, the best known regularization model proposed by the contemporary genus Tikhonov. Subsequently, Rudin, Osher and Fatemin proposed Total Variation (TV) regularization and a classical ROF model, which retained edge information to a greater extent while restoring images, with the disadvantage of generating a step effect in the restored images. In Order to overcome the deficiency of TV regularization, High-Order Total Variation (HTV) regularization, Fractional Order Total Variation (FOTV) regularization, Generalized Total Variation (TGV) regularization, Overlapping Group Sparse (OGS) regularization, and the like have been proposed in succession. Researchers propose a series of image restoration models based on different regularization terms, such as FTVd model, LLT model and FastTV model.
In degraded images, the most common additive noise is white gaussian noise, and cauchy noise is another additive noise that is highly similar to gaussian noise. Although some gaussian noise can be eliminated by eliminating gaussian noise, part of useful information is lost in the restored image. In order to accurately remove the Kouchy noise, Chang and the like research an image restoration method with the Kouchy noise based on a recursive algorithm of a Markov random field model; achim et al remove Cauchy noise using binary maximization posterior estimation in complex wavelet domain; nikolova and the like remove Cauchy noise in a color image by an image segmentation method; the distribution characteristics of Sciac noise and the like are as Cauchi noise, and a Cauchi denoising model is established based on TV regularization; mei improved the model proposed by f.sciaccitano.
Recently, Yang et al, mixed TV regularization and HTV regularization, proposed the HTVAM model to remove Cauchy noise and blur; ding et al, consider using OGS regularization, and propose the OGSTVL1 model.
The probability density function of known Cauchy noise is
Where γ > 0 is the scaling parameter and σ ∈ R is the localization parameter, with default σ ═ 0 in the study. For example, a probability density function of Cauchy noise, a Maximum A Posteriori (MAP) method is applied, and a data fidelity item of the Cauchy noise under a regularization method can be constructed<log(γ2+(Hu-f)2),1>X。
Due to the outstanding expression of TV regularization in image restoration, Sciac, et al, using the above fidelity term, combined with TV regularization, propose the following denoising model in the paper "spatial adaptive for restoring blue images with Cauchy noise",
wherein the second term is a penalty term, f0Is the result of the median filtering operation on the degraded image. The model can effectively remove Cauchy noise and simultaneously retain the edge information of the image; the disadvantage is that the median filtering operation is used in the penalty phase, and the image restoration result is unsatisfactory.
As for the problem of the model (1), Mei optimizes the model in a paper Cauchy noise removal by non-conditional ADMM with conversion rules, only a data fidelity item and a TV regular item are reserved to establish the model (2), a median filtering operation is avoided,
on experimental results, the model (2) can be superior to the model (1) with the disadvantages that the new non-convex model is too dependent on the initialization of parameters and the restored image still has the step effect.
Li et al and Lysaker et al have considered using a mixture of a total variation regularization term and a higher order total variation regularization term, and have achieved a good effect in image processing. Yang et al in the paper "Total variation and high-order Total variation adaptive model for reconstructing blue images with Cauchy noise" adopts this hybrid regularization scheme and adds an adaptive regularization parameter g to TV and HTV, respectively1And g2An image restoration model contaminated by Cauchy noise is proposed,
wherein HrMean filter with representative size rThe wave filter, M, alpha > 0 is a positive parameter. Under the framework of an Alternating direction method with multipliers (ADMM), an HTVAM algorithm is provided, the method can exert the excellent performance of TV regularization, and the step effect of the TV regularization method is inhibited by using HTV, and the adaptive parameters ensure wider applicability. The disadvantage is that the time cost is too high, which is a disadvantage of the adaptive adjustment of the regularization parameters.
The overlapping group sparse regularization based on the total variation can obtain good results when processing Gaussian noise and impulse noise. The Ding applied OGSTV regularization, a new model was proposed in the paper Total variation with overlapping group space for publishing images under Cauchy noise,
where the third term is OGSTV canonical. Under the ADMM framework, the OGSTVL1 algorithm is proposed to solve model (3). The model (4) can be regarded as the improvement of the model (1) again, and the method has the advantages that the step effect brought by directly using TV regular patterns can be effectively inhibited, and the method does not occupy too much time like the model (3), and has the problems that the texture detail processing capacity of the image needs to be improved, and the smoothness is not good enough.
Through the above analysis, the problems and defects of the prior art are as follows: for Cauchy noise and blur in a degraded image, the conventional technology mostly adopts a regular optimization method based on total variation, and the texture details of the obtained restored image in a local area are not clear enough; meanwhile, the fuzzy and noise processing has obvious noise point or step effect, the smoothness is not good enough, and the required time is relatively high.
The difficulty in solving the above problems and defects is: different regularization terms have different specific effects in image processing, and have different processing effects on different noises. For image restoration work under Cauchy noise, a proper regular scheme needs to be constructed, which is the key point and difficulty of the image restoration work, and only a proper regular term can realize effective constraint on a fidelity term. For multivariate image restoration models, the solution of non-convex models has certain difficulty. For parameters in the model, adaptive adjustment can be applied to more extensive degraded images, but the model is required to learn the texture structure of the natural image widely, so that the difficulty of model solution and the computational complexity are greatly increased.
The significance for solving the problems and the defects is as follows: the solution of the above problems can effectively improve the quality of medical imaging and synthetic aperture radar imaging. The medical imaging of high definition is favorable to medical staff to the state of an illness of patient to in time put forward suitable treatment scheme, effectively reduce patient's death rate, reduce doctor-patient risk to a certain extent, the actual life of giving people brings a great deal of facility. The SAR system on the airplane can shoot ground objects through a high-altitude cloud layer, so that accurate navigation and flight safety are guaranteed; the SAR system on the satellite can work all weather and effectively identify camouflage and penetration cover. The realization of the above functions requires that the Cauchy noises with different sizes in the imaging are removed, and finally, the image with high application value can be obtained.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an image restoration method under Cauchy noise and application thereof.
The image restoration method under the Cauchy noise introduces non-convex l based on HTV in the image restoration problem for processing the Cauchy noisepThe regular function is combined with the OGSTV regular function to provide a mixed regular scheme suitable for Cauchy noise, a non-convex optimization model is further provided, and finally the solution of the model is realized by using an alternating direction multiplier method. The new mixing regular can realize the complementation of the two, the non-convex regular item can keep sharp edge information while smoothing the local texture part, and the overlapping group sparse regular has smooth step effect. In an actual application environment, the degraded image is used as input information to be applied to the method, and a clear digital image subjected to denoising and deblurring can be obtained.
Further, in the image restoration method under Cauchy noise, any one of the mechanisms is selectedThinking the image matrix u belongs to Rn×nThe degradation process contaminated by cauchy noise is expressed as:
where H denotes the fuzzy operator, n1,n2Representing two standard normal distribution matrixes, ξ represents the level value of Cauchy noise, and the proportion parameter in the Cauchy distribution probability density function is
f (x), u (x) are two independent random variables obeying the Cauchy distribution, which represent the number matrix of the degraded image and the ideal image respectively, such as MAP estimation theory, when the conditional probability P (u | f) reaches the maximum, the corresponding probability is
I.e. the optimal estimate.
As a regularization method, an optimization model for removing Cauchy noise is established:
wherein, alpha > 0 represents the regular parameter of the balance data fidelity term and the regular term, mu > 0 represents the punishment parameter, and omega > 0 is the regular parameter of the regular term.
Further, three auxiliary variables z ═ u, q ═ v are introduced2u, v ═ Hu, the optimization model for removing the Cauchy noise is converted from the unconstrained optimization problem to the constrained optimization problem, namely
Then, obtaining an augmented lagrange function, specifically:
wherein λ is1,λ2,λ3Beta is a positive parameter for amplifying Lagrange multiplier, and beta is more than 0; iterative solution, if the solution obtained after the k iteration is
The method of the (k + 1) th iteration is explained below.
Further, the variable u is iteratively updated:
further elaboration of the last row of the above equation with respect to the variable u is derived and made to be 0 can yield:
when the full variation and the high-order full variation are cyclic boundary conditions, the variable u can be updated by using two-dimensional fast fourier transform.
Further, the variable z is iteratively updated:
and selecting an MM algorithm for the subproblems of the variable z to carry out iterative solution.
Further, the variable q is iteratively updated:
for this form of optimization problem, use l1And (4) solving by using a re-weighted iterative algorithm.
Further, the variable v is iteratively updated:
the variable v can be updated by applying a traditional Newton iteration method.
Further, the update of the lagrangian multiplier:
after each iteration update, a calculation is required
The numerical value of (c). When crit is less than epsilon or k is more than N, the iteration is terminated; otherwise k equals k +1, and the iterative operation is continued.
By combining all the technical schemes, the invention has the advantages and positive effects that: the mixing and regularizing method comprises the following steps: the method comprises the steps of establishing a regular model under a new regular scheme by using a non-convex regular function based on a high-order total variation (HTV) and an Overlapping Group Sparse Total Variation (OGSTV) regular function, and solving the model by a fast algorithm under the framework of an alternative direction multiplier method to obtain a restored image after denoising and deblurring. The novel method comprises the following specific steps: acquiring a degraded image consisting of an original image and Cauchy noise (which can contain blur and needs to acquire the scale of a blur kernel); determining the size of a proportional parameter in the Cauchy distribution according to the size of the Cauchy noise; determining a corresponding data fidelity term, and establishing a minimization regularization model under Cauchy noise by using a mixed regularization scheme; and (3) solving the model by a rapid algorithm under the framework of an alternative direction multiplier method, such as obtaining a restored image by a stable solution of the model. The method can effectively remove the fuzzy and Cauchy noises in the image, the novel mixed regular scheme can overcome the defects under single regular, reduce or avoid the step effect, keep the smoothness and the detail texture characteristics of the image and greatly reduce the time for restoring the image. Through numerical simulation experiments, the method has advantages in the aspects of peak signal-to-noise ratio, structural similarity and operation time, and can also show good recovery effect in the aspects of visual sense.
When only Cauchy noise is processed, the novel civilization can better keep the smoothness and the detail texture characteristics of the image and can reduce or avoid the step effect; when the Cauchy noise and the fuzzy phenomenon are processed simultaneously, the processing capacity of the new method for processing noise points is stronger, the Cauchy noise is removed to a greater extent while the fuzzy is inhibited, and the obtained restored image is higher in definition. For the two cases, the advantages of the new invention in the time dimension are relatively prominent. Through a plurality of times of numerical simulation experiments, the method has advantages in the aspects of peak signal-to-noise ratio and structural similarity, and can also show good recovery effect in the aspects of vision and sense.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained by using these drawings without creative efforts.
Fig. 1 is a flowchart of an image restoration method under cauchy noise according to an embodiment of the present invention.
Fig. 2(a) is an original image effect diagram when the noise level is ξ ═ 0.02, which is provided by the embodiment of the present invention.
Fig. 2(b) is a degraded image effect diagram when the noise level is ξ 0.02, which is provided by the embodiment of the present invention.
Fig. 2(c) is a denoising effect diagram of the present invention when the noise level is ξ ═ 0.02, which is provided by the embodiment of the present invention.
Fig. 2(d) is a diagram of the denoising effect of OGSTVL1 when the noise level is ξ ═ 0.02, according to the embodiment of the present invention.
Fig. 2(e) is a diagram of the denoising effect of the HTVAM when the noise level is ξ ═ 0.02 according to the embodiment of the present invention.
Fig. 3(a) is an original image effect diagram when the noise level is ξ ═ 0.04 provided by the embodiment of the present invention.
Fig. 3(b) is a degraded image effect diagram when the noise level is ξ 0.04 provided by the embodiment of the invention.
Fig. 3(c) is a denoising effect diagram of the present invention when the noise level is ξ ═ 0.04, which is provided by the embodiment of the present invention.
Fig. 3(d) is a diagram of the denoising effect of OGSTVL1 when the noise level is ξ ═ 0.04, according to the embodiment of the present invention.
Fig. 3(e) is a diagram of the denoising effect of the HTVAM when the noise level is ξ ═ 0.04 according to the embodiment of the present invention.
Fig. 4(a) is an original image effect diagram when the noise level is ξ 0.02, the window is 9 × 9, and the standard deviation is 1, which is provided by the embodiment of the present invention, and is a gaussian blur.
Fig. 4(b) is a degraded image effect diagram when the noise level is ξ 0.02, the window is 9 × 9, and the standard deviation is 1, which is provided by the embodiment of the present invention.
Fig. 4(c) is a diagram of the denoising effect of the present invention when gaussian blur with a noise level ξ of 0.02, a window 9 × 9, and a standard deviation of 1 is provided according to the embodiment of the present invention.
Fig. 4(d) is a diagram of the denoising effect of OGSTVL1 when gaussian blur with a noise level ξ of 0.02, a window of 9 × 9, and a standard deviation of 1 is provided according to the embodiment of the present invention.
Fig. 4(e) is a diagram of the denoising effect of the HTVAM when the gaussian blur is provided with a noise level ξ of 0.02, a window 9 × 9, and a standard deviation of 1 according to the embodiment of the present invention.
FIG. 5 is a flow chart comparing experiments of the present invention with the OGSTVL1 model and the HTVAM model, provided by embodiments of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In view of the problems in the prior art, the present invention provides an image restoration method under cauchy noise, and the following describes the present invention in detail with reference to the accompanying drawings.
As shown in fig. 1, an image restoration method under cauchy noise according to an embodiment of the present invention includes:
for any ideal image matrix u e Rn×nThe degradation process, which is contaminated by cauchy noise, can be expressed as:
where H denotes the fuzzy operator, n1,n2Representing two standard normal distribution matrices and ξ represents the magnitude of the level value of cauchy noise. In the present invention, the scale parameter in the Cauchy distribution probability density function is empirically selected as
Let f (x), u (x) be two independent random variables obeying the Cauchy distribution, which represent the number matrix of the degraded image and the ideal image respectively, such as MAP estimation theory, and when the conditional probability P (u | f) reaches the maximum, it corresponds to
I.e. the optimal estimate.
Such as a regularization method, in combination with the foregoing description and associated regularization functions, an optimized model for removal of cauchy noise can be established,
wherein, alpha > 0 represents the regular parameter of the balance data fidelity term and the regular term, mu > 0 represents the punishment parameter, and omega > 0 is the regular parameter of the regular term.
Knowing that the third term of the model (5) is a non-convex regular function, the objective function is a non-convex function. In the studies on models (1) - (4), 8 μ γ has been demonstrated2The function is convex in nature when the value is more than or equal to 1, and the invention is still carried out under the condition on parameter selection. The specific operation steps of the invention, i.e. the solution scheme of the model, are described in detail below.
First, three auxiliary variables, z ═ u, q ═ v ═ are introduced2u, v ═ Hu, the model (5) is transformed from an unconstrained optimization problem to a constrained optimization problem (6), i.e.
Under the ADMM framework, we can solve.
Then, its augmented lagrange function can be written as (6), specifically:
wherein λ is1,λ2,λ3For the purpose of extending the Lagrangian multiplier, beta > 0 is a positive parameter. Based on the traditional ADMM algorithm, the solution can be iterated. If the solution obtained after the kth iteration is
The detailed updates for the u, z, q, v variables in the (k + 1) th iteration are as follows.
Further elaboration of the last row of the above equation with respect to the variable u is derived and made to be 0 can yield:
when full variation and high order full variation are cycle boundary conditions +T▽,(▽2)T(▽2) For a cyclic block matrix, which can be diagonalized using a two-dimensional Fast Fourier Transform (FFT), u in the above equation can be solved by equation (7),
here, F-1Respectively representing the FFT function and its inverse.
For this minimization problem, the solution is iterated using the MM algorithm (MM) proposed by Liu in article "Total Variation with overlaying Group space for Image distribution under Image Noise", and the method is applied to the minimization problem.
First, let
The formula (8) is rewritten into the following form,
for this form of optimization problem, use l1And (3) solving by using a re-weighted iterative algorithm (Iterativelre-weighted l1, IRL 1).
And (4) observing the last line of the formula (9), easily knowing that the right side of the equal sign is a quadratic function, and solving by applying a Newton iteration method. Order to
The gradient Q '(v) and the blackplug matrix (Hessian matrices) Q' (v) of Q (v), that is, Q (v) can be obtained separately
As in the conventional newton iteration method, we select the iteration number k to be 5, so that the iterative formula of the formula (9) can be obtained,
where newton iterations start with l ═ 0, and vk+1,0＝vk,vk+1＝vk+1,5。
Up to this point, the update of each variable in the (k + 1) th iteration is achieved.
In summary, the solving method of the solving model (4) is as follows.
The technical scheme of the invention is further explained by combining a comparative experiment.
In order to further highlight the capability of the invention in restoring images polluted by Cauchy noise and have advantages compared with other models, the invention is experimentally compared with the OGSTVL1 model and the HTVAM model, and the three aspects of PSNR, SSIM and time required for restoring the images are considered. Blur and noise are added to varying degrees during image degradation. In order to see the details of the present invention in the denoising and deblurring processes, experiments were performed in two categories.
In the first category, only the denoising capability of the model is compared, and the part is verified by experiments under two conditions of the noise level xi being 0.02 and xi being 0.04 respectively. Specific image restoration results are shown in fig. 2(a) to 2(e) and fig. 3(a) to 3 (e).
In which quantitative indices for evaluation of the recovery results are reported in tables 1 and 2.
Table 1 denoised data with a noise level ξ 0.02
Table 2 denoised data with a noise level ξ of 0.04
From the visual effect of the restored image, the method has better processing capability on image details and has larger effect on protecting the edge information of the image. From quantitative evaluation, the removal effect of the method on the Cauchy noise is superior to other achievements, and the method has strong advantages in the aspect of running time. In conclusion, the method has strong advantages in the field of removing the Cauchy noise in the image.
Table 3 restored data under different blurs with a noise level ξ 0.02
Second, add blur to the image, and then add Cauchy noise. Here, motion blur, mean blur, and gaussian blur are added to the image, respectively, and the magnitude of cauchy noise is ξ ═ 0.02, and different methods are applied to perform image restoration. The quality evaluation results of the restored images under different algorithms are recorded in the table 3, so that the quality of the model can be quantitatively compared; for visual comparison, the experimental images with gaussian blur are shown in fig. 4 for comparison. Compared with other two methods, the method has more advantages in processing noise points under different blurs, is beneficial to keeping the smooth characteristic of the image, and is superior to other models in performance.
The specific operation flow of the invention is shown in fig. 5. For an experiment of an ideal image, the ideal image needs to be degraded manually, namely, specified types of blur and noise are added manually; for images that have undergone degradation, the fourth step may be performed directly. It should be noted that, for an image containing blur, the present invention needs to know the type and scale of the blur to perform restoration, which is a common disadvantage of the existing deblurring problem and a direction of future research; this problem is not taken into account if there is no blur in the image.
Compared with the de-noising restored images shown in the figures 2 and 3, the image obtained by the new invention has better smooth effect, the texture characteristics of the local area are kept more prominent, and the processing on noise is better; the advantages of the new algorithm are further illustrated in conjunction with the experimental data of tables 1 and 2. For the image deblurring problem, fig. 4 only shows the experimental result under gaussian blur, so that the new invention can clearly see that the noise recognition and processing capabilities are stronger and the suppression effect on blur is better when the blur is removed; the new invention has excellent image restoration capability for the deblurring problems under the mean value blurring and the motion blurring, and is in sharp contrast with other technical inventions. The novel method shows strong applicability to different degraded images, and numerous experimental results jointly verify the creativity and advantages of the novel method in the field of image processing.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (6)
1. An image restoration method under Cauchy noise, comprising the steps of:
acquiring a degraded image composed of an original image and Cauchy noise;
determining the size of a proportional parameter in Cauchy distribution according to the size of Cauchy noise;
determining a corresponding data fidelity term, and establishing a minimization regularization model under Cauchy noise by using a mixed regularization scheme;
solving the model based on Iteravely re-weighted 11 algorithm and majority minimization algorithm under the framework of an alternative direction multiplier method, thereby obtaining a restored image;
the image restoration method under the Cauchy noise introduces non-convex l based on HTV in a model for removing the Cauchy noisepA regularization function, while hybrid using OGSTV regularization; the non-convex regular term keeps sharp edge information while smoothing the local texture part, and the overlapping group sparse regular has a smooth step effect;
carrying out iterative solution on the model by using an alternating direction multiplier method; first, three auxiliary variables are introduced
Converting the optimization model for removing the Cauchy noise from an unconstrained optimization problem into a constrained optimization problem, namely:
then, obtaining an augmented lagrange function, specifically:
wherein λ is1，λ2，λ3Beta is more than 0 and is a positive parameter for increasing Lagrange multiplier;
the solving of the model specifically comprises the following steps:
step one, initializing parameters and variables:
maximum number of iterations
Parameters beta, alpha, omega, p in a given model;
step two, solving minimization for each variable alternately, namely:
step three, calculating
Step four, when crit is less than epsilon or k is more than N, iteration is terminated; otherwise k is k +1, returning to the step two to continue the calculation.
2. The image restoration method under cauchy noise according to claim 1, characterized in that: obtaining a degraded image consisting of an original image and Cauchy noise, and obtaining a matrix u epsilon R for any ideal imagen×nThe degradation process contaminated by cauchy noise is expressed as:
where H denotes the fuzzy operator, n1，n2Representing two standard normal distribution matrixes, ξ representing the level value size of Cauchy noise, f (x), u (x) are two independent random variables obeying the Cauchy distribution and respectively represent a digital matrix of a degraded image and an ideal image.
3. The cauchy noise lower of claim 1The image restoration method of (2), characterized by: determining the size of a proportional parameter in the Cauchy distribution according to the size of the Cauchy noise; the image degradation process comprises determining a proportion parameter in a Cauchy distribution probability density function as
4. The image restoration method under cauchy noise according to claim 1, characterized in that: determining a data fidelity term, e.g., MAP estimation theory, when the conditional probability P (u | f) is maximized, it corresponds to
The optimal estimated value is obtained; rewriting u using Bayes' formula*The expression of (a), namely:
is a data fidelity item in the new model.
5. The image restoration method under cauchy noise according to claim 1, characterized in that: the minimum regularization model under the Cauchy noise is established by combining a mixed regularization scheme as follows:
wherein, alpha > 0 represents the regular parameter of the balance data fidelity term and the regular term, mu > 0 represents the punishment parameter, and omega > 0 is the regular parameter of the regular term.
6. An image information data processing terminal for implementing the image restoration method under Cauchy noise according to any one of claims 1 to 5.
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