CN106952240A - A method for image de-blurring - Google Patents

Abstract

Motion blur method is gone the invention discloses a kind of image, methods described includes：Step 1：The unlimited student t Distribution Mixed Models based on Di Li Cray processes are set up, as image gradient distributed model and psf model, unlimited student t Distribution Mixed Model numbers are automatically obtained according to observed image；Step 2：Using image gradient distributed model and psf model as prior image model and point spread function prior model, image is carried out using MAP estimation method to go motion blur to handle, and estimate model parameter using variational Bayesian, realize Number of Models adaptively selected, the degree of fitting being distributed to image gradient is improved, realizes that accurately image removes the technique effect of motion blur.

Description

A method for image de-blurring

technical field

The present invention relates to the field of image processing, in particular to an image motion blur removal method.

Background technique

The ill-posedness of the image deblurring problem can be well-conditioned by introducing an image prior model, and establishing a suitable image prior model becomes the key to realizing image deblurring. Image deblurring algorithms based on statistical models have relative advantages. Firstly, the prior distribution model about the image is established, and then the original image, point spread function and parameters are derived based on certain specific criteria, so as to achieve image de-blurring.

Although the shape of the gray distribution of different types of images varies greatly, the shape of the image gradient distribution is very similar. In recent years, studies on the statistical characteristics of natural images have shown that the gradient distribution of natural images obeys heavy-tailed distribution, that is, natural images have strong local continuity, and each pixel in the image is often different from its surrounding pixels. Large, there will be a large jump only at the edge of the image, so this feature of the natural image can be described by the statistics of its gradient distribution. The gradient value of a natural image is mostly zero or close to zero, the closer the gradient value is to zero, the greater the probability, and the farther away from zero, the smaller the probability.

This image gradient distribution model subject to heavy-tailed distribution is widely used as image prior in the image motion blur problem. Based on the advantages of finite mixture model modeling, Rob Fergus et al. used finite Gaussian mixture model to approximate this distribution. However, most of the images have nonlinear and non-Gaussian characteristics, and are limited to the fitting ability of Gaussian distribution, so the Gaussian mixture model cannot be completely , Accurately and effectively describe these image information. At the same time, the finite Gaussian mixture model is sensitive to outliers, and its robustness needs to be improved.

In the field of image de-blurring, the image prior model also depends on the parameters in the component function of the model, such as the mean and variance of the Gaussian distribution. These parameters are also regarded as random variables and described by the corresponding probability distribution. The advantage of this is that when uncertain factors appear in the process of image restoration, the error between the restored image and the actual original image is small.

Determining the number of model components is a key issue in finite mixture models. When using a mixed model to model the image gradient distribution model, if the number of models selected is too large, overfitting will occur, and when the number of models selected is too small, underfitting will result, and the data cannot be accurately calculated. describe. Therefore, the selection accuracy of the number of models determines the quality of the image de-blurring effect.

At present, the existing method for determining the number of models is to select different numbers of models in a large range for data modeling based on empirical values, and then judge the modeling results according to another model selection criterion, and select the best modeling results The corresponding model number is taken as the optimal model number. However, such methods depend on the reliability of empirical values, and separate model selection from parameter estimation, which increases the amount of calculation.

To sum up, in the process of realizing the technical solution of the invention of the present application, the inventor of the present application found that the above-mentioned technology has at least the following technical problems:

In the prior art, the existing image motion blur removal method relies on empirical values when determining the number of models, which has the technical problems of low reliability and large amount of calculation.

Contents of the invention

The present invention provides an image de-blurring method, which solves the technical problems that the existing image de-blurring method relies on empirical values when determining the number of models, and has a low degree of reliability and a large amount of calculation. It realizes the adaptive selection of the number of models, improves the fitting degree of the image gradient distribution, and realizes the technical effect of precise image motion blur removal.

In order to solve the above technical problems, the present application provides a method for image motion blur removal, the method comprising:

Step 1: Establish an infinite Student-t distribution mixture model based on the Dirichlet process, as an image gradient distribution model and a point spread function model, and automatically obtain the number of infinite Student-t distribution mixture models according to the observed image;

Step 1: Establish an infinite Student-t distribution mixture model based on the Dirichlet process, as an image gradient distribution model and a point spread function model, which can automatically obtain the number of mixture models according to the observed image;

The mathematical model is as follows:

in, is the likelihood function, p(h) respectively represent the prior distribution of the image in the gradient domain and the prior distribution of the point spread function, is the real value of the original clear image in the gradient domain, h is the real value of the point spread function, is the estimated value of the original clear image in the gradient domain, is an estimate of the point spread function.

Step 2: Use the image gradient distribution model and the point spread function model as the image prior model and the point spread function prior model respectively, use the maximum a posteriori estimation method to de-blur the image, and use the variational Bayesian inference to estimate Model parameters.

The image gradient distribution obeys the heavy-tailed distribution, and the mixture model is used to fit the distribution, and the image gradient distribution model is established. The model component function is a Student-t distribution, and the number of model components tends to infinity.

The mathematical model is as follows:

Among them, St() represents the student-t distribution, the mean value is 0, Λ _h represents the accuracy of the point spread function distribution, w represents the degree of freedom of the point spread function distribution, Λ _f represents the accuracy of the original clear image distribution in the gradient domain, and v represents The degree of freedom of the distribution of the original clear image in the gradient domain, π() represents the label probability scale coefficient.

Further, the infinite Student-t distribution mixed model is used to fit the point spread function, and the point spread function model is established. The mathematical model of the point spread function is:

Among them, St(·) represents the Student-t distribution with a mean of 0, Λ represents the accuracy, v represents the degree of freedom, and π(·) represents the label probability scale coefficient.

Based on the Dirichlet process, the parameter prior model in the image gradient distribution model and point spread function model is established, including:

Using the Dirichlet process prior assumption to automatically infer the number of model components and fit the image gradient distribution model and point spread function distribution model component parameters.

A random sampling distribution G is first obtained from a Dirichlet process, then we obtain from G an i.i.d. sequence given When , the distribution of the Nth sample can be expressed by

In the formula, suppose express The set of different values of , n _j represents the number of variables whose value is θ _j . Indicates the number concentrated in mass point θ _j . The probability of taking the value of _θj is The probability of being different from the previous value is Therefore the sequence The number of 'ingredients' produced may be countably infinite. by adding the same value Divide into a group to get the clustering of the set {1,2,...N-1}.

The folding stick representation of the Dirichlet process can be defined by formula (1), formula (2), formula (3), formula (4) and formula (5):

V _j |α～Beta(1,α) (3)

The strength parameter α plays a very important role in determining the number of model 'components'. When α→0, the whole stick is broken into one component, that is, the probability that the new parameters are obtained from the basic distribution G ₀ is very high. Conversely, when α→∞, the length of the stick becomes infinitely small, and G converges to the actual distribution.

From the zigzagging model, we can view DP as an infinite mixture model. The data x is obtained from the Dirichlet process, and a hidden variable z is introduced at the same time, whose value is equal to j to indicate that the data x and parameters Associated. The Dirichlet process prior mixture model on the random mixing scale G ₀ is called Dirichlet Process Mixture (Dirichlet Process Mixture, DPM). data set The process generated from the DPM model based on the zigzag stick representation is shown in (6) to (9):

V _n |α～Beta(1,α),n={1,2,…} (6)

z _n |{V ₁ ,V ₁ ,…}～Mult(π(V)) (8)

Where Mult represents a multinomial distribution. member function Usually a Gaussian distribution is chosen.

Further, based on the MAP estimation criterion, the variational Bayesian inference is used to estimate the parameters in the image gradient distribution model and the point spread function model, and the realization of image de-blurring includes:

First, initialize the model parameters in the image gradient distribution model and point spread function model: CX

Accuracy matrix obtained by K-mean algorithm with The initial value of the precision of the noise distribution <Λ _noise >=1, the initial value of the original clear image f is the observed image g<f>=g, the initial value of the point spread function

Then, carry out the E step in the EM algorithm to calculate the variational posterior q(z _f ) and q(z _h ) of the hidden parameters;

Then, the M step in the EM algorithm is performed to calculate the variational posterior of other parameters

Then, calculate the lower bound L ^t (q), where t represents the number of iterations, L ^t (q) is the lower bound of the t-th iteration, L ^t-1 (q) is the lower bound of the t-1th iteration, and ε is the threshold if it satisfies Then the loop ends, otherwise jump to step E in the EM algorithm.

The Student's t-distribution has longer tails than the Gaussian distribution, so it provides a robust alternative to the Gaussian distribution. Tzikas et al. use a finite student's t-distribution mixture model to approximate this heavy-tailed image gradient distribution.

This application aims at the disadvantage that the number of models needs to be set in advance when the finite mixture model is used to model the image gradient distribution model, and proposes an adaptive model number selection method, so that the number of models does not depend on the empirical value, and can be automatically obtained from the observation data. Acquired to improve the fit of the model to the gradient distribution of the image.

The selection of the number of adaptive models established on the one hand realizes that the number of model components does not need to be determined in advance according to empirical values, but is automatically obtained from the image; on the other hand, it truly reflects the gradient distribution of different image structures.

Using Dirichlet process prior assumptions to automatically infer the number of model components and accurately fit the parameters of each model component, and use Student's t-distribution as the model component function.

Aiming at the main problems faced in establishing an effective and reliable adaptive model selection, the technical route of this application introduces the Dirichlet process hybrid model.

For the model selection problem, the Dirichlet process mixture model provides a non-parametric Bayesian framework for the unknown number of model members in advance, decomposes a complex distribution into infinite distribution components, and determines the weight of each distribution. In this way, within the set fitting error range, the number of components can be automatically determined. A Dirichlet process mixture model is a type of mixture model. The number of members in the mixture model is treated as a random variable whose value can be adaptively obtained from the observation data.

The introduction of the Dirichlet process mixture model means that the number of models is infinite. In fact, due to the limited observation image data, the number of models should be limited, and the corresponding model component weights and model parameters are also limited. To address this issue, consider constructing a truncated broken stick representation of the Dirichlet process, applying the truncation to the variational distribution instead of the Dirichlet process. Compared with the Gaussian distribution, the Student's t-distribution has a longer tail, so it has better robustness and anti-noise, so the model chooses the Student's t-distribution as the model member function.

The self-adaptive model selection is realized by establishing the student's t-distribution model represented by the folding stick, the number of models can be obtained automatically from the image, and the true value of the model number of the gradient distribution model of different image structures can be obtained by the self-adaptive model selection.

One or more technical solutions provided by this application have at least the following technical effects or advantages:

It realizes the adaptive selection of the number of models, improves the fitting degree of the image gradient distribution, and realizes the technical effect of precise image motion blur removal.

Description of drawings

The drawings described here are used to provide a further understanding of the embodiments of the present invention, constitute a part of the application, and do not constitute a limitation to the embodiments of the present invention;

FIG. 1 is a schematic flowchart of an image motion blur removal method in the present application.

detailed description

The present invention provides an image de-blurring method, which solves the technical problems that the existing image de-blurring method relies on empirical values when determining the number of models, and has a low degree of reliability and a large amount of calculation. It realizes the adaptive selection of the number of models, improves the fitting degree of the image gradient distribution, and realizes the technical effect of precise image motion blur removal.

In order to understand the above-mentioned purpose, features and advantages of the present invention more clearly, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, under the condition of not conflicting with each other, the embodiments of the present application and the features in the embodiments can be combined with each other.

In the following description, many specific details are set forth in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from the scope of this description. Therefore, the protection scope of the present invention is not limited by the following disclosure. The limitations of specific examples.

The specific mathematical model is:

According to the principle of maximum a posteriori estimation, the estimated value of the original clear image in the gradient domain can be obtained and an estimate of the point spread function as follows:

In the formula, is the likelihood function, p(h) represent the prior distribution of the image in the gradient domain and the prior distribution of the point spread function, respectively.

The image prior distribution can be fitted by an infinite student-t mixture model (iSMM, infinite student’s-t MixtureModel), as follows:

In the formula, St(·) represents the Student-t distribution with a mean of 0, _Λf represents the accuracy, v represents the degree of freedom, and π(·) represents the label probability proportional coefficient.

Similarly, the prior distribution of the point spread function is also fitted by iSMM, as follows:

In the formula, St(·) represents the Student-t distribution with a mean of 0, Λ represents the accuracy, v represents the degree of freedom, and π(·) represents the label probability proportional coefficient.

Consider a mean of 0 and a variance of Gaussian white noise, as follows:

In the formula, N(·) represents Gaussian distribution with a mean value of 0, and Λ _noise represents precision.

For many practical applications of probability, it is often not feasible to obtain their posterior distribution or to compute the expectation of the probability distribution exactly. In order to obtain the posterior distribution or expectation, an approximate strategy, Variational Bayesian Inference (Variational Bayesian Inference) is used.

use Represents a collection of hidden variables and unknown parameters.

To facilitate variational Bayesian inference, appropriate prior distributions should be imposed on these parameters. When the mean is known, the conjugate prior distribution of the parameter Λ is a gamma distribution:

p(Λ _noise )＝Gam(Λ _noise |a _e ,b _e ) (-3)

Apply the gamma distribution to the hyperparameter due to its conjugate relationship with the length of the stick:

Since there is no conjugate prior on v, the variable v in the Student-t distribution is treated as a parameter rather than a random variable.

data observation and an unknown random variable The joint distribution of is as follows:

p(h,Φ _h )=p(h|Φ _h )p(Φ _h )

＝p(h|z _h ,Λ _h ,u _h )p(Λ _h )p(u _h |v _h )p(z _h |V _h )

p(V _h |α _h )p(α _h )) (-8)

In the formula

Includes methods for updating model parameters and methods for updating point spread functions and gradient maps:

Approximates the true posterior distribution for a set of parameters with a family of variational posterior distributions. Due to the infinite set of parameters, it is practically infeasible to reason about the posterior probabilities of these parameters with Variational Bayes. To solve this problem, consider the truncated zigzag representation. There are mainly two kinds of truncated zigzag representations in the previous literature. One is to apply truncation to sampling-based inference to truncate Dirichlet processes, and the other is to apply truncation to variational distributions instead of Dirichlet processes. It is the second truncation type that is chosen in variational Bayesian inference. The model here is complete, only the variational distribution is truncated. First fix a value K and set the variational posterior on V to have the property q(V _K )=1, which means that when k>K, π _k (V)=0. K is a variational parameter, which can be set freely, so it is not part of the prior model.

For variational Bayesian inference, the logarithmic likelihood function logp(X) of observed data X is defined as formula (-9):

logp(X)=L(q)+KL(q||p) (-9)

The definitions of functions L(q) and KL(q||p) are shown in formula (-10) and formula (-11) respectively:

The function KL(q||p) is called the Kullback-Leibler divergence (KL divergence) of the true posterior probability p(Φ|X) and the approximate posterior probability q(Φ). KL(q||p)≥0 if and only if q(Φ)=p(Φ|X). Therefore L(q) is called the lower bound of logp(X). Maximizing the lower bound on q(Φ) is equivalent to minimizing the KL divergence.

In variational posterior inference, the posterior distribution takes the same form as the prior distribution. The variational distribution cluster hypothesis is decomposed into formula (-12):

According to formula (-6), (-7), (-8), (-10) and (-12) can be written as (-13) expression.

By sequentially iterating each decomposition factor of q(Φ), the variational distribution q(Φ) can maximize L(q), while the other factors are fixed to obtain the variational distribution q(Φ). This derivation process is an iterative process. Use <·> to denote the expectation of the relevant variable with respect to the variational distribution.

about The derivative of , the result is shown in the formula (-14):

Since each observation and the implicit random variable of h with The variational distribution of should satisfy formulas (-20) and (-21) defined in:

According to the constraints defined in equations (-20) and (-21), the variational distribution with Rewrite the expressions defined by equations (-22) and (-23).

The definitions of ρ _nj and τ _mi in the formula are shown in formulas (-24) and (-25):

For the variational posterior with Its distribution is derived as a gamma distribution, and the results are shown in formulas (-26) and (-27):

parameter with Represented in formulas (-28)(-29) and (-30)(-31)(-47), respectively.

The resulting variational posterior distribution with is the gamma distribution, and its distribution is shown in formulas (-32) and (-33):

parameter with The definitions are shown in formulas (-34), (-35) and (-36), (-37) respectively:

Variational posterior distribution with It is derived to obey the beta distribution, and its definition is shown in the formula (-38) (-39):

parameter with The definitions of are shown in formulas (-40)(-41) and (-42)(-43) respectively:

The variational posterior distributions q(α _f ) and q(α _h ) obey the gamma distribution, and their distributions are shown in formulas (-44) and (-45):

parameter with The definitions of are shown in formula (-46)(-47)(-48)(-49):

By setting the gradient of the logarithmic likelihood function of the complete data to zero, the nonlinear equations represented by the formulas (-50)(-51) and (-52)(-53) are obtained, and the new equations are obtained by solving the nonlinear equations value.

The obtained variational posterior distribution q(Λ _noise ) is a gamma distribution, and its distribution is shown in formula (-54)

Expected expressions for the posterior probabilities of equations (-14) to (-54) are given in (a-1)-(a-22).

Based on the variational distribution, the lower bound defined in Eq. can be written as the equation defined in Eq. (-55)

The value of the lower bound can be obtained by calculating formula (-55). Each expression in formula (-55) is given in detail in (b-1)-(b-27). At the end of each variational inference, the convergence of the model can be judged by the value of the lower bound.

The variational Bayesian inference of this model is described as follows.

1. Initialization:

Accuracy matrix obtained by K-mean algorithm with <Λ _noise >=1, <f>=g and

2. Step E:

Let formula (-13) be about hidden variable with The gradient of is equal to zero to get the hidden variable with The variational posterior distribution of , the variational posterior distribution is represented by formulas (-22), (-26) and (-23), (-27). about variables The variational posterior distributions for and h are defined in Equations (-14) and (-17), respectively.

3. M step:

The derived variational posterior distributions of random variables {μ _f , Λ _f , V _f , α _f } and {μ _h , Λ _h , V _h , α _h } are expressed in formulas (-26), (- 32), (-38), (-44) and (-27), (-33), (-39), (-44).

Solving the nonlinear equations (-50) and (-52) yields the values of the hyperparameters _wf and _wh .

Calculate the lower bound L ^t (q) (the superscript t represents the number of iterations), if the condition of formula (-56) is satisfied, the loop ends, otherwise jump to step E.

return value: and h.

This section gives the formulation of the expectation of the variational posterior distribution.

In the formula, Tr(·) represents the trace of the matrix, and ψ(·) represents the double gamma function.

<lnp(Λ _noise )>＝a _e lnb _e -ψ(a _e )+(a _e -1)<lnΛ _noise >-b _e <Λ _noise > (b-8)

The above-mentioned technical solutions in the embodiments of the present application have at least the following technical effects or advantages:

It realizes the adaptive selection of the number of models, improves the fitting degree of the image gradient distribution, and realizes the technical effect of precise image motion blur removal.

While preferred embodiments of the invention have been described, additional changes and modifications to these embodiments can be made by those skilled in the art once the basic inventive concept is appreciated. Therefore, it is intended that the appended claims be construed to cover the preferred embodiment as well as all changes and modifications which fall within the scope of the invention.

Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and equivalent technologies thereof, the present invention also intends to include these modifications and variations.

Claims (6)

1. An image de-blurring method, is characterized in that, the method comprises: Step 1: Establish an infinite Student-t distribution mixture model based on the Dirichlet process, as an image gradient distribution model and a point spread function model, and automatically obtain the number of infinite Student-t distribution mixture models according to the observed image; Step 2: Use the image gradient distribution model and the point spread function model as the image prior model and the point spread function prior model respectively, use the maximum a posteriori estimation method to de-blur the image, and use the variational Bayesian inference to estimate Model parameters. 2. The image de-blurring method according to claim 1, wherein the maximum a posteriori mathematical model for de-blurring the image is: $\begin{array}{c}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Proportional;</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&Proportional;</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>\end{array}$ Among them: p(▽g|▽f,h) is the likelihood function, p(▽f), p(h) represent the prior distribution of the image in the gradient domain and the prior distribution of the point spread function, respectively, and ▽f is the original The real value of the clear image in the gradient domain, h is the real value of the point spread function, is the estimated value of the original clear image in the gradient domain, is an estimate of the point spread function. 3. The image de-blurring method according to claim 1, characterized in that, utilizes the infinite Student-t distribution mixture model to fit the image gradient distribution, and sets up the image gradient distribution model, wherein the image gradient distribution modulus component function is Student- The t distribution, the mathematical model of the image gradient distribution model is: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; \&dtri;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>$ Among them, St() represents the Student-t distribution with a mean value of 0, Λ _f represents the accuracy of the original clear image distribution in the gradient domain, v represents the degree of freedom of the original clear image distribution in the gradient domain, and π() represents the label probability scale coefficient. 4. image de-blurring method according to claim 1, is characterized in that, utilizes infinite student-t distribution mixed model fitting point spread function, sets up point spread function model, point spread function mathematical model is: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$ Among them, St() represents the Student-t distribution with a mean value of 0, Λ _h represents the accuracy of the point spread function distribution, w represents the degree of freedom of the point spread function distribution, and π() represents the label probability scale coefficient. 5. The image de-blurring method according to claim 1, characterized in that, based on the Dirichlet process, the parameter prior model in the image gradient distribution model and the point spread function model is established, and the prior assumption of the Dirichlet process is utilized Automatically infer the number of model components and fit the component parameters of the image gradient distribution model and point spread function distribution model. 6. The image de-blurring method according to claim 1, characterized in that, based on the MAP estimation criterion, using variational Bayesian inference to estimate the parameters in the image gradient distribution model and the point spread function model, to realize image de-blurring Specifically include: First, initialize the model parameters in the image gradient distribution model and point spread function model: CX Accuracy matrix obtained by K-mean algorithm with The initial value of the precision of the noise distribution <Λ _noise >=1, the initial value of the original clear image f is the observed image g<f>=g, the initial value of the point spread function Then, carry out the E step in the EM algorithm to calculate the variational posterior q(z _f ) and q(z _h ) of the hidden parameters; Then, the M step in the EM algorithm is performed to calculate the variational posterior of other parameters Then, calculate the lower bound L ^t (q), where t represents the number of iterations, L ^t (q) is the lower bound of the t-th iteration, L ^t-1 (q) is the lower bound of the t-1th iteration, and ε is the threshold if it satisfies Then the loop ends, otherwise jump to step E in the EM algorithm.