CN111028168A - High-energy flash image deblurring method containing noise blur - Google Patents

High-energy flash image deblurring method containing noise blur Download PDF

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CN111028168A
CN111028168A CN201911239919.5A CN201911239919A CN111028168A CN 111028168 A CN111028168 A CN 111028168A CN 201911239919 A CN201911239919 A CN 201911239919A CN 111028168 A CN111028168 A CN 111028168A
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CN111028168B (en
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王佳妤
李庆武
许金鑫
王肖霖
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Changzhou Campus of Hohai University
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Abstract

The invention discloses a method for deblurring a high-energy flash image containing noise blur. Firstly, obtaining a high-energy flash blurred image, establishing a posterior probability model, and rapidly deblurring the high-energy flash blurred image through Gibbs sampling in a frequency domain to obtain an initial deblurred image and uncertainty of parameters. The ringing artifact is suppressed by adopting a differential filtering method. And then removing noise in the gradient domain through an iterative denoising network, and restoring a final clear image by using the denoised gradient image as a depth denoising prior. The denoising network and the iteration times are determined by the noise parameters estimated by the MCMC method. The method can well solve the problems of large operation amount and poor denoising performance of the MCMC method, can retain richer image detail information while effectively inhibiting ringing and noise, and obviously improves the recovery quality of the high-energy flash image.

Description

High-energy flash image deblurring method containing noise blur
Technical Field
The invention belongs to the technical field of image processing, and relates to a deblurring method for a high-energy flash image.
Background
Flash photography is a widely used non-destructive inspection technique that uses the penetration of X-rays and their nature of interaction with matter to diagnose information within an object. However, the imaging quality of the high-energy flash photographic image is greatly affected by the interference of blur, noise, and the like, which brings great difficulty in obtaining highly accurate information inside the object. Therefore, the method has very important significance and application value for removing the image blur and quickly recovering a clear image.
Image deblurring is the restoration of a sharp image given a blurred image and a blur kernel, but the morbid nature of the deblurring problem results from the randomness of noise and the limited bandwidth of the blur kernel. If the image is deblurred by using a direct deconvolution method such as wiener filtering, the obtained image may contain converted noise, and the noise is highly dependent on a clear image and a blur kernel. In order to overcome this problem, researchers have conducted intensive research and many advances in image deblurring technologies, mainly including the development of generative models and the application of discriminant models, but neither the generative model-based image deblurring method nor the discriminant model-based image deblurring method can quantify the uncertainty of unknown parameters. The image deblurring method based on the Bayes theory sets prior distribution and a likelihood function containing error information according to hypothesis and experience, then optimizes the prior distribution to obtain posterior distribution, but is influenced by the complexity of the posterior distribution, and the complete posterior probability distribution cannot be drawn in the Bayes theory. The MCMC (Markov Chain Monte Carlo method, Markov Chain Monte Carlo) method can approximately express the distribution situation of posterior probability by numerical sampling in combination with Bayes theory, and then obtains the statistic of the parameters to be solved. However, such methods are computationally inefficient, prone to ringing, and suffer from severe performance degradation as the noise level of the blurred image increases.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the deblurring method of the high-energy flash image has the advantages that the calculated amount of deblurring of the high-energy flash image is large, the high-energy flash image is seriously influenced by noise, the deblurring method of the high-energy flash image containing noise blur is provided, the deblurring calculated amount can be obviously reduced, noise and ringing artifacts can be effectively inhibited, and the texture details of the image are kept.
In order to solve the technical problem, the invention provides a method for deblurring a high-energy flash image containing noise blur, which comprises the following steps:
step 1: acquiring a high-energy flash photographic image b and a preset fuzzy kernel k, and constructing an image deblurring model;
step 2: establishing a posterior probability model by combining a Bayes theory to obtain posterior probability density of a clear image x, a noise precision parameter lambda and a prior precision parameter delta; and setting the number of sampling times N of the modelsampleAnd number of aged samples NbInitializing an initial value λ of a noise accuracy parameter0And a priori precision parameter initial value delta0；
And step 3: gibbs sampling is applied to each parameter on a frequency domain, and a Markov chain is dynamically constructed, namely samples are extracted from conditional probability distribution of a clear image x, a noise precision parameter lambda and a prior precision parameter delta which need to be solved; when each Markov chain is stable, calculating the sample mean value of each parameter to obtain an initial deblurred image
Figure BDA0002305921180000021
The estimated values of the regularization parameter tau and the noise standard deviation 1/lambda;
and 4, step 4: removing ringing artifacts in the high-energy flash photographic image by adopting a differential filtering method;
and 5: and designing an iterative denoising network, processing the high-energy flash photographic images with vertical gradients and horizontal gradients, removing noise in the images, and restoring a final clear image by taking the denoised gradient images as depth denoising priors.
The invention achieves the following beneficial effects:
the invention accelerates the solution of the deblurring problem, reduces the operation amount, and can obtain the estimated value of the parameter and the uncertainty quantization at the same time; the image restored by the method provided by the invention contains less noise and ringing artifacts, has richer image texture details and better subjective visual effect.
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FIG. 1 is a flow chart of a method of deblurring a noise-blurred high-energy flashlight image of the present invention;
fig. 2 is a diagram of the image deblurring algorithm steps based on efficient MCMC.
Detailed Description
The invention is further described below. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The invention describes a method for deblurring a high-energy flash image containing noise blur, which comprises the following specific steps:
step 1: acquiring a high-energy flash photographic image b and a preset fuzzy kernel k, and constructing an image deblurring model;
the image blur degradation process can be expressed as:
b＝Kx+n (1)
where, b ═ vec (b), x ═ vec (x), n ═ vec (n), and vec denotes the column vector of the superimposed matrix, and the image matrix is converted into a vector form.
Figure RE-GDA0002387028840000031
For sharp images to be solved, x represents the vector form of the sharp image x, nxAnd nyRepresenting the number of rows and columns, respectively, of the image matrix.
Figure RE-GDA0002387028840000032
In order to blur the image, the image is blurred,
Figure RE-GDA0002387028840000033
for fuzzy matrices, assume
Figure RE-GDA0002387028840000034
Is an independent and identically distributed Gaussian random vector, the standard deviation of the Gaussian random vector is 1/lambda, lambda is a noise precision parameter, wherein,
Figure RE-GDA0002387028840000035
representing the vector real number domain.
And (3) constructing an image deblurring model by combining Tikhonov (Gihonov) regularization and depth denoising prior:
Figure BDA0002305921180000036
wherein, the first item is a data fidelity item; the second term is a statistical a priori constraint term, wherein,
Figure BDA0002305921180000037
the third term is a depth denoising prior constraint term, wherein, rho (phi) represents the regularization of the image x gradient, tau and ξ are regularization parameters for balancing each constraint term.
Figure BDA0002305921180000038
Representing gradient operators, including horizontal gradient operators
Figure BDA0002305921180000039
And vertical gradient operator
Figure BDA00023059211800000310
The final solution of the deblurring model (2) is obtained by stepwise solving: constructing a posterior probability density function according to a Tikhonov regularization formula (3), and applying Gibbs sampling to realize rapid deblurring on a frequency domain to obtain an initial deblurred image, an estimated value of a noise parameter and the like; suppressing ringing artifacts in the image by adopting a differential filtering method to obtain a ringing-removed image f; then, designing a denoising model of the iterative denoising network, as shown in formula (4), removing noise in a gradient domain through the iterative denoising network, and recovering a final clear image x by using the denoised gradient image as a depth denoising prior. The denoising network and the iteration times are determined by the noise parameters estimated by the MCMC method. The overall flow chart of the present invention is shown in fig. 1.
Figure BDA00023059211800000311
Figure BDA00023059211800000312
Step 2: establishing a posterior probability model by combining a Bayes theory to obtain posterior probability density of a clear image x, a noise precision parameter lambda and a prior precision parameter delta variable;
bayesian theorem states that for the observed data b, a posterior probability density p (x | b) can be obtained. The method commonly used to solve the inverse problem is to calculate the maximum value of p (x | b), which is equivalent to solving the minimum value of-lnp (x | b), i.e., the Maximum A Posteriori (MAP) estimation method.
The MCMC method samples each parameter from the conditional probability distribution of each parameter, and then obtains the estimated value of the parameter and the uncertainty quantification of the parameter through the sample mean value of the parameter.
First, a likelihood function p (b | x, λ) is defined according to equation (1),
Figure BDA00023059211800000313
wherein oc represents a proportional amount. In the context of bayesian statistics, the regularization term corresponds to the selection of the prior probability density p (x | δ). Suppose that
Figure BDA0002305921180000041
Wherein the content of the first and second substances,
Figure BDA0002305921180000042
representing a gaussian distribution. Then the prior probability density for x | δ is:
Figure BDA0002305921180000043
the choice of Gauss prior p (x | δ) will be such that p (b | x, λ) p (x | δ) is still a Gaussian distribution for x, i.e. p (x | δ) is a conjugate priorλ,βλ)，δ～Γ(αδ,βδ) Wherein, αλ，αδ，βλ，βδIs a gamma distribution parameter.
After considering the parameters obeying the distribution, the posterior probability density can be defined as:
Figure BDA0002305921180000044
and step 3: gibbs sampling is applied to each parameter on a frequency domain, and a Markov chain is dynamically constructed, namely samples are extracted from conditional probability distribution of a clear image x, a noise precision parameter lambda and a prior precision parameter delta which need to be solved; when each Markov chain is stable, calculating the sample mean value of each parameter to obtain an initial deblurred image
Figure BDA00023059211800000412
An estimate of the regularization parameter τ (i.e., δ/λ) and the noise standard deviation 1/λ;
under the condition of a periodic boundary, the fuzzy matrix K and the precision matrix L are both block circulant matrices (BCCBs). The accuracy matrix L is defined based on the Markov random field (GMRF), i.e. at each pixel position i, a neighborhood is defined
Figure BDA0002305921180000045
Let x beiIs close to its neighborhood
Figure BDA0002305921180000046
And is average value of
Figure BDA0002305921180000047
Obey the following distribution:
Figure BDA0002305921180000048
in the formula, niIndicating the number of pixels contained in the neighborhood. The neighborhood of the one-dimensional space includes left and right pixels, and the neighborhood of the two-dimensional space includes left and right and up and down pixels. The joint probability density for x can be defined by equation (4) and a precision matrix L, L satisfying the following form:
Figure BDA0002305921180000049
under the condition of cycle boundary, let L be array (L).,1) Wherein L is.,1Representing the first column of the precision matrix L. Meanwhile, n in the formula (6)xnyMust be nxny-1, or by the rank of L.
Given a
Figure BDA00023059211800000410
And
Figure BDA00023059211800000411
where K bccb (K), L bccb (L), and the solution for x is performed in the frequency domain, we can obtain:
Figure BDA0002305921180000051
wherein the content of the first and second substances,
Figure BDA0002305921180000052
and
Figure BDA0002305921180000053
namely, the precision matrix l, the fuzzy kernel k and the fuzzy image b are subjected to Fast Fourier Transform (FFT), and the calculation is carried out on the frequency domain.
Figure BDA0002305921180000054
Is a random matrix that follows a standard normal distribution. real represents the operation of the real part. ifft denotes an inverse fast fourier transform.
As shown in fig. 2, the basic idea of the high-efficiency MCMC-based image deblurring algorithm is as follows: establishing a posterior probability model by combining Bayes theory, and dynamically constructing a Markov chain for each parameter by using Gibbs sampling on a frequency domain, namely extracting samples from the conditional probability distribution of x, lambda and delta. After each Markov chain reaches a stable state, calculating the sample mean value of each parameter, which can be regarded as an effective estimation for the original data, and then obtaining an initial deblurred image
Figure BDA0002305921180000055
And estimates of the regularization parameter τ (i.e., δ/λ) and the noise standard deviation 1/λ.
And 4, step 4: the non-blind deblurring method based on outlier processing (reference: Handling of outliers in-noise-texture deconstruction) does not produce particularly severe ringing artifacts, but has the problem that the background and texture details are too smooth. For scenes with complex backgrounds or rich texture details, the method has poor processing effect. In contrast, an image processed by the efficient MCMC algorithm may retain more detailed information. Thus, non-blind deblurring of the blurred image b results in an image x1Obtaining a deblurred image according to step 3
Figure BDA0002305921180000057
Calculating the difference image of the two deblurred images, performing bilateral filtering to remove ringing artifacts, and removing ringing artifacts from the difference image
Figure BDA0002305921180000058
Subtracting the difference image after filtering to obtain a ring-removing image f;
the non-blind deblurring method based on the abnormal value processing mainly divides image pixels into two categories for processing. And recovering pixels which meet the linear model by using a traditional deconvolution method, and adopting a non-blind deblurring algorithm based on an expected maximum value (EM) for pixels which do not meet the linear model. Outliers are explicitly detected and processed in a deconvolution process to further recover outlier pixels.
And 5: and designing an iterative denoising network, processing the noisy images of the vertical gradient and the horizontal gradient, removing the noise of the images, and restoring a final clear image by taking the denoised gradient images as depth denoising priors.
The denoising model (4) can be obtained by introducing auxiliary variables
Figure BDA0002305921180000056
And penalty weights β, solved using a semi-quadratic splitting method, thus, model (4) can be equivalently transformed into:
Figure BDA0002305921180000061
solving equation (11) can be converted to alternately solving the following two sub-problems:
Figure BDA0002305921180000062
Figure BDA0002305921180000063
it can be seen that equation (12) represents the gradient image denoising module, and equation (13) represents the restoration module with respect to x. x, applying the restoring module to the iterative denoising network, namely, guiding the restoration of the image by the denoising gradient image output by the iterative denoising network as a depth denoising prior.
If g is obtained by the formula (12)lThe solution of (2) can be solved by fast fourier transform to obtain equation (13), and the clear image x is effectively recovered:
Figure BDA0002305921180000064
in the formula (I), the compound is shown in the specification,
Figure BDA0002305921180000065
and
Figure BDA0002305921180000066
respectively representing a fast fourier transform and an inverse fast fourier transform,
Figure BDA0002305921180000067
represents the complex conjugate of the fast fourier transform,
Figure BDA0002305921180000068
is a hyper-parameter.
Step 5.1: the network weights are trained and then fixed in the recovery module for x. After the x recovery module, the fixed hyper-parameters are used to train and update the network weights in the next iteration. The loss function C for training the iterative denoising network is set as:
Figure BDA0002305921180000069
in the formula, f (·) is a denoising mapping obtained by a denoising network, theta is a weight parameter of the network, N is the number of each batch of training samples, | ·| luminance1Represents L1Norm, x0Representing a true sharp image.
Step 5.2: and performing end-to-end training by using a fixed network weight. Training of the hyper-parameter gamma through a loss function CγTo achieve the following:
Figure BDA00023059211800000610
in the formula, x represents an output image of the final restoration module.
The forward propagation function of the recovery block for x is defined by equation (14), and the gradient update equation in the backward propagation is obtained as follows:
Figure BDA0002305921180000071
wherein the content of the first and second substances,
Figure BDA0002305921180000072
then, the expression for updating the hyper-parameter γ is:
Figure BDA0002305921180000073
wherein D, H, E and LxAre respectively as
Figure BDA0002305921180000074
And
Figure BDA0002305921180000075
in the form of a vector.
The above embodiments are merely illustrative of the present invention, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the basic concept of the present invention, and these modifications and improvements should be construed as the scope of the present invention.

Claims (10)

1. A method for deblurring a high-energy flash image with noise blur, comprising the steps of:
step 1: acquiring a high-energy flash photographic image b and a preset fuzzy kernel k, and constructing an image deblurring model;
step 2: establishing a posterior probability model by combining a Bayes theory to obtain posterior probability density of a clear image x, a noise precision parameter lambda and a prior precision parameter delta; and setting the number of sampling times N of the modelsampleAnd number of aged samples NbInitializing an initial value λ of a noise accuracy parameter0And a priori precision parameter initial value delta0；
And step 3: gibbs sampling is applied to each parameter on a frequency domain, and a Markov chain is dynamically constructed, namely samples are extracted from conditional probability distribution of a clear image x, a noise precision parameter lambda and a prior precision parameter delta which need to be solved; when each Markov chain is stable, calculating the sample mean value of each parameter to obtain an initial deblurred image
Figure FDA0002305921170000018
The estimated values of the regularization parameter tau and the noise standard deviation 1/lambda;
and 4, step 4: removing ringing artifacts in the high-energy flash photographic image by adopting a differential filtering method;
and 5: and designing an iterative denoising network, processing the high-energy flash photographic images with vertical gradients and horizontal gradients, removing noise in the images, and restoring a final clear image by taking the denoised gradient images as depth denoising priors.
2. The method of deblurring a noise-blurred high-energy flash image as claimed in claim 1, wherein the high-energy flash photographic image b is subjected to blur degradation as expressed by:
b＝Kx+n (1)
wherein, b ═ vec (b), x ═ vec (x), n ═ vec (n), vec represents the column vector of the superimposed matrix, and converts the image matrix into vector form;
Figure FDA0002305921170000011
for sharp images to be solved, x represents the vector form of the sharp image x, nxAnd nyRepresenting the number of rows and columns of the image matrix respectively,
Figure FDA0002305921170000012
in order to blur the image, the image is blurred,
Figure FDA0002305921170000013
in order to blur the matrix, the matrix is,
Figure FDA0002305921170000014
is an independent and identically distributed Gaussian random vector with standard deviation of 1/lambda and lambda as noise precision parameter
Figure FDA0002305921170000015
Representing the vector real number domain.
3. The method for deblurring the noisy blurred high-energy flashlight image according to claim 2, wherein an image deblurring model is constructed by combining Tikhonov regularization and depth denoising prior:
Figure FDA0002305921170000016
wherein, the first item is a data fidelity item; the second term is a statistical a priori constraint term, wherein,
Figure FDA0002305921170000017
the third term is a depth denoising prior constraint term, wherein rho (phi) represents the regularization of the x gradient of the image, tau and ξ are regularization parameters for balancing the constraint terms;
Figure FDA0002305921170000021
representing gradient operators, including horizontal gradient operators
Figure FDA0002305921170000022
And vertical gradient operator
Figure FDA0002305921170000023
4. The method of deblurring a noise-blurred high-energy flashlight image according to claim 3, wherein in step 2, the likelihood function p (bix, λ) is defined according to equation (1),
Figure FDA0002305921170000024
wherein oc represents a proportional amount. In the context of bayesian statistics, the regularization term corresponds to the selection of the prior probability density p (x | δ); is provided with
Figure FDA0002305921170000025
Wherein the content of the first and second substances,
Figure FDA0002305921170000026
represents a gaussian distribution; then the prior probability density for x | δ is:
Figure FDA0002305921170000027
in the formula, delta is a prior precision parameter; the choice of gaussian prior p (x | δ) will be such that p (b | x, λ) p (x | δ) is still gaussian distributed for x, i.e. p (x | δ) is a conjugate prior; λ and δ are used as random parameters, and the corresponding distribution is called a super-first-order distribution;let λ, δ obey a gamma distribution, i.e., λ - Γ, respectively (α)λ,βλ)，δ～Γ(αδ,βδ) Wherein αλ，αδ，βλ，βδIs a gamma distribution parameter;
after considering that each parameter obeys the distribution, the posterior probability density is:
Figure FDA0002305921170000028
5. the method of claim 4, wherein Gibbs sampling is applied to each parameter in the frequency domain to dynamically construct a Markov chain, and after each Markov chain is stabilized, the mean value of the samples of each parameter is calculated to obtain an initial deblurred image
Figure FDA0002305921170000029
The estimated values of the regularization parameter tau and the noise standard deviation 1/lambda;
under the condition of a periodic boundary, the fuzzy matrix K and the precision matrix L are both block cyclic matrices; the accuracy matrix L is defined based on a Markov random field, i.e. at each pixel position i, a neighborhood is defined
Figure FDA00023059211700000210
Let xiIs close to its neighborhood
Figure FDA00023059211700000211
Is a mean value of
Figure FDA00023059211700000212
Obey the following distribution:
Figure FDA00023059211700000213
in the formula, niRepresents the number of pixels included in the neighborhood;the neighborhood of the one-dimensional space comprises left and right pixels, and the neighborhood of the two-dimensional space comprises left and right pixels, upper and lower pixels; l satisfies the following form:
Figure FDA0002305921170000031
under the condition of cycle boundary, let
Figure FDA00023059211700000314
Wherein L is.,1A first column representing the precision matrix L; meanwhile, n in the formula (6)xnyQuilt nxny-1 is replaced;
given a
Figure FDA0002305921170000032
And
Figure FDA0002305921170000033
wherein, K ═ bccb (K),
Figure FDA00023059211700000315
the solution for x is performed in the frequency domain, resulting in:
Figure FDA0002305921170000034
wherein the content of the first and second substances,
Figure FDA0002305921170000035
and
Figure FDA0002305921170000036
i.e. to the accuracy matrix
Figure FDA00023059211700000316
Carrying out fast Fourier transform on the fuzzy kernel k and the fuzzy image b, and converting to a frequency domain for calculation;
Figure FDA0002305921170000037
a random matrix obeying a standard normal distribution; real represents the operation of the real part; ifft denotes an inverse fast fourier transform.
6. The method of claim 5, wherein the step 4 of removing ringing artifacts comprises the following steps:
carrying out non-blind deblurring on the blurred image b by using a method based on abnormal value processing to obtain an image x1And the initial deblurred image
Figure FDA0002305921170000038
Comparing, calculating the difference image of the two deblurred images, performing bilateral filtering to remove ringing artifact, and filtering to obtain the final image
Figure FDA0002305921170000039
Subtracting the filtered difference image to obtain a derringing image f:
Figure FDA00023059211700000310
7. the method for deblurring the noise-blurred high-energy flashlight image of claim 6, wherein a denoising model of an iterative denoising network is designed:
Figure FDA00023059211700000311
removing noise in a gradient domain through an iterative denoising network, and recovering a final clear image x by taking a denoised gradient image as a depth denoising prior, wherein the steps are as follows:
auxiliary variable is introduced into denoising model formula (4)
Figure FDA00023059211700000312
And a penalty weight β, and a penalty weight,solving by using a semi-quadratic splitting method; equivalently converting the denoising model into:
Figure FDA00023059211700000313
solving equation (11) translates into alternately solving the following two sub-problems:
Figure FDA0002305921170000041
Figure FDA0002305921170000042
equation (12) represents the gradient image denoising module, and equation (13) represents the restoration module with respect to x; the x recovery module is applied to the iterative denoising network, namely, a denoising gradient image output by the iterative denoising network is used as a depth denoising prior to guide the recovery of the image;
the solution of gl is obtained by equation (12), and equation (13) is solved by fast fourier transform to recover the sharp image x:
Figure FDA0002305921170000043
in the formula (I), the compound is shown in the specification,
Figure FDA0002305921170000044
and
Figure FDA0002305921170000045
respectively representing a fast fourier transform and an inverse fast fourier transform,
Figure FDA0002305921170000046
represents the complex conjugate of the fast fourier transform,
Figure FDA0002305921170000047
is a hyper-parameter.
8. The method of deblurring a noise-blurred high-energy flashlight image of claim 7, wherein the step of solving equation (11) is as follows:
step 5.1: training network weights, and then fixing the weights in a recovery module of x; after the recovery module of x, training and updating the network weight in the next iteration by using the fixed hyper-parameter;
step 5.2: end-to-end training is carried out by using a fixed network weight; training of the hyper-parameter gamma through a loss function CγTo achieve the following:
Figure FDA0002305921170000048
in the step 5.1, a loss function C for training the iterative denoising network is set as follows:
Figure FDA0002305921170000049
in the formula, f (·) is a denoising mapping obtained by a denoising network, theta is a weight parameter of the network, N is the number of each batch of training samples, | ·| luminance1Represents L1Norm, x0Representing a true sharp image.
9. The method for deblurring a noise-blurred high-energy flashlight image as claimed in claim 8, wherein in the step 5.2, the gradient updating formula in the backward propagation is as follows:
Figure FDA0002305921170000051
wherein the content of the first and second substances,
Figure FDA0002305921170000052
10. the method of deblurring a noisy blurred high energy flash image according to claim 9, wherein in step 5.2, the expression for updating the hyper-parameter γ is as follows:
Figure FDA0002305921170000053
wherein D, H, E and LxAre respectively as
Figure FDA0002305921170000054
And
Figure FDA0002305921170000055
in the form of a vector.
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