CN107767351A - A kind of image recovery method of blind deblurring - Google Patents
A kind of image recovery method of blind deblurring Download PDFInfo
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Abstract
The invention discloses a kind of image recovery method of blind deblurring, belong to image processing field.Utilize lq/l2Norm is solved using multi-scale method by thick yardstick to thin yardstick progressive alternate as regularization priori item, during with disintegrating method solving model, uses l1The high-frequency information of norm fidelity item more new estimation image, when picture rich in detail recovers, closing threshold formula is used to be provided in the form of analytic solutions, algorithm speed is improved, meanwhile, when updating fuzzy core, it is proposed linear increment weight parameter, to fuzzy core by the multi-scale method convergence from coarse to fine progressively estimated, further improve fuzzy core, de-blurred image quality is improved.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a blind deblurring image recovery method.
Background
Image restoration is a large field in image processing, has wide application, and is becoming a hot spot of current research. The main purpose of image restoration is to make the degraded image undergo a certain processing treatment, remove the degradation factor and restore the degraded image into the original image with maximum fidelity. Conventional image restoration assumes that a degradation model of an image is known.
In practical application, the point spread function of the image degradation system is generally unknown, and only observation data of the degraded image is used, and little prior knowledge about the system and the original image is added to estimate the original image, which is called blind image restoration.
The prior art is not high enough in deblurred image quality, needs to be further improved, and meanwhile, the arithmetic speed is also needed to be further improved in algorithm, and the convergence of a blur kernel is not good enough.
Disclosure of Invention
In view of the above-described deficiencies in the prior art, the present invention provides a blind deblurring image restoration method, which can further improve the convergence of a blur kernel and improve deblurred image quality.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a blind deblurring image recovery method comprises the following steps:
step 1, establishing an image fuzzy model as follows:
wherein f represents a blurred image, k represents a blurred kernel matrix, u represents a clear image, and n represents noise in the imaging process;
step 2, utilizing discrete filter Generating high frequency informationConstructing a concave-convex norm ratio regularization model as follows:
wherein k is greater than or equal to 0 and sigma i k i ＝1，k i Representing elements in the blurring kernel matrix k, λ and λ 1 Phi is a constant value, y is high-frequency information of a blurred image, x is high-frequency information of a sharp image, q is a number of the equation power and 0<q<1；
Step 3, solving the concave-convex norm ratio regularization model in the step 2 to obtain a clear image;
step 3-1, updating high-frequency information x of the clear image;
step 3-1-1, fidelity item selection l 1 Norm, solving model:
step 3-1-2, i | purple sweet in step 3-1-1x|| 2 Regarding as a constant, the solution model in the step 3-1-1 is converted into non-convex | x | calculation q Regularization model of norm:
and 3-1-3, introducing an auxiliary variable v and a weight parameter theta, and converting the regularization model in the step 3-1-2 into:
wherein the content of the first and second substances,
θ i ＝c i θ 0 (7)；
in the formula, theta 0 Denotes an initial value of a weight parameter θ, c i Linear with the dimension i, c i ＝2i；
Step 3-1-4, replacing constant term lambda | x | non-conducting phosphor with beta 2 And respectively solving v and x in the regularization model conversion of the step 3-1-3, wherein a solving formula is as follows:
step 3-1-5, respectively deriving the solving formula of step 3-1-4:
in the formula, x k+1 The value of x in the step (k + 1) is shown, and delta t is an iteration step length;
step 3-2, updating a fuzzy core k;
step 3-2-1, fidelity item selection l 2 The square term of the norm, the solution model is:
step 3-2-2, in the updating process of the fuzzy core k, calculating the weight of the fuzzy core k by using an IRLS method:
wherein λ is 1 And ψ is a constant value, k 0 As initial blur kernel, w k Weight of the fuzzy kernel k which is updated;
step 3-2-3, solving a fuzzy kernel function k in the finest scale according to the step 3-2-1 and the step 3-2-2;
step 3-3, obtaining a recovery image;
step 3-3-1, under the condition that the fuzzy core is known, the image model solution is changed into non-blind image deconvolution, and the solution model is as follows:
step 3-3-2, let D = Du, where D representsOperation, separating variable u from D and increasing l 2 Squared terms of norm, introducing corresponding regularization factor β, of step 3-3-1The model is converted into:
step 3-3-3, performing derivation on the model in the step 3-3-2, and obtaining an optimal solution by using a two-dimensional fast Fourier method, wherein the optimal solution corresponds to the recovered clear image:
when solving for d, the threshold formula is:
wherein, the first and the second end of the pipe are connected with each other,
the invention utilizes q /l 2 The norm is used as a regularized prior term, a multi-scale method is adopted to carry out iterative solution from a coarse scale to a fine scale step by step, and l is used when a splitting method is used for solving the model 1 The norm fidelity item updates the high-frequency information of the estimated image, when a clear image is recovered, a closed threshold formula is adopted and given in the form of an analytic solution, the algorithm speed is improved, meanwhile, when a fuzzy kernel is updated, a linear increasing weight parameter is provided, the fuzzy kernel is estimated step by step from coarse to fine according to a multi-scale method, the convergence of the fuzzy kernel is further improved, and the deblurred image quality is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flow chart of a method of blind deblurring image recovery in accordance with an alternative embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art based on the embodiments of the present invention without inventive step, are within the scope of the present invention.
As shown in fig. 1, a blind deblurring image restoration method includes the following steps:
step 1, establishing an image fuzzy model as follows:
wherein f represents a blurred image, k represents a blurred kernel matrix, u represents a sharp image, and n represents noise in the imaging process;
step 2, utilizing discrete filter Generating high frequency informationConstructing a concave-convex norm ratio regularization model as follows:
wherein k is greater than or equal to 0 and sigma i k i ＝1，k i Representing elements in the blurring kernel matrix k, λ and λ 1 Phi is a constant value, y is high frequency information of a blurred image, x is high frequency information of a sharp image, and q is a number of equation powers and 0<q<1；
Step 3, solving the concave-convex norm ratio regularization model in the step 2 to obtain a clear image;
step 3-1, updating high-frequency information x of the clear image;
step 3-1-1, fidelity item selection l 1 Norm, solving model:
step 3-1-2, i | x | purple sweet in step 3-1-1 2 Regarding as a constant, the solution model in the step 3-1-1 is converted into non-convex | x | calculation q Regularization model of norm:
and 3-1-3, introducing an auxiliary variable v and a weight parameter theta, and converting the regularization model in the step 3-1-2 into:
wherein the content of the first and second substances,
θ i ＝c i θ 0 (7)；
in the formula, theta 0 Denotes an initial value of a weight parameter θ, c i Linear with the dimension i, c i ＝2i；
Step 3-1-4, replacing constant term lambda | x | non-conducting phosphor with beta 2 And respectively solving v and x in the regularization model conversion of the step 3-1-3, wherein a solving formula is as follows:
step 3-1-5, respectively deriving the solving formulas of step 3-1-4:
in the formula, x k+1 Representing the x value of the k +1 step, and delta t is an iteration step;
step 3-2, updating a fuzzy kernel k;
step 3-2-1, fidelity item selection l 2 The square term of the norm, the solution model is:
step 3-2-2, in the updating process of the fuzzy kernel k, calculating the weight of the fuzzy kernel k by using an iterative least square method IRLS method:
wherein λ is 1 And psi is constantValue, k 0 As initial blur kernel, w k Weight of the updated fuzzy kernel k;
step 3-2-3, solving a fuzzy kernel function k in the finest scale according to the step 3-2-1 and the step 3-2-2;
step 3-3, obtaining a recovery image;
step 3-3-1, under the condition that the fuzzy kernel is known, the image model solution is changed into non-blind image deconvolution, and the solution model is as follows:
step 3-3-2, let D = Du, where D representsOperation, separating variable u from D and increasing l 2 The square term of the norm, introducing a corresponding regularization factor β, and the model of step 3-3-1 is transformed into:
step 3-3-3, performing derivation on the model in the step 3-3-2, and obtaining an optimal solution by using a two-dimensional fast Fourier method, wherein the optimal solution corresponds to the recovered clear image:
when solving for d, the threshold formula is:
wherein the content of the first and second substances,
the above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (4)
1. A blind deblurring image restoration method is characterized by comprising the following steps:
step 1, establishing an image fuzzy model as follows:
wherein f represents a blurred image, k represents a blurred kernel matrix, u represents a sharp image, and n represents noise in the imaging process;
step 2, utilizing discrete filterGenerating high frequency informationConstructing a concave-convex norm ratio regularization model as follows:
wherein k is greater than or equal to 0, sigma i k i ＝1，k i Representing elements in the blurring kernel matrix k, λ and λ 1 Phi is a constant value, y is high frequency information of a blurred image, x is high frequency information of a sharp image, and q is a number of equation powers and 0<q<1；
Step 3, solving the concave-convex norm ratio regularization model in the step 2 to obtain a clear image;
step 3-1, updating high-frequency information x of the clear image;
step 3-2, updating a fuzzy core k;
and 3-3, obtaining a restored image.
2. The blind deblurring image recovery method according to claim 1, characterized in that in step 3-1, the specific steps are: step 3-1-1, fidelity item selection l 1 Norm, solving model:
step 3-1-2, i | x | purple sweet in step 3-1-1 2 Regarded as a constant, the solution model of step 3-1-1 is converted into a model about non-convex | x | | calculation of luminance q Regularization model of norm:
step 3-1-3, introducing an auxiliary variable v and a weight parameter theta, and converting the regularization model in the step 3-1-2 into:
wherein the content of the first and second substances,
θ i ＝c i θ 0 (7)；
in the formula, theta 0 Denotes an initial value of a weight parameter θ, c i Linear with the dimension i, c i ＝2i；
3-1-4, replacing a constant term lambda | x | non-calculation with beta 2 And respectively solving v and x in the regularization model conversion of the step 3-1-3, wherein a solving formula is as follows:
step 3-1-5, respectively deriving the solving formula of step 3-1-4:
in the formula, x k+1 Denotes the value of x at step k +1, Δ t being the iteration step.
3. The blind deblurring image recovery method according to claim 1, characterized in that in step 3-2, the specific steps are:
step 3-2-1, fidelity item selection l 2 The square term of the norm, the solution model is:
step 3-2-2, in the updating process of the fuzzy kernel k, calculating the weight of the fuzzy kernel k by using an IRLS method:
wherein λ is 1 And ψ is a constant value, k 0 As an initial blur kernel, w k Weight of the updated fuzzy kernel k;
and 3-2-3, solving the fuzzy kernel function k in the finest scale according to the step 3-2-1 and the step 3-2-2.
4. The blind deblurring image recovery method according to claim 1, characterized in that in step 3-2, the specific steps are:
step 3-3-1, under the condition that the fuzzy core is known, the image model solution is changed into non-blind image deconvolution, and the solution model is as follows:
step 3-3-2, let D = Du, where D representsOperation, separating variable u from D and increasing l 2 The square term of the norm, introducing a corresponding regularization factor β, and the model of step 3-3-1 is transformed into:
step 3-3-3, performing derivation on the model in the step 3-3-2, and obtaining an optimal solution by using a two-dimensional fast Fourier method, wherein the optimal solution corresponds to the recovered clear image:
when solving for d, the threshold formula is:
wherein, the first and the second end of the pipe are connected with each other,
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