CN113689336A - Power equipment infrared image non-blind super-resolution method - Google Patents

Power equipment infrared image non-blind super-resolution method Download PDF

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CN113689336A
CN113689336A CN202110982645.XA CN202110982645A CN113689336A CN 113689336 A CN113689336 A CN 113689336A CN 202110982645 A CN202110982645 A CN 202110982645A CN 113689336 A CN113689336 A CN 113689336A
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王艳
王龄婕
刘秉聪
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North China Electric Power University
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Abstract

The invention discloses a non-blind super-resolution method for infrared images of power equipment, which comprises the following steps: s1) based on the infrared image of the power equipment, improving the compressed sensing basic model according to the image degradation model to construct a compressed sensing super-resolution model; s2) based on the compressed sensing super-resolution model, combining image deconvolution prior information, introducing image edge distribution prior constraint, constructing a compressed sensing non-blind super-resolution model, and reconstructing an infrared image of the power equipment; s3) extracting the significant edge region in the reconstructed infrared image of the power equipment by adopting a double-prior secondary estimation mode, distinguishing the edge region from a smooth region according to the generated label image, and adjusting the normal term intensity by adopting different lambda values to obtain a reconstruction result. The non-blind super-resolution method for the infrared image of the power equipment can effectively solve the problems of fuzzy infrared image and low resolution of the power equipment.

Description

Power equipment infrared image non-blind super-resolution method
Technical Field
The invention relates to the technical field of infrared image resolution improvement, in particular to a non-blind super-resolution method for infrared images of power equipment.
Background
With the construction of the power internet of things and the development of sensor technology, image information in a power system is diversified and explosively increased. The image information of infrared, ultraviolet, visible light and other equipment acquired by various inspection means has the data characteristics of large volume, quick growth and low value density. One of the manifestations is that the resolution of the acquired infrared image is low, the image is blurred, and this undoubtedly limits the further application of the thermal imaging technology in fault location, image recognition and the like. Due to the limitation of equipment installation cost, data transmission and storage capacity, the hardware performance of the existing infrared sensor is greatly improved, and certain difficulty exists. Therefore, in order to better apply the infrared diagnosis technology, it is necessary to process the acquired low-resolution infrared image through a background algorithm, so that the visual effect of the infrared image is improved, and the image content information is enriched.
The super-resolution technology which is emerging in recent years provides a new idea for solving the problem. The problem to be solved by the super-resolution method is to reconstruct a high resolution image from the known low resolution image. Existing methods can generally be divided into three categories: the first method omits a complex fuzzy process commonly existing in the process of forming a low-resolution image, considers that the low-resolution image is absolutely clear, and only improves the resolution, and research results show that the influence of the accuracy of a fuzzy kernel on the super-resolution reconstruction problem is even greater than that of a selected super-resolution model, so that when an actual shot image is processed, a good effect similar to an experimental result of the actual shot image cannot be obtained; the second method is a blind super-resolution method, which solves the problem of fuzzy kernel estimation and the problem of high-resolution image reconstruction at the same time, but because joint restoration of the fuzzy kernel and the high-resolution image is generally difficult and a suboptimal reconstruction result is easily generated, the blind super-resolution method has less research; the third method is a non-blind super-resolution method, which solves the image blur kernel by a classical blur kernel estimation method, and then adopts the proposed non-blind method to reconstruct the image super-resolution by using the known blur kernel and the low-resolution image, and the method is a main research method at the present stage.
In the prior art, three common methods for image super-resolution include an interpolation method, a learning method and a reconstruction method. Wherein: the interpolation method has the advantages that due to the inherent smooth benefit, the reconstructed image is generally fuzzy, the detail texture is not clear, and although the algorithm principle is simple and the operation is fast, the interpolation method is not high in practical application value; the learning method needs a large amount of high-definition images to carry out early-stage training on a model, when a training sample and the characteristics of a reconstructed object have deviation, false textures are easily added to the image, the infrared image obtained by reconstruction is extremely adversely affected in the later-stage fault diagnosis, and due to the large demand on the sample, the method is difficult to be practically applied to a power grid with a relatively extensive data acquisition and storage mode at present; the reconstruction method realizes super-resolution reconstruction of the image by combining prior information in a Bayesian framework or introducing regularization in the inverse problem of the Bayesian framework according to the image degradation principle, is not limited by samples, is flexible to use, has a good reconstruction effect, and is easy to popularize and apply in a large scale in a power grid.
Disclosure of Invention
The invention aims to provide a non-blind super-resolution method for infrared images of power equipment, which can effectively solve the problems of fuzzy infrared images and low resolution of the power equipment.
In order to achieve the purpose, the invention provides the following scheme:
a non-blind super-resolution method for infrared images of power equipment comprises the following steps:
s1) improving the image degradation model based on the infrared image of the power equipment to construct a compressed sensing super-resolution model; in particular, the method comprises the following steps of,
the image degradation model is:
Figure RE-GDA0003293245100000021
in the formula: y is a low resolution image; x is a high resolution image; k is a blur kernel;
Figure RE-GDA0003293245100000022
for operation of convolution(ii) a ↓ is a downsampling process; n is noise;
the objective function of the improved compressed sensing super-resolution model is as follows:
Figure RE-GDA0003293245100000023
in the formula: phil,ΦrGenerating a row-column sampling matrix according to a cubic interpolation downsampling principle, and finishing downsampling of the two-dimensional signal under the combined action; Ψ is a sparse transformation matrix, ΨTIs a transpose of Ψ; xs＝ΨTX，XsIs a two-dimensional sparse signal; eta is a penalty coefficient;
s2) based on the compressed sensing super-resolution model, combining image deconvolution prior information, introducing image edge distribution prior constraint, constructing a compressed sensing non-blind super-resolution model, and reconstructing an infrared image of the power equipment; in particular, the method comprises the following steps of,
fitting the edge of the infrared image of the power equipment by adopting random distribution, and recording the edge as
Figure RE-GDA0003293245100000024
Wherein alpha is more than 0 and less than or equal to 2; if alpha is more than 0 and less than 1, the distribution is the super Laplace distribution, alpha-1 is the Laplace distribution, and alpha-2 is the Gaussian distribution; according to bayes' theorem, the posterior probability of a sharp image is written as p (X | Y) ═ p (Y | X) p (X), so the maximum posterior probability solution of X is:
Figure RE-GDA0003293245100000031
in the formula: the first item is a data fidelity item, passing through L2Norm constraint realization; the second term can be deformed into
Figure RE-GDA0003293245100000032
Wherein f isiFor each derivative filter, the value of subscript i is i ═ x, y, xx, yy, xy };
at this time, a compressed sensing non-blind super-resolution model can be constructed as follows:
Figure RE-GDA0003293245100000033
in the formula: lambda is an edge distribution prior constraint intensity coefficient;
s3) extracting the significant edge region in the reconstructed infrared image of the power equipment by adopting a double-prior secondary estimation mode, distinguishing the edge region from a smooth region according to the generated label image, and adjusting the normal term intensity by adopting different lambda values to obtain a reconstruction result.
Optionally, the adjusting the intensity of the positive rule term by using different λ values in step S3), specifically includes:
s31) making the edge distribution prior parameter alpha in the formula (4) take the value of 2, solving the formula (4) to obtain a preliminary reconstruction image X1；
S32) using a filter bank { f }x,fy,fxx,fyy,fxyFor the preliminary reconstructed image X1Filtering to obtain edge images in all directions;
s33) performing threshold contraction on the edge images in all directions, wherein the contraction mode is as follows:
Figure RE-GDA0003293245100000034
in the formula:
Figure RE-GDA0003293245100000035
is the shrink threshold; sigma is a proportionality coefficient; the shrinkage result is recorded as Xi＝{Xx,Xy,Xxx,Xyy,Xxy}；
S34) solving
Figure RE-GDA0003293245100000036
Integrating the salient edges in all directions into the final image salient edge result
Figure RE-GDA0003293245100000037
S35) will
Figure RE-GDA0003293245100000038
Is less than
Figure RE-GDA0003293245100000039
Setting the element of (1) to be 0 and setting the other elements to be 1 to generate a binary image;
s36) carrying out mathematical morphology processing on the binary image, successively carrying out opening and closing operations once respectively, removing noise of the binary image, and obtaining a final label image XlabIn finding XlabAnd then carrying out self-adaptive control on the lambda value in the following mode:
Figure RE-GDA0003293245100000041
and will be(m,n)And (4) substituting the formula (4), and solving the formula (4) to complete the image super-resolution reconstruction.
Optionally, the solving of the equation (4) in step S36), where the solving method under different α values specifically includes: introducing an auxiliary variable into the formula (4) by adopting a semi-quadratic splitting method, and solving the model in an alternating iteration mode; the model after introducing the auxiliary variables is as follows:
Figure RE-GDA0003293245100000042
in the formula: g, XsIs an auxiliary variable; epsilon, eta and eta' are penalty coefficients, the values of which increase with the increase of the iteration times, and when the values are large enough, the formula (7) and the formula (4) are considered to be solved;
an auxiliary variable solving method comprises the following steps:
because the values of the alpha are different,
Figure RE-GDA0003293245100000043
the item representation mode and the solving method are different, so variables G and X are given firstlysWherein G adoptsSolving by a gradient descent method; fixed XsAfter X, the objective function is:
Figure RE-GDA0003293245100000044
the derivative of equation (8) with respect to G is:
Figure RE-GDA0003293245100000045
the iteration step size is then determined by a non-monotonic linear search method, i.e. when the following conditions are met:
Figure RE-GDA0003293245100000046
determining the iteration step size as sigma(n)If the inequality is not satisfied, let σ(n)'＝0.6σ(n)And will be(n)' judging again by the formula (10) until the inequality is established; wherein the non-zero constant theta is equal to [0,1 ]]，C(n)The determination method comprises the following steps:
C(n+1)＝(τQ(n)C(n)+f(G(n+1)))/Q(n+1) (11)
in the formula: c(0)＝f(G(0))，f(G(n)) The value of formula (8) at the nth iteration of G; constant tau epsilon 0,1]；Q(n+1)The calculation method is as follows:
Q(n+1)＝τQ(n)+1 (12)
in the formula: q (0)1, when G | |(n+1)-G(n)||2< upsilon, where upsilon is a sufficiently small positive constant, the iteration is complete;
Xsafter the variables G and X are fixed, solving the variables in a soft threshold shrinkage mode, wherein an objective function is as follows:
Figure RE-GDA0003293245100000051
the solution is:
Figure RE-GDA0003293245100000052
in the formula: sign (·) is a sign function;
Figure RE-GDA00032932451000000513
is a component multiplication;
the method for solving the image to be reconstructed comprises the following steps:
the method for solving the image X to be reconstructed is given in each case, and when α is 2, G and X are fixedsThe objective function is:
Figure RE-GDA0003293245100000053
at the moment, the Gaussian prior is adopted for preliminary reconstruction, the purpose is only to extract the significant edge of the image, so that the lambda uniformly takes a larger value of 0.1 multiplied by 10-2Equation (15) derives the variable X and makes the derivative 0 available:
Figure RE-GDA0003293245100000054
in the formula: k, FiRespectively convolution operators k, fiThe matrix form of (a) can be directly solved for X by applying two-dimensional fast fourier transform:
Figure RE-GDA0003293245100000055
in the formula:
Figure RE-GDA0003293245100000056
representing a fast fourier transform;
Figure RE-GDA0003293245100000057
representing the inverse fast Fourier transformTransforming;
Figure RE-GDA0003293245100000058
is composed of
Figure RE-GDA0003293245100000059
Complex conjugation of (a);
Figure RE-GDA00032932451000000510
representing a component multiplication; the formula is divided by the corresponding element;
when in the objective function
Figure RE-GDA00032932451000000511
In the process, a non-blind super-resolution model is constructed in a self-adaptive regularization mode, and the target function is as follows:
Figure RE-GDA00032932451000000512
in the formula: m and N are the number of pixel points in the row and column directions of the image respectively; lambda [ alpha ](m,n)Determining a value according to the calculation mode of the formula (6); introduction of an auxiliary variable w using a semi-quadratic splitting methodiThe objective function is deformed as:
Figure RE-GDA0003293245100000061
equation (19) can be divided into the solution of the X sub-problem and the w sub-problem, where when the X sub-problem is solved, the objective function is:
Figure RE-GDA0003293245100000062
the solving method is the same as the formula (15), and X can be obtained through fast Fourier transform:
Figure RE-GDA0003293245100000063
solving the w subproblem after solving X, and enabling
Figure RE-GDA0003293245100000064
The objective function is abbreviated as:
Figure RE-GDA0003293245100000065
by taking the derivative of equation (22) and making the derivative 0, one can obtain:
Figure RE-GDA0003293245100000066
the further modification is that:
Figure RE-GDA0003293245100000067
let the root of equation (24) be r when r is between
Figure RE-GDA0003293245100000068
And v, the solution w 'of formula (24) is r, otherwise w' is 0.
Optionally, the constructing of the compressed sensing basic model in step S1) specifically includes:
an image is a two-dimensional signal and is marked as X, pixel points of the two-dimensional signal are expanded according to columns and then are converted into a one-dimensional signal X, the one-dimensional signal X is sparsely represented by a sparse transformation matrix psi when a CS principle is applied to signal reconstruction, and when an image acquisition fuzzy process is not considered, the model is as follows:
y＝ΦΨxs＝Axs (25)
in the formula: x ═ Ψ xs；xsIs a sparse signal; a phi psi is a sensing matrix, and x is solved by measuring signal ysThus according to Ψ xsObtaining a signal x to be reconstructed, and solving the xsThe objective function of (a) is:
Figure RE-GDA0003293245100000071
according to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a power equipment infrared image non-blind super-resolution method, which is based on a compressed sensing super-resolution model and combines image deconvolution prior information to provide the compressed sensing non-blind super-resolution model, and performs self-adaptive control on regular term intensity coefficients in the reconstruction process for further improving the quality of reconstructed images and inhibiting the generation of artifact ringing; compared with the existing classical non-blind super-resolution method, the method can effectively inhibit the generation of artifact ringing in the deblurring process, has better visual effect of the reconstructed image, and contains richer detail texture information. The method provided by the invention can be directly used, and a large amount of original high-definition images are not required to be adopted for training the model in the early stage, so that the method has the advantage of easy popularization; according to experimental results, the method provided by the invention can better improve the definition level of the edge outline of the image and enrich the detail texture information of the image; compared with the prior art, the method of the invention has the advantages that: the method has the advantages that any training sample is not needed, the method can be directly used, the performance of the method is obviously improved, the quality of the infrared image acquired by the low-precision infrared sensor can be better improved, and a good foundation is provided for the wide application of the infrared diagnosis technology of the power equipment.
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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 needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a non-blind super-resolution method for infrared images of an electric power device according to an embodiment of the present invention;
FIG. 2a is an infrared image of an exemplary power device according to an embodiment of the present invention;
FIG. 2b is a fitting result of the gradient probability density curve and different distributions of the infrared image of the power device according to the embodiment of the present invention;
FIG. 3a is a low resolution blurred image according to an embodiment of the present invention;
FIG. 3b is a reconstruction result of the method according to the embodiment of the present invention;
FIG. 3c is a strong regularization reconstruction result according to an embodiment of the present invention;
FIG. 3d is a weak regularization reconstruction result according to an embodiment of the present invention;
FIG. 4 is a flow chart of a method for adaptive regularization term strength adjustment according to an embodiment of the present invention;
FIG. 5 is a non-blind super-resolution model solving process according to an embodiment of the present invention;
FIG. 6a is an infrared image of embodiment one of the present invention;
FIG. 6b is a reconstruction result of the first infrared image according to the method of Keys;
FIG. 6c is a reconstruction result of an infrared image according to the method of Glasner according to embodiment of the present invention;
fig. 6d is a reconstruction result of the infrared image of embodiment one of the present invention by using the method proposed by Dong;
fig. 6e is a reconstruction result of the infrared image of embodiment one of the present invention by using the method proposed by Zhao;
FIG. 6f is a reconstruction of an IR image according to embodiment one of the present invention using the methods described herein;
FIG. 7a is an infrared image of example two of the present invention;
FIG. 7b shows the result of reconstruction of the second IR image according to the method of Keys;
FIG. 7c shows the result of reconstruction of infrared image II by the method of Glasner according to an embodiment of the present invention;
fig. 7d is a reconstruction result of the infrared image of the second embodiment of the present invention by using the method proposed by Dong;
fig. 7e is a reconstruction result of the infrared image of embodiment two using the method proposed by Zhao;
FIG. 7f is a reconstruction of an infrared image of example two using the methods described herein;
FIG. 8a is a comparison graph of AG index values of infrared images reconstructed by different methods according to the embodiment of the present invention;
fig. 8b is a comparison graph of IE index values of infrared images reconstructed by different methods according to the 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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a non-blind super-resolution method for infrared images of power equipment, which can effectively solve the problems of fuzzy infrared images and low resolution of the power equipment.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the non-blind super-resolution method for infrared images of power equipment provided by the embodiment of the invention includes the following steps:
s1) based on the infrared image of the power equipment, improving the compressed sensing basic model according to the image degradation model to construct a compressed sensing super-resolution model; in particular, the method comprises the following steps of,
the image degradation model is:
Figure RE-GDA0003293245100000081
in the formula: y is a low resolution image; x is a high resolution image; k is a blur kernel;
Figure RE-GDA0003293245100000093
performing convolution operation; ↓ is a downsampling process; n is noise;
the objective function of the improved compressed sensing super-resolution model is as follows:
Figure RE-GDA0003293245100000091
in the formula: phil,ΦrGenerating a row-column sampling matrix according to a cubic interpolation downsampling principle, and finishing downsampling of the two-dimensional signal under the combined action; Ψ is a sparse transformation matrix, ΨTIs a transpose of Ψ; xs＝ΨTX，XsIs a two-dimensional sparse signal; eta is a penalty coefficient;
step S1), a compressed sensing super-resolution basic model is established, the model shown in the formula (2) does not contain any prior information except sparse constraint, if the image is reconstructed directly according to the formula (2), due to the problem of unsuitability, the effect of deconvolution deblurring of the reconstructed image is difficult to achieve, and therefore other prior information is required to be introduced as constraint according to the image statistical rule; the deblurring method with the best performance at present generally adopts edge statistical information output by a group of filters to be matched with edge statistical information of a clear image, and the edge statistical information is used as prior constraint of the deblurring problem; the distributions commonly used for fitting the image gradient include Gaussian (Gaussian) distribution, Laplacian (Laplacian) distribution and Hyper-Laplacian (Hyper-Laplacian) distribution, if edge distribution is assumed to be Gaussian distribution, the deblurring problem has an analytic solution in a frequency domain, and an image can be efficiently restored through fast fourier transform, however, a clear infrared image usually has non-Gaussian edges as shown in fig. 2a to 2b, and therefore fitting the image gradient by using Gaussian distribution tends to result in poor visual effect; another common method is to assume that the image edge conforms to the laplacian distribution, however, due to the "heavy tail" property of the real-world image edge distribution, the fitting effect of the laplacian distribution is also poor; therefore, in the method at the present stage, the image edge distribution is mostly fitted by adopting the super-Laplace distribution which can better fit the characteristic of the heavy tail, and the image edge distribution is used as prior information, so that the aim of deconvolution deblurring is fulfilled;
s2) based on the compressed sensing super-resolution model, combining image deconvolution prior information, introducing image edge distribution prior constraint, constructing a compressed sensing non-blind super-resolution model, and reconstructing an infrared image of the power equipment; in particular, the method comprises the following steps of,
fitting the edge of the infrared image of the power equipment by adopting random distribution, and recording the edge as
Figure RE-GDA0003293245100000092
Wherein alpha is more than 0 and less than or equal to 2; if alpha is more than 0 and less than 1, the distribution is the super Laplace distribution, alpha-1 is the Laplace distribution, and alpha-2 is the Gaussian distribution; according to bayes' theorem, the posterior probability of a sharp image is written as p (X | Y) ═ p (Y | X) p (X), so the maximum posterior probability solution of X is:
Figure RE-GDA0003293245100000101
in the formula: the first item is a data fidelity item, passing through L2Norm constraint realization; the second term can be deformed into
Figure RE-GDA0003293245100000102
Wherein f isiFor each derivative filter, the value of subscript i is i ═ x, y, xx, yy, xy };
at this time, a compressed sensing non-blind super-resolution model can be constructed as follows:
Figure RE-GDA0003293245100000103
in the formula: lambda is an edge distribution prior constraint intensity coefficient;
FIG. 3a shows a low-resolution blurred image, which is based on a compressed sensing super-resolution model, and combines image deconvolution prior information to provide a compressed sensing non-blind super-resolution model, but the model still needs to be further improved at this time because the value of an edge distribution prior constraint intensity coefficient does not consider the difference of image internal pixel point semantics, and the whole image is constrained by the same value, which leads to strong regularization, that is, when the value is large, the reconstructed image is subjected to edge reconstructionThe edge texture is fuzzy, and the reconstructed image has artifact ringing during weak regularization, so that the quality of the reconstructed image is reduced; as shown in fig. 3c, when strong regularization is adopted to constrain the image edge prior information, i.e. λ is 0.1 × 10-1In the process, the reconstruction result does not contain ringing artifacts, but the texture of the edge of the equipment is fuzzy, the image contrast is low, and the visual effect is poor; as shown in fig. 3d, when weak regularization is adopted for constraint, i.e., λ is 0.1 × 10-4In the process, the reconstructed image is clearer, the contrast of the texture at the edge of the equipment is high, but the smooth area in the image has obvious ringing effect; and the present invention further employs step S3);
s3) extracting the significant edge region in the reconstructed infrared image of the power device by using a double-prior quadratic estimation, distinguishing the edge region from the smooth region according to the generated label image, and adjusting the intensity of the positive terms by using different λ values to obtain a better reconstruction result, as shown in fig. 3b, the edge texture of the reconstructed image is clear and does not contain ringing artifacts.
As shown in fig. 4, the main body of the adaptive regularization term intensity adjustment method adopted by the present invention is to perform secondary reconstruction on an image according to a model of formula (4) by using different priors as constraints; extracting a significant edge of a reconstructed image by adopting a Gaussian prior which is convenient to solve for a first reconstruction model to generate a label image; and the secondary reconstruction adopts the super Laplacian prior with good effect as constraint, and the regularization strength of different pixel points is adaptively adjusted according to the label image.
In step S3), adjusting the positive rule intensity by using different λ values specifically includes:
s31) making the edge distribution prior parameter alpha in the formula (4) take the value of 2, solving the formula (4) to obtain a preliminary reconstruction image X1；
S32) using a filter bank { f }x,fy,fxx,fyy,fxyFor the preliminary reconstructed image X1Filtering to obtain edge images in all directions;
s33) performing threshold contraction on the edge images in all directions, wherein the contraction mode is as follows:
Figure RE-GDA0003293245100000111
in the formula:
Figure RE-GDA0003293245100000112
is the shrink threshold; sigma is a proportionality coefficient; the shrinkage result is recorded as Xi＝{Xx,Xy,Xxx,Xyy,Xxy}；
S34) solving
Figure RE-GDA0003293245100000113
Integrating the salient edges in all directions into the final image salient edge result
Figure RE-GDA0003293245100000119
S35) will
Figure RE-GDA0003293245100000114
Is less than
Figure RE-GDA0003293245100000115
Setting the element of (1) to be 0 and setting the other elements to be 1 to generate a binary image;
s36) carrying out mathematical morphology processing on the binary image, successively carrying out opening and closing operations once respectively, removing noise of the binary image, and obtaining a final label image XlabIn finding XlabAnd then carrying out self-adaptive control on the lambda value in the following mode:
Figure RE-GDA0003293245100000116
and will be(m,n)And (4) substituting the formula (4), and solving the formula (4) to complete the image super-resolution reconstruction.
In step S36), the solving method for equation (4) under different values of α includes: introducing an auxiliary variable into the formula (4) by adopting a semi-quadratic splitting method, and solving the model in an alternating iteration mode; the model after introducing the auxiliary variables is as follows:
Figure RE-GDA0003293245100000117
in the formula: g, XsIs an auxiliary variable; epsilon, eta and eta' are penalty coefficients, the values of which increase with the increase of the iteration times, and when the values are large enough, the formula (7) and the formula (4) are considered to be solved;
an auxiliary variable solving method comprises the following steps:
because the values of the alpha are different,
Figure RE-GDA0003293245100000118
the item representation mode and the solving method are different, so variables G and X are given firstlysThe solving method of (1), wherein G is solved by a gradient descent method; fixed XsAfter X, the objective function is:
Figure RE-GDA0003293245100000121
the derivative of equation (8) with respect to G is:
Figure RE-GDA0003293245100000122
the iteration step size is then determined by a non-monotonic linear search method, i.e. when the following conditions are met:
Figure RE-GDA0003293245100000123
determining the iteration step size as sigma(n)If the inequality is not satisfied, let σ(n)'＝0.6σ(n)And will be(n)' judging again by the formula (10) until the inequality is established; wherein the non-zero constant theta is equal to [0,1 ]]，C(n)The determination method comprises the following steps:
C(n+1)＝(τQ(n)C(n)+f(G(n+1)))/Q(n+1) (11)
in the formula: c(0)＝f(G(0))，f(G(n)) The value of formula (8) at the nth iteration of G; constant tau epsilon 0,1]；Q(n+1)The calculation method is as follows:
Q(n+1)＝τQ(n)+1 (12)
in the formula: q (0)1, when G | |(n+1)-G(n)||2< upsilon, where upsilon is a sufficiently small positive constant, the iteration is complete;
Xsafter the variables G and X are fixed, solving the variables in a soft threshold shrinkage mode, wherein an objective function is as follows:
Figure RE-GDA0003293245100000124
the solution is:
Figure RE-GDA0003293245100000125
in the formula: sign (·) is a sign function;
Figure RE-GDA0003293245100000126
is a component multiplication;
the method for solving the image to be reconstructed comprises the following steps:
the method for solving the image X to be reconstructed is given in each case, and when α is 2, G and X are fixedsThe objective function is:
Figure RE-GDA0003293245100000127
at the moment, the Gaussian prior is adopted for preliminary reconstruction, the purpose is only to extract the significant edge of the image, so that the lambda uniformly takes a larger value of 0.1 multiplied by 10-2To suppress the generation of ringing artifacts, equation (15) derives the variable X and makes the derivative 0:
Figure RE-GDA0003293245100000131
in the formula: k, FiRespectively convolution operators k, fiThe matrix form of (a) can be directly solved for X by applying two-dimensional fast fourier transform:
Figure RE-GDA0003293245100000132
in the formula:
Figure RE-GDA0003293245100000133
representing a fast fourier transform;
Figure RE-GDA0003293245100000134
representing an inverse fast fourier transform;
Figure RE-GDA0003293245100000135
is composed of
Figure RE-GDA0003293245100000136
Complex conjugation of (a);
Figure RE-GDA0003293245100000137
representing a component multiplication; the formula is divided by the corresponding element;
when in the objective function
Figure RE-GDA0003293245100000138
In the process, a non-blind super-resolution model is constructed in a self-adaptive regularization mode, and the target function is as follows:
Figure RE-GDA0003293245100000139
in the formula: m and N are the number of pixel points in the row and column directions of the image respectively; lambda [ alpha ](m,n)Determining a value according to the calculation mode of the formula (6); introduction of an auxiliary variable w using a semi-quadratic splitting methodiThe objective function is deformed as:
Figure RE-GDA00032932451000001310
equation (19) can be divided into the solution of the X sub-problem and the w sub-problem, where when the X sub-problem is solved, the objective function is:
Figure RE-GDA00032932451000001311
the solving method is the same as the formula (15), and X can be obtained through fast Fourier transform:
Figure RE-GDA00032932451000001312
solving the w subproblem after solving X, and enabling
Figure RE-GDA00032932451000001313
The objective function is abbreviated as:
Figure RE-GDA00032932451000001314
by taking the derivative of equation (22) and making the derivative 0, one can obtain:
Figure RE-GDA0003293245100000141
the further modification is that:
Figure RE-GDA0003293245100000142
let the root of equation (24) be r when r is between
Figure RE-GDA0003293245100000143
And v, the solution w 'of formula (24) is r, otherwise w' is 0.
Step S1), the constructing of the compressed sensing basic model specifically includes:
an image is a two-dimensional signal and is marked as X, pixel points of the two-dimensional signal are expanded according to columns and then are converted into a one-dimensional signal X, the one-dimensional signal X is sparsely represented by a sparse transformation matrix psi when a CS principle is applied to signal reconstruction, and when an image acquisition fuzzy process is not considered, the model is as follows:
y＝ΦΨxs＝Axs (25)
in the formula: x ═ Ψ xs；xsIs a sparse signal; a phi psi is a sensing matrix, and x is solved by measuring signal ysThus according to Ψ xsObtaining a signal x to be reconstructed, and solving the xsThe objective function of (a) is:
Figure RE-GDA0003293245100000144
however, since equation (26) only considers the image down-sampling process and does not consider the blurring convolution process, it is necessary to improve the image down-sampling process according to the image degradation model to obtain a better reconstruction effect.
The above respectively shows the calculation modes of the unknown variables in the compressed sensing non-blind super-resolution method, and when α takes different values, the overall solving process of equation (4) is shown in fig. 5.
In this section, a non-blind super-resolution reconstruction experiment is performed on the low-resolution fuzzy infrared image to verify the performance of the algorithm, and the experimental environment is as follows: intel (R) core (TM) i5-9300H CPU @2.40GHz, memory 16.00GB, using MATLAB R2019a programming, sparse basis Ψ using Daubechies-8 wavelet basis, adjusted by trial and error to obtain the following fixed parameters: β ═ η ═ 1, ∈ ═ 0.25,. sigma ═ 0.3, and ∈max＝βmax＝η'max＝256。
In a contrast experiment for reconstructing an actually shot low-Resolution blurred power equipment infrared Image, a contrast method selects Keys (Keys R. C. customer correlation interpretation and Processing for digital Image Processing [ J ]. IEEE transaction on optics, speed, and signal Processing, 1981, 29 (6): 1153 1160.), Glasser (Glasser D, Banon S, Irani M. Super-Resolution from a Single Image [ C ]// IEEE 12th international correlation on computer vision. IEEE, 2009: 356.), Dong (Dong W, Zhang L, Shi G, et al. non-linear spatial localization for prediction [ J ]. J. 12. J. Image Processing [ J. sub.S. (Zhang W.),83, S.), 2016, 25(8): 3683-: 945 and 952)), because an actually shot power equipment infrared image does not have an original high-resolution clear image, an original image-free evaluation index is adopted to quantify a reconstruction result, and the adopted indexes are an image Average Gradient (AG) and an Information Entropy (IE) index; the AG calculation mode is as follows:
Figure RE-GDA0003293245100000151
in the formula: f. ofx(i, j) and fy(i, j) are the results of the image operation by the Sobel difference operator in the image row direction and the image column direction respectively, and the greater the AG index is, the more layers in the image are and the clearer the edge is;
the information entropy is defined as:
Figure RE-GDA0003293245100000152
in the formula: and p (i) is the frequency of the pixel point with the gray value i appearing in the image, and the larger the finally obtained IE value is, the richer the information contained in the image is.
Selecting 10 actually-shot fuzzy low-resolution power equipment infrared images for super-resolution reconstruction, and providing specific reconstruction result images of two images and objective evaluation parameter values of all 10 images, wherein the first infrared image is shown in fig. 6a, the experimental result is shown in fig. 6b to 6f, the second infrared image is shown in fig. 7a, and the experimental result is shown in fig. 7b to 7 f.
As can be seen from fig. 6a to 7f, when the method of the present invention reconstructs an actually photographed low-resolution infrared image, compared with the comparative method, the detail texture and the edge contour are significantly clearer, and the image quality is significantly improved; in order to further quantify the performance of the method, AG and IE indexes are adopted to evaluate the reconstruction result, as shown in FIG. 8, the AG and IE indexes of the reconstructed image obtained by the method have obvious advantages compared with the comparative method, which shows that the reconstructed image has clearer internal texture and more information, and the objective evaluation indexes are verified with subjective visual effect, so that the performance advantages of the method are reflected.
The invention provides a power equipment infrared image non-blind super-resolution method, which is based on a compressed sensing super-resolution model and combines image deconvolution prior information to provide the compressed sensing non-blind super-resolution model, and performs self-adaptive control on regular term intensity coefficients in the reconstruction process for further improving the quality of reconstructed images and inhibiting the generation of artifact ringing; compared with the existing classical non-blind super-resolution method, the method can effectively inhibit the generation of artifact ringing in the deblurring process, has better visual effect of the reconstructed image, and contains richer detail texture information. The method provided by the invention can be directly used, and a large amount of original high-definition images are not required to be adopted for training the model in the early stage, so that the method has the advantage of easy popularization; according to experimental results, the method provided by the invention can better improve the definition level of the edge outline of the image and enrich the detail texture information of the image; compared with the prior art, the method of the invention has the advantages that: the method has the advantages that any training sample is not needed, the method can be directly used, the performance of the method is obviously improved, the quality of the infrared image acquired by the low-precision infrared sensor can be better improved, and a good foundation is provided for the wide application of the infrared diagnosis technology of the power equipment.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (4)

1. A non-blind super-resolution method for infrared images of power equipment is characterized by comprising the following steps:
s1) based on the infrared image of the power equipment, improving the compressed sensing basic model according to the image degradation model to construct a compressed sensing super-resolution model; in particular, the method comprises the following steps of,
the image degradation model is:
Figure RE-FDA0003293245090000011
in the formula: y is a low resolution image; x is a high resolution image; k is a blur kernel;
Figure RE-FDA0003293245090000012
performing convolution operation; ↓ is a downsampling process; n is noise;
the target function of the compressed sensing super-resolution model obtained by improvement is as follows:
Figure RE-FDA0003293245090000013
in the formula: phil,ΦrGenerating a row-column sampling matrix according to a cubic interpolation downsampling principle, and finishing downsampling of the two-dimensional signal under the combined action; Ψ is a sparse transformation matrix, ΨTIs a transpose of Ψ; xs＝ΨTX，XsIs a two-dimensional sparse signal; eta is a penalty coefficient;
s2) based on the compressed sensing super-resolution model, combining image deconvolution prior information, introducing image edge distribution prior constraint, constructing a compressed sensing non-blind super-resolution model, and reconstructing an infrared image of the power equipment; in particular, the method comprises the following steps of,
fitting the edge of the infrared image of the power equipment by adopting random distribution, and recording the edge as
Figure RE-FDA0003293245090000017
Wherein alpha is more than 0 and less than or equal to 2; if alpha is more than 0 and less than 1, the distribution is the super Laplace distribution, alpha-1 is the Laplace distribution, and alpha-2 is the Gaussian distribution; according to bayes' theorem, the posterior probability of a sharp image is written as p (X | Y) ═ p (Y | X) p (X), so the maximum posterior probability solution of X is:
Figure RE-FDA0003293245090000014
in the formula: the first item is a data fidelity item, passing through L2Norm constraint realization; the second term can be deformed into
Figure RE-FDA0003293245090000015
Wherein f isiFor each derivative filter, the value of subscript i is i ═ x, y, xx, yy, xy };
at this time, a compressed sensing non-blind super-resolution model can be constructed as follows:
Figure RE-FDA0003293245090000016
in the formula: lambda is an edge distribution prior constraint intensity coefficient;
s3) extracting the significant edge region in the reconstructed infrared image of the power equipment by adopting a double-prior secondary estimation mode, distinguishing the edge region from a smooth region according to the generated label image, and adjusting the normal term intensity by adopting different lambda values to obtain a reconstruction result.
2. The non-blind super-resolution method for the infrared images of the power equipment according to claim 1, wherein the adjusting of the regular term intensity by using different λ values in step S3) specifically comprises:
s31) making the edge distribution prior parameter alpha in the formula (4) take the value of 2, solving the formula (4) to obtain a preliminary reconstruction image X1；
S32) using a filter bank { f }x,fy,fxx,fyy,fxyFor the preliminary reconstructed image X1Filtering to obtain edge images in all directions;
s33) performing threshold contraction on the edge images in all directions, wherein the contraction mode is as follows:
Figure RE-FDA0003293245090000021
in the formula:
Figure RE-FDA0003293245090000022
is the shrink threshold; sigma is a proportionality coefficient; the shrinkage result is recorded as Xi＝{Xx,Xy,Xxx,Xyy,Xxy}；
S34) solving
Figure RE-FDA0003293245090000023
Integrating the direction significant edges as a final image significant edge result ^ X;
s35) will be less than X
Figure RE-FDA0003293245090000024
Setting the element of (1) to be 0 and setting the other elements to be 1 to generate a binary image;
s36) carrying out mathematical morphology processing on the binary image, successively carrying out opening and closing operations once respectively, removing noise of the binary image, and obtaining a final label image XlabIn finding XlabAnd then carrying out self-adaptive control on the lambda value in the following mode:
Figure RE-FDA0003293245090000025
will be lambda(m,n)And (4) substituting the formula (4), and solving the formula (4) to complete the image super-resolution reconstruction.
3. The power equipment infrared image non-blind super-resolution method according to claim 2, wherein in step S36), the solving method of equation (4) is performed, and the solving method under different α values specifically includes: introducing an auxiliary variable into the formula (4) by adopting a semi-quadratic splitting method, and solving the model in an alternating iteration mode; the model after introducing the auxiliary variables is as follows:
Figure RE-FDA0003293245090000026
in the formula: g, XsIs an auxiliary variable; epsilon, eta and eta' are penalty coefficients, the values of which increase with the increase of the iteration times, and when the values are large enough, the formula (7) and the formula (4) are considered to be solved;
an auxiliary variable solving method comprises the following steps:
because the values of the alpha are different,
Figure RE-FDA0003293245090000031
the item representation mode and the solving method are different, so variables G and X are given firstlysThe solving method of (1), wherein G is solved by a gradient descent method; fixed XsAfter X, the objective function is:
Figure RE-FDA0003293245090000032
the derivative of equation (8) with respect to G is:
Figure RE-FDA0003293245090000033
the iteration step size is then determined by a non-monotonic linear search method, i.e. when the following conditions are met:
f(G(n)+σ(n)dG (n))≤C(n)+θσ(n)▽f(G(n))dG (n) (10)
determining the iteration step size as sigma(n)If the inequality is not satisfied, let σ(n)'＝0.6σ(n)And will be(n)' judging again by the formula (10) until the inequality is established; wherein the non-zero constant theta is equal to [0,1 ]]，C(n)The determination method comprises the following steps:
C(n+1)＝(τQ(n)C(n)+f(G(n+1)))/Q(n+1) (11)
in the formula: c(0)＝f(G(0))，f(G(n)) The value of formula (8) at the nth iteration of G; constant tau epsilon 0,1]；Q(n+1)The calculation method is as follows:
Q(n+1)＝τQ(n)+1 (12)
in the formula: q(0)1, when G | |(n+1)-G(n)||2< upsilon, where upsilon is a sufficiently small positive constant, the iteration is complete;
Xsafter the variables G and X are fixed, solving the variables in a soft threshold shrinkage mode, wherein an objective function is as follows:
Figure RE-FDA0003293245090000034
the solution is:
Figure RE-FDA0003293245090000035
in the formula: sign (·) is a sign function;
Figure RE-FDA0003293245090000036
is a component multiplication;
the method for solving the image to be reconstructed comprises the following steps:
the method for solving the image X to be reconstructed is given in each case, and when α is 2, G and X are fixedsThe objective function is:
Figure RE-FDA0003293245090000041
at the moment, the Gaussian prior is adopted for preliminary reconstruction, the purpose is only to extract the significant edge of the image, so that the lambda uniformly takes a larger value of 0.1 multiplied by 10-2Equation (15) derives the variable X and makes the derivative 0 available:
Figure RE-FDA0003293245090000042
in the formula: k, FiRespectively convolution operators k, fiThe matrix form of (a) can be directly solved for X by applying two-dimensional fast fourier transform:
Figure RE-FDA0003293245090000043
in the formula:
Figure RE-FDA0003293245090000044
representing a fast fourier transform;
Figure RE-FDA0003293245090000045
representing an inverse fast fourier transform;
Figure RE-FDA0003293245090000046
is composed of
Figure RE-FDA0003293245090000047
Complex conjugation of (a);
Figure RE-FDA0003293245090000048
representing a component multiplication; the formula is divided by the corresponding element;
when in the objective function
Figure RE-FDA0003293245090000049
In the process, a non-blind super-resolution model is constructed in a self-adaptive regularization mode, and the target function is as follows:
Figure RE-FDA00032932450900000410
in the formula: m and N are the number of pixel points in the row and column directions of the image respectively; lambda [ alpha ](m,n)Determining a value according to the calculation mode of the formula (6); introduction of an auxiliary variable w using a semi-quadratic splitting methodiThe objective function is deformed as:
Figure RE-FDA00032932450900000411
equation (19) can be divided into the solution of the X sub-problem and the w sub-problem, where when the X sub-problem is solved, the objective function is:
Figure RE-FDA00032932450900000412
the solving method is the same as the formula (15), and X can be obtained through fast Fourier transform:
Figure RE-FDA0003293245090000051
solving the w subproblem after solving X, and enabling
Figure RE-FDA0003293245090000052
The objective function is abbreviated as:
Figure RE-FDA0003293245090000053
by taking the derivative of equation (22) and making the derivative 0, one can obtain:
Figure RE-FDA0003293245090000054
the further modification is that:
Figure RE-FDA0003293245090000055
let the root of equation (24) be r when r is between
Figure RE-FDA0003293245090000056
And v, the solution w 'of formula (24) is r, otherwise w' is 0.
4. The power equipment infrared image non-blind super-resolution method according to claim 1, wherein the construction of the compressed sensing basic model in step S1) specifically includes:
an image is a two-dimensional signal and is marked as X, pixel points of the two-dimensional signal are expanded according to columns and then are converted into a one-dimensional signal X, the one-dimensional signal X is sparsely represented by a sparse transformation matrix psi when a CS principle is applied to signal reconstruction, and when an image acquisition fuzzy process is not considered, the model is as follows:
y＝ΦΨxs＝Axs (25)
in the formula: x ═ Ψ xs；xsIs a sparse signal; a phi psi is a sensing matrix, and x is solved by measuring signal ysThus according to Ψ xsObtaining a signal x to be reconstructed, and solving the xsThe objective function of (a) is:
Figure RE-FDA0003293245090000057
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