CN107507135A - Image reconstructing method based on coding aperture and target - Google Patents
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Abstract
The invention belongs to technical field of computer vision, to propose a kind of improved non-blind point spread function number estimation method, the picture quality after lifting reconstruct.To reach above-mentioned purpose, the present invention adopts the technical scheme that, the image reconstructing method based on coding aperture and drone design, comprises the following steps：Design coding aperture is placed in the nearly detector end of camera lens；Design target is placed at the light cylinder front end of infrared image light source；The point spread function of infrared image is obtained by fuzzy core derivation algorithm model；L is used by analyzing Infrared Image Features model0Norm constrains as image regulation, and blurred picture is reconstructed recovery according to the point spread function above solved.Present invention is mainly applied to image procossing occasion.
Description
Technical Field
The invention belongs to the technical field of computer vision, and particularly relates to the field of digital image processing and computational photography, in particular to an image reconstruction method based on coded aperture and target design.
Background
The requirements of the society on the image imaging quality are higher and higher at present. Compared with a visible light imaging system, the imaging system is more and more widely applied to the fields of national economy, military, national defense and the like by virtue of the strong capability of penetrating smoke and water vapor. In the space optical imaging, due to the influences of factors such as diffraction and aberration of an optical system, atmospheric disturbance, relative compound motion of a space camera and a shooting scene, camera defocusing and the like, an image obtained by the camera has a blurring phenomenon, and the interpretation of an interested target in the image is influenced. With the improvement of imaging quality requirements, an image deblurring technology gradually becomes a research hotspot in the field of optical imaging, so that an accurate estimation point spread function in image deblurring is a key step for image reconstruction.
For the problem of image restoration, the conventional methods such as Wiener filtering, inverse filtering, constrained least square filtering, etc. are sensitive to noise and disturbance of a point spread function. To overcome the ill-posed nature of the inverse problem solution, restoration methods based on regularization and partial differential equations have emerged. The method carries out feature modeling on the image, applies prior knowledge to carry out regularization constraint on an inverse problem, and further solves a stable global minimum solution. The earliest occurring regularization methods, e.g. Tikhonov regularization method, use L2The norm method models the image, and the pixel value distribution of the image is considered to satisfy a quadratic function, so that the method can well remove noise but is vulnerable to image details. The method aims at the problems of high complexity and low operation speed of an iterative algorithm. However, the above methods involve many and complicated parameters, and all of them are set according to empirical values, and the parameters are not adaptively selected according to the structure and characteristics of the image. Different image restoration only adopts the same parameter setting, and certain images cannot be restored well or cannot reach the optimal solution. In order to solve the problem of inaccurate point spread function estimation in the image deblurring problem and better realize image restoration, the invention utilizes a coding aperture to carry out self-adaptive interpolationThe line design target carries out point spread function estimation, and an improved image reconstruction solving model is provided.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an improved non-blind point diffusion function estimation method and improves the quality of the reconstructed image. In order to achieve the above object, the present invention adopts a technical solution that an image reconstruction method based on a coded aperture and a target design comprises the following steps: designing a coding aperture and placing the coding aperture at the tail end of a camera lens close to a detector; designing a target and placing the target at the front end of an optical cylinder of an image light source; solving an algorithm model through a fuzzy kernel to obtain a point spread function of the image; by using L2And the norm is used as an image regularization constraint, and the fuzzy image is reconstructed and restored according to the point spread function solved in the foregoing.
Designing a coding aperture and placing the coding aperture at the tail end of a camera lens close to a detector; designing a target and placing the target at the front end of an optical cylinder of an image light source, and specifically comprising the following steps:
1) the mathematical model of image blur is expressed as the following formula:
f＝h*u+n (1)
wherein f is a blurred image, u is an original image, H is a point spread function PSF, n is white gaussian noise, x represents convolution, and if H is expressed in a matrix form H, the formula is expressed as:
f＝SHu+n(2)
wherein, S is the matrix form of the camera sampling function, namely the down-sampling matrix of the camera, the defocusing deblurring problem is to estimate the original image u by solving a maximum posterior probability problem, and the minimum value of the energy function E is used to solve the maximum posterior probability problem to realize the performance optimization of the coding aperture:
wherein,expressing the minimum value of the energy function, | ·| non-woven phosphor2Represents L2The norm of the number of the first-order-of-arrival,representing the noise-to-signal ratio of the image prior, expressed asWhere σ represents the standard deviation of white Gaussian noise, AξThe average power spectrum of a plurality of natural images is represented, mu (u) is a measurement of an original image u in an image space, and the average power spectrum expression of the plurality of natural images is as follows according to the 1/f rule of the natural images:
u is the original image, ξ is the frequency, u (ξ) is the representation of u on the frequency spectrum。Constructing a performance evaluation standard of the coding aperture:
wherein HξIn the form of a matrix of point spread functions corresponding to frequency ξ, for each frequency ξ,the amplified degree of noise is reflected, and the optimal aperture has the minimum R (H), which also means that the image reconstruction recovery result is more accurate; optimizing to obtain a low-resolution coding aperture by using a genetic algorithm, improving the resolution of the coding aperture by using a gradient descent method, and then placing the designed coding aperture at the tail end of a near detector of a camera lens;
2) the method comprises the steps of designing targets with remarkable geometric characteristics in all directions, respectively placing the targets at the front ends of light cylinders of image light sources for shooting images of different subsequent patterns, and shooting the images by using a coding aperture and the targets, so that the different patterns retain more frequency spectrum information of the images.
Solving an algorithm model through a fuzzy kernel to obtain a point spread function of the image; by using L2The norm is used as an image regularization constraint, and the fuzzy image is reconstructed and restored according to the point spread function solved in the front, and the method specifically comprises the following steps: the method comprises the following steps of shooting a light source image of a preset design target by using a lens provided with a coding aperture, wherein the shot image i is planar, simulating the mapping by using a planar response w (i), defining d as a geometric distortion function in consideration of distortion existing in a real camera, and constructing an image imaging model to represent the following form:
b＝v(d(w(i)))*h+n (6)
b is the shot image, h is the PSF of the lens deviation, v is the halo phenomenon caused by the camera lens, the original image u to be solved is generated through the distortion of the radiation model, and the
u＝v(d(w(i))) (7)
Equation (6) can be converted to:
using the optical information of the blur kernel as a prior, the above problem becomes the following optimization problem:
wherein | · | purple sweet2Is L2The norm of the number of the first-order-of-arrival,gradient operators, the first term being a data match term, λ, μ, γ being parameters, the second and third terms being a kernel sparse term and a kernel smooth term constrained by the parameters λ and μ, respectively,is an ideal fuzzy kernelIs a spectral density function constraint parameter of the PSF,F*(b) is the conjugate of F (b), the estimated value of the PSF is obtained through an optimization formula (10), and image reconstruction is carried out according to the point spread function.
The original image is estimated by solving the maximum a posteriori problem using energy function minimization, and the image reconstruction solution model is as follows:
whereinTo solve the data item of the model, | ·| non-woven phosphor2Is L2Norm, J (u) is the smoothing term, η is the parameter,the expression is to find the minimum of the energy function. u h is expressed in matrix form:
u*h＝SHu＝Au (11)
wherein A is equal to SH, and a smooth term of a solution model, namely a TV regular term, namely a total variation term J (u), is represented as:
||·||2is L2The norm of the number of the first-order-of-arrival,the gradient of u (x) is expressed as the gradient Grad J (u) of J (u) solved by the Euler-Lagrangian equation:
where div (. circle.) denotes divergence, using a smoothed TV regularization term, J (u) instead of J (u), the formula is:
whereinIs replaced byRepresenting the variable value, div (·) representing the divergence, the gradient Grad J of the TV regularization term after substitution (u) becomes:
given a point spread function, adopt L2And carrying out regularization constraint on the norm to reconstruct the image, and solving according to a Richardon-Lucy method to obtain the following multiplication iterative formula:
where, represents a dot product between elements, t represents the number of iterations, f is a blurred image, ATThe transpose of A η is a parameter, Grad J (u) represents J And (u) obtaining a final original image u by iterative solution.
The invention has the technical characteristics and effects that:
aiming at the problem of image reconstruction in image restoration work, the method provides an improved reconstruction method, retains the detail information of the image to the maximum extent by designing a coding aperture and an imaging target, estimates the point spread function of the image more accurately by a non-blind estimation method, and reconstructs and restores the blurred image according to the solved point spread function.
1. The method has simple program and easy realization, can be integrated into hardware, so that a camera or other imaging equipment can directly carry out the work of solving the image point diffusion function and reconstructing the image, and the dependence on external equipment is reduced.
2. The method is characterized in that a coding aperture and a group of targets with remarkable geometric characteristics in all directions of space are designed by self, and image detail information is reserved to the maximum extent for subsequent image reconstruction.
3. And providing a point spread function solving model to obtain the point spread function of the image.
4. And designing an image reconstruction optimization model, performing image reconstruction of non-blind estimation of the scene image, and comparing the image reconstruction with a blind estimation reconstruction method of the scene image.
Drawings
FIG. 1 is a flow chart of a practical implementation;
FIG. 2 is a schematic illustration of a fuzzy process of design;
FIG. 3 is a designed coded aperture (rightmost view is an assembled sleeve);
FIG. 4 is a designed target pattern. In the figure: (a) four hurdles are commonly used, (b) - (h) 6 homemade targets;
FIG. 5 is a flow chart of a point spread function non-blind estimation;
fig. 6 is a comparison of image reconstruction results based on blind estimation of a point spread function and non-blind estimation of a point spread function. (a) Clear target map, (b) blurred target map, (c) blind estimated image reconstruction result, (d) non-blind estimated image reconstruction result
Detailed Description
The technical scheme adopted by the invention is an image reconstruction method based on coding aperture and target design. And (3) adopting a performance evaluation standard of the coded aperture imaging system, and optimizing a coded aperture model by using a genetic algorithm and a coordinate descent method according to the evaluation standard to manufacture the coded aperture. Meanwhile, in order to retain the detail information of the image to the maximum extent, a target pattern with remarkable geometric characteristics in all directions is designed, a function model for point spread function estimation is constructed, and L is adopted2And the norm is used as an image regularization constraint, and the fuzzy image is reconstructed and restored according to the point spread function solved in the foregoing.
1) The mathematical model of image blur can be expressed as the following equation:
f＝h*u+n (1)
where f is the blurred image, u is the original image, h is the point spread function, and n is white gaussian noise, a stands for convolution. If H is expressed in matrix form H, the formula can be expressed as:
f＝SHu+n (2)
wherein S is a matrix form of a camera sampling function, namely a down-sampling matrix of the camera, the defocusing deblurring problem is to estimate an original image u by solving a maximum posterior probability problem, and the minimum value of an energy function E is used for solving the maximum posterior probability problem so as to realize the performance optimization of the coding aperture.
Wherein,expressing the minimum value of the energy function, | ·| non-woven phosphor2Represents L2The norm of the number of the first-order-of-arrival,represents the noise-to-signal ratio of the image a priori and can be expressed as sigma2/AξWhere σ represents the standard deviation of white Gaussian noise, AξRepresenting the average power spectrum of multiple natural images. μ (u) is a measurement of the original image u in the image space, and according to the 1/f rule of the natural image, the average power spectrum of a plurality of natural images can be expressed as:
u is an original image, xi is frequency, u (xi) is a representation form of u on a frequency spectrum, and a performance evaluation standard of the coding aperture is constructed:
wherein HξIn the form of a matrix of point spread functions corresponding to frequency ξ, for each frequency ξ,reflecting the degree to which noise is amplified, the optimal aperture has the smallest R (H), and genetic algorithms are designed and used to optimize to obtain a low resolution coded aperture, for an aperture with a resolution of L × L, the probability is as much as 2L×LIn one embodiment, the high resolution is used to optimize the selection process directly for such multiple possibilities. For this purpose, a search method using a genetic algorithm is used:
a.g is 0, g represents the iteration number of the genetic algorithm, and the initial iteration number is 0; the initial random binary sequences with length L × L of K ═ 4000 are generated, i.e. the set containing only 0,1, where L ═ 11.
B. An iterative process, which is a cyclic iterative process from G-1: G, wherein G-60
a. The optimal selection process in the genetic algorithm reforms each binary sequence b into an aperture matrix with a resolution of L × L. The evaluation is performed using equation (5), and the optimal Z-400 results are selected as the optimal solution set of the one-iteration results.
b. The following calculation process of this step is repeated until the number of sequence sets is restored from Z to K. And (3) crossing: randomly selecting and copying two subsequences from the optimal set Z in the step a, then ordering the two subsequences according to bit alignment, and then, selecting the two subsequences according to the probability p1The exchange of bit values was performed at 0.2 and two new subsequences were obtained. Mutation: for the two new sequences obtained in the previous step, the probability p is used2The value of each bit of each new sequence is flipped by 0.06.
C. And calculating the performance evaluation values of all the sequences which are reserved, and obtaining the optimal result of the genetic algorithm step. For the low-resolution coding aperture obtained by the genetic algorithm, the resolution of the coding aperture is improved by a gradient descent method to obtain a high-resolution coding aperture:
A. firstly, the coding aperture with low resolution is gradually increased to high resolution gradually by using a bicubic interpolation mode. Such as from 11 x 11 to 14 x 14 for the first time.
B. And optimizing the performance of the coded aperture by using a coordinate descent method, performing binary inversion on each element of the coded aperture matrix along the horizontal and vertical two-dimensional directions, and evaluating and calculating an aperture performance value of the newly generated coded aperture by using a performance evaluation standard. Only changing the element value of one coding aperture matrix each time until each element of the coding aperture matrix is traversed, and keeping the result of the optimal aperture performance value. And repeating the iteration process until the performance evaluation standard index of the coding aperture is converged and the aperture is not changed.
C. And repeating the steps A and B until the performance evaluation standard index of the coding aperture is converged with the improvement of the resolution, the coding aperture is not changed obviously any more, and the resolution of the coding aperture is finally improved from low resolution 11 multiplied by 11 and converged to high resolution 47 multiplied by 47. Thus, the final code aperture pattern is obtained.
The coded aperture was made from a stainless steel sheet according to the pattern and then placed at the near detector end of the camera lens.
2) The traditional four-hurdle board target is difficult to estimate a reliable point spread function from the target imaging of the collimator because of the lack of geometric characteristic information in all directions; therefore, a CAD (computer aided design) software is used for designing target patterns with remarkable geometric characteristics in all directions, and various types of targets are manufactured by using stainless steel sheets and are respectively placed in front of an image light source for subsequent image shooting.
3) Point spread function estimation by an improved non-blind method: for conventional blind estimation, a fuzzy kernel optimization model is constructed:
wherein | · | purple2Is L2Norm, f is the blurred image, s is the sampling function, u is the original image, h is the point spread function, x represents the convolution, and γ is the equilibrium parameter. The result of the blur kernel estimation based on pixel intensity values directly solved by the above equation is inaccurate, so h is estimated inside the gradient domain:
wherein q is2＝s*u，Represents a gradient operator, | · | | luminance2Is L2And (4) norm. The corresponding algorithm is as follows:
A. inputting: blurred image f
B. Let i equal 1 → 5
a. Solving forObtaining u, wherein P (u) is constrained, and lambda is a parameter;
b. solving the formula (6) to obtain a fuzzy kernel h;
c.λ←max{λ/1.1,1e-4}；
C. and (3) outputting: the blur kernel h and the potential original image u resulting from the intermediate process.
The negative values in the kernel are reset to 0 after the estimated kernel is obtained and h is normalized to have a sum of elements of 1. In the non-blind estimation of the point spread function proposed by the present invention, the convergence of light is through the focal plane front lens, assuming that the captured image i is planar, then this mapping can be simulated by a planar response w (i), considering the distortion phenomenon existing in a real camera, and defining d as a geometric distortion function, then this image imaging model can be expressed as follows:
b＝v(d(w(i)))*h+n (8)
b is a shot image, h is PSF of lens deviation, v is a halo phenomenon caused by a camera lens, n is Gaussian noise, and an original image u to be solved is generated through radiation model distortion so as to enable
u＝v(d(w(i))) (9)
Equation (8) may become:
b＝u*h+n(10)
using the optical information of the blur kernel as a priori, then the above problem can become the following optimization problem:
wherein | · | purple sweet2Is L2The norm of the number of the first-order-of-arrival,gradient factors, the first term being a data match term, λ, μ, γ being parameters, the second and third terms being a kernel sparse term and a kernel smooth term constrained by the parameters λ and μ, respectively.Is an ideal fuzzy kernelThe magnitude of the spectral density function of (a) ((b))F*(b) Is the conjugate of f (b), is the spectral density function constraint parameter of the PSF. An estimated value of the PSF is obtained by the optimization formula (12). For a blurred image and an original image with the same scale, the blurred image can be regarded as a result of convolution of the original image and a blur kernel, and the mathematical language under an ideal case (without considering noise) is expressed as follows:
f＝u*h (12)
wherein u is the original image, h is the blur kernel, i.e. the point spread function, and f is the observed blurred image. In order to ensure the accuracy of non-blind convolution kernel estimation, firstly, preprocessing is carried out on a blurred image and a Group Truth (GT) image, and the preprocessing comprises sample-by-sample mean subtraction and feature standardization, so that the stationarity of data is ensured. Secondly, the blurred image and the GT image are calibrated through rotation translation and scale scaling operations, and consistency of the images is guaranteed. And (3) in consideration of solving feasibility and algorithm complexity, converting the fuzzy kernel solving algorithm model to a frequency domain by utilizing Fourier transform, completing the conversion from space domain deconvolution operation to frequency domain point division operation, finally converting the result of the fuzzy kernel solving algorithm model obtained in the frequency domain to a time domain by Fourier inversion transform to obtain a final point spread function, and carrying out image reconstruction according to the point spread function.
4) The original image is estimated using energy function minimization to solve the maximum a posteriori problem. The image reconstruction solving model provided by the invention is as follows:
whereinTo solve the data item of the model, | ·| non-woven phosphor2Is L2Norm, J (u) is the smoothing term, η is the parameter,the expression is to find the minimum of the energy function. u h is expressed in matrix form:
u*h＝SHu＝Au (14)
where A is equal to SH, the smooth term of the solution model, i.e., the TV regular term (total variation term) J (u), is represented as:
||·||2is L2The norm of the number of the first-order-of-arrival,the gradient of u (x), which is solved by the Euler-Lagrangian equation, and the gradient Grad J (u) of J (u) is:
where div (·) denotes divergence. Since the gradient of the TV regularization term is directly applied at pixel xIt is not defined, and it is difficult to minimize directly with the TV regularization term, so the smooth TV regularization term, J, is used (u) instead of J (u), the formula is:
whereinIs replaced byRepresenting the variable value, div (·) representing the divergence, the gradient Grad J of the TV regularization term after substitution (u) becomes:
given a point spread function, adopt L2And (3) regularizing and constraining the norm to reconstruct an image, and solving according to a Richardon-Lucy (RL) method to obtain the following multiplication iterative formula:
where, represents a dot product between elements, t represents the number of iterations, f is a blurred image, ATThe transpose of A η is a parameter, Grad J (u) represents J (u) gradient. And obtaining a final original image u through iterative solution.
The invention provides an image reconstruction method based on a coding aperture and a target (as shown in the flow chart of figure 1). The following detailed description is made with reference to the accompanying drawings and examples:
1) the blurring process of an image is shown in fig. 2, and the mathematical model of the image blurring can be expressed as the following formula:
f＝h*u+n (1)
where f is the blurred image, u is the original image, h is the PSF (point spread function), n is white gaussian noise, and x represents the convolution. If H is expressed in matrix form H, the formula can be expressed as:
f＝SHu+n (2)
wherein S is a matrix form of a camera sampling function, namely a down-sampling matrix of the camera, the defocusing deblurring problem is to estimate an original image u by solving a maximum posterior probability problem, and the minimum value of an energy function E is used for solving the maximum posterior probability problem so as to realize the performance optimization of the coding aperture.
Wherein,expressing the minimum value of the energy function, | ·| non-woven phosphor2Is L2The norm of the number of the first-order-of-arrival,represents the noise-to-signal ratio of the image a priori and can be expressed as sigma2/AξWhere σ represents the standard deviation of white Gaussian noise, AξRepresenting the average power spectrum of multiple natural images. μ (u) is a measurement of the original image u in the image space, and according to the 1/f rule of the natural image, the average power spectrum of a plurality of natural images can be expressed as:
u is an original image, xi is frequency, u (xi) is a representation form of u on a frequency spectrum, and a performance evaluation standard of the coding aperture is constructed:
wherein HξIn the form of a matrix of point spread functions corresponding to frequency ξ, for each frequency ξ,reflecting the degree to which noise is amplified, the best aperture has the smallest R (H), and genetic algorithms are designed and used to optimize the resulting low resolution coded aperture for an aperture with a resolution of L × L, with a probability of up to 2L×LIn one embodiment, the high resolution is used to optimize the selection process directly for such multiple possibilities. The search method using the genetic algorithm:
c.g is 0, g represents the iteration number of the genetic algorithm, and the initial iteration number is 0; the initial random binary sequences with length L × L of K ═ 4000 are generated, i.e. the set containing only 0,1, where L ═ 11.
D. An iterative process, which is a cyclic iterative process from G-1: G, wherein G-60
c. The optimal selection process in the genetic algorithm reforms each binary sequence b into an aperture matrix with a resolution of L × L. The evaluation is performed using equation (5), and the optimal Z-400 results are selected as the optimal solution set of the one-iteration results.
d. The following calculation process of this step is repeated until the number of sequence sets is restored from Z to K. And (3) crossing: randomly selecting and copying two subsequences from the optimal set Z in the step a, then ordering the two subsequences according to bit alignment, and then, selecting the two subsequences according to the probability p1The exchange of bit values was performed at 0.2 and two new subsequences were obtained. Mutation: for the two new sequences obtained in the previous step, the probability p is used2The value of each bit of each new sequence is flipped by 0.06.
C. And calculating the performance evaluation standard values of all the sequences which are reserved, and obtaining the optimal result of the genetic algorithm step.
For the low-resolution coding aperture obtained by the genetic algorithm, the resolution of the coding aperture is improved by a gradient descent method to obtain a high-resolution coding aperture:
D. firstly, the coding aperture with low resolution is gradually increased to high resolution gradually by using a bicubic interpolation mode. Such as a first increase from 11 × 11 to 14 × 14
E. And optimizing the performance of the coded aperture by using a coordinate descent method, performing binary inversion on each element of the coded aperture matrix along the horizontal and vertical two-dimensional directions, and evaluating and calculating an aperture performance value of the newly generated coded aperture by using a performance evaluation standard formula. Only changing the element value of one coding aperture matrix each time until each element of the coding aperture matrix is traversed, and keeping the result of the optimal aperture performance value. And repeating the iteration process until the performance evaluation standard index of the coding aperture is converged and the aperture is not changed.
F. And repeating the steps A and B until the performance evaluation standard index of the coding aperture is converged with the improvement of the resolution, the coding aperture is not changed obviously any more, and the resolution of the coding aperture is finally improved from low resolution 11 multiplied by 11 and converged to high resolution 47 multiplied by 47. Thus, the final code aperture pattern is obtained.
The coded aperture of fig. 3 was patterned with a stainless steel sheet and then placed at the near detector end of the camera lens.
2) The conventional four-hurdle plate target (fig. 4a) has difficulty in estimating a reliable point spread function from the target imaging of the collimator due to the lack of geometric feature information in various directions; therefore, the method designs targets with remarkable geometric characteristics in all directions by using CAD (computer aided design) software, manufactures the targets with various styles by using a stainless steel sheet, and places the targets in front of an image light source for subsequent image shooting, wherein the designed patterns are shown in figures 4 b-h. In order to obtain as large a shot pattern as possible, the target patterns we designed this time are as close to the target edge as possible. These targets will be imaged and then point spread function estimation will be performed on the obtained.
3) Point spread function estimation by an improved non-blind method: for the traditional blind estimation method, a fuzzy kernel optimization model is constructed:
wherein | · | purple2Is L2Norm, f is the blurred image, s is the sampling function of the camera, u is the original image, h is the point spread function, x represents the convolution, and γ is the equilibrium parameter. The result of the blur kernel estimation based on pixel intensity values directly solved by the above equation is inaccurate, so h is estimated inside the gradient domain:
wherein q is2＝s*u，Represents a gradient operator, | · | | luminance2Is L2And (4) norm. The corresponding algorithm is as follows:
A. inputting: a blurred image f;
B. let i equal 1 → 5
a. Solving forObtaining u, wherein P (u) is constrained, and lambda is a parameter;
b. solving equation (14) to obtain fuzzy kernel h
c.λ←max{λ/1.1,1e-4}
C. And (3) outputting: the blur kernel h and the potential raw sharp image u resulting from the intermediate process.
The negative values in the kernel are reset to 0 after the estimated kernel is obtained and h is normalized to have a sum of elements of 1. In the non-blind estimation of the point spread function proposed by the invention, the convergence of light is through the focal plane front lens, the image i taken is assumed to be planar, then, the mapping can be simulated by a planar response w (i), and considering the distortion phenomenon existing in a real camera, d is defined as a geometric distortion function, then the image imaging model can be expressed as follows:
b＝v(d(w(i)))*h+n (8)
b is a shot image, h is a PSF of lens deviation, v is a halo phenomenon caused by a camera lens, and n is gaussian noise. U, i.e. the original image to be solved, is generated by radiation model warping
u＝v(d(w(i))) (9)
Equation (8) may become:
b＝u*h+n (10)
using the optical information of the blur kernel as a priori, then the above problem can become the following optimization problem:
wherein | · | purple sweet2Is L2The norm of the number of the first-order-of-arrival,gradient factors, the first term being a data match term, λ, μ, γ being parameters, the second and third terms being a kernel sparse term and a kernel smooth term constrained by the parameters λ and μ, respectively.Is an ideal fuzzy kernelThe magnitude of the spectral density function of (a) ((b))F*(b) Is the conjugate of f (b), is the spectral density function constraint parameter of the PSF. An estimated value of the PSF is obtained by the optimization formula (12). For a blurred image and a sharp image with the same scale, the blurred image can be regarded as a result of convolution of an original image and a blur kernel, and the mathematical language under an ideal condition (without considering noise) is expressed as follows:
f＝u*h (12)
wherein u is the original image, h is the blur kernel, and f is the observed blur image. As shown in fig. 5, to ensure the accuracy of the non-blind convolution kernel estimation, the blurred image and the GT image in the project are first preprocessed, including sample-by-sample mean reduction and feature normalization, to ensure the stationarity of the data. Secondly, the blurred image and the GT image are calibrated through rotation translation and scale scaling operations, and consistency of the images is guaranteed. And (3) in consideration of solving feasibility and algorithm complexity, converting the fuzzy kernel solving algorithm model to a frequency domain by utilizing Fourier transform, completing the conversion from space domain deconvolution operation to frequency domain point division operation, finally converting the result of the fuzzy kernel solving algorithm model obtained in the frequency domain to a time domain by Fourier inversion transform to obtain a final point spread function, and carrying out image reconstruction according to the point spread function.
4) The original image is estimated using energy function minimization to solve the maximum a posteriori problem. The image reconstruction solving model provided by the invention is as follows:
whereinTo solve the data item of the model, | ·| non-woven phosphor2Is L2Norm, J (u) is the smoothing term, η is the parameter,the expression is to find the minimum of the energy function. u h is expressed in matrix form:
u*h＝SHu＝Au (14)
where A is equal to SH, the smooth term of the solution model, i.e., the TV regular term (total variation term) J (u), is represented as:
||·||2is L2The norm of the number of the first-order-of-arrival,the gradient of u (x), which is solved by the Euler-Lagrangian equation, and the gradient Grad J (u) of J (u) is:
where div (·) denotes divergence. Since the gradient of the TV regularization term is directly applied at pixel xIt is not defined, and it is difficult to minimize directly with the TV regularization term, so the smooth TV regularization term, J, is used (u) instead of J (u), the formula is:
whereinIs replaced byRepresenting the variable value, div (·) representing the divergence, the gradient Grad J of the TV regularization term after substitution (u) becomes:
given a point spread function, adopt L2And (3) regularizing and constraining the norm to reconstruct an image, and solving according to a Richardon-Lucy (RL) method to obtain the following multiplication iterative formula:
where, represents a dot product between elements, t represents the number of iterations, f is a blurred image, ATThe transpose of A η is a parameter, Grad J (u) represents J (u) gradient. And obtaining a final original image u through iterative solution.
In an actual scene, a camera with a coding aperture is used for shooting different target patterns to obtain a blurred image, and image reconstruction results are compared. In the experimental result of fig. 6, it can be seen that the non-blind estimation of the point spread function provided by the present invention can effectively eliminate the interference of noise, and obtain a clearer image reconstruction result. In the image reconstruction result based on the non-blind estimation of the point spread function, the reconstruction result can be seen to basically recover the geometric characteristics of a clear target image, and the edges are relatively sharp.
Claims (2)
1. An image reconstruction method based on coding aperture and target design is characterized by comprising the following steps: designing coded light and placing the coded light at the tail end of a camera lens close to a detector; designing a target and placing the target at the front end of an optical cylinder of an image light source; solving an algorithm model through a fuzzy kernel to obtain a point spread function of the image; by using L2And the norm is used as an image regularization constraint, and the fuzzy image is reconstructed and restored according to the point spread function solved in the foregoing.
2. The image reconstruction method based on coded aperture and target design of claim 1, wherein the coded aperture is designed and placed near the end of the camera lens near the detector; designing a target and placing the target at the front end of an optical cylinder of an image light source, and specifically comprising the following steps:
1) the mathematical model of image blur is expressed as the following formula:
f＝h*u+n (1)
wherein f is a blurred image, u is an original image, H is a point spread function PSF, n is white gaussian noise, x represents convolution, and if H is expressed in a matrix form H, the formula is expressed as:
f＝SHu+n (2)
wherein, S is the matrix form of the camera sampling function, namely the down-sampling matrix of the camera, the defocusing deblurring problem is to estimate the original image u by solving a maximum posterior probability problem, and the minimum value of the energy function E is used to solve the maximum posterior probability problem to realize the performance optimization of the coding aperture:
<mrow> <mtable> <mtr> <mtd> <mrow> <mi>u</mi> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <mi>u</mi> </munder> <mi>E</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>|</mo> <mi>f</mi> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <mi>u</mi> </munder> <mo>|</mo> <mo>|</mo> <mi>u</mi> <mo>*</mo> <mi>h</mi> <mo>-</mo> <mi>f</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>C</mi> <mo>&CenterDot;</mo> <mi>u</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
wherein,expressing the minimum value of the energy function, | ·| non-woven phosphor2Represents L2The norm of the number of the first-order-of-arrival,representing the noise-to-signal ratio of the image a priori, denoted as σ2/AξWhere σ represents the standard deviation of white Gaussian noise, AξThe average power spectrum of a plurality of natural images is represented, mu (u) is a measurement of an original image u in an image space, and the average power spectrum expression of the plurality of natural images is as follows according to the 1/f rule of the natural images:
<mrow> <msub> <mi>A</mi> <mi>&xi;</mi> </msub> <mo>=</mo> <munder> <mo>&Integral;</mo> <mi>u</mi> </munder> <mo>|</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>&xi;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
u is an original image, xi is frequency, u (xi) is a representation form of u on a frequency spectrum, and a performance evaluation standard of the coding aperture is constructed:
<mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>H</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mi>&xi;</mi> </munder> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mi>&xi;</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mo>/</mo> <msub> <mi>A</mi> <mi>&xi;</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
wherein HξIn the form of a matrix of point spread functions corresponding to frequency ξ, for each frequency ξ,the amplified degree of noise is reflected, and the optimal aperture has the minimum R (H), which also means that the image reconstruction recovery result is more accurate; optimizing to obtain a low-resolution coding aperture by using a genetic algorithm, improving the resolution of the coding aperture by using a gradient descent method, and then placing the designed coding aperture at the tail end of a near detector of a camera lens;
2) the method comprises the steps of designing targets with remarkable geometric characteristics in all directions, respectively placing the targets at the front ends of light cylinders of image light sources for shooting images of different subsequent patterns, and shooting the images by using a coding aperture and the targets, so that the different patterns retain more frequency spectrum information of the images.
Solving an algorithm model through a fuzzy kernel to obtain a point spread function of the image; by using L2Norm as positive of imageAnd then, transforming constraint, and reconstructing and restoring the fuzzy image according to the point spread function solved in the previous step, wherein the method specifically comprises the following steps: the method comprises the following steps of shooting a light source image of a preset design target by using a lens provided with a coding aperture, wherein the shot image i is planar, simulating the mapping by using a planar response w (i), defining d as a geometric distortion function in consideration of distortion existing in a real camera, and constructing an image imaging model to represent the following form:
b＝v(d(w(i)))*h+n (6)
b is the shot image, h is the PSF of the lens deviation, v is the halo phenomenon caused by the camera lens, the original image u to be solved is generated through the distortion of the radiation model, and the
u＝v(d(w(i))) (7)
Equation (6) can be converted to:
b＝u*h+n (8)
using the optical information of the blur kernel as a priori, then the above problem becomes the following optimization problem:
<mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mi>h</mi> </munder> <mi>E</mi> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>h</mi> <mo>-</mo> <mover> <mi>b</mi> <mo>^</mo> </mover> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&lambda;</mi> <mo>|</mo> <mo>|</mo> <mi>h</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&mu;</mi> <mo>|</mo> <mo>|</mo> <mo>&dtri;</mo> <mi>h</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&gamma;</mi> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>-</mo> <mo>|</mo> <mi>F</mi> <mo>(</mo> <mover> <mi>h</mi> <mo>^</mo> </mover> <mo>)</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mi>h</mi> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
wherein | · | purple sweet2Is L2The norm of the number of the first-order-of-arrival,gradient operators, the first term being a data match term, λ, μ, γ being parameters, the second and third terms being a kernel sparse term and a kernel smooth term constrained by the parameters λ and μ, respectively,is an ideal fuzzy kernelIs a spectral density function constraint parameter of the PSF,f x (b) is the conjugate of F (b), an estimated value of the PSF is obtained through an optimization formula (10), and image reconstruction is carried out according to the point spread function.
The original image is estimated by solving the maximum a posteriori problem using energy function minimization, and the image reconstruction solution model is as follows:
<mrow> <munder> <mi>argmin</mi> <mi>u</mi> </munder> <mo>|</mo> <mo>|</mo> <mi>u</mi> <mo>*</mo> <mi>h</mi> <mo>-</mo> <mi>f</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&eta;</mi> <mi>J</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
whereinTo solve the data item of the model, | ·| non-woven phosphor2Is L2Norm, J (u) is the smoothing term, η is the parameter,the expression is to find the minimum of the energy function. u h is expressed in matrix form:
u*h＝SHu＝Au (11)
wherein A is equal to SH, and a smooth term of a solution model, namely a TV regular term, namely a total variation term J (u), is represented as:
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <mo>|</mo> <mo>|</mo> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mi>d</mi> <mi>x</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
||·||2is L2The norm of the number of the first-order-of-arrival,the gradient of u (x) is expressed as the gradient Grad J (u) of J (u) solved by the Euler-Lagrangian equation:
<mrow> <mi>G</mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi> </mi> <mi>J</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
where div (. circle.) denotes divergence, using a smoothed TV regularization term, J (u) instead of J (u), the formula is:
<mrow> <msub> <mi>J</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <msqrt> <mrow> <msup> <mi>&epsiv;</mi> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </msqrt> <mi>d</mi> <mi>x</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
whereinIs replaced byRepresenting the variable value, div (·) representing the divergence, the gradient Grad J of the TV regularization term after substitution (u) becomes:
<mrow> <mi>G</mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi> </mi> <msub> <mi>J</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>v</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <msup> <mi>&epsiv;</mi> <mn>2</mn> </msup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mo>&dtri;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
given a point spread function, adopt L2And carrying out regularization constraint on the norm to reconstruct the image, and solving according to a Richardon-Lucy method to obtain the following multiplication iterative formula:
<mrow> <msup> <mi>u</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>u</mi> <mi>t</mi> </msup> <mo>&CenterDot;</mo> <msup> <mi>A</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mfrac> <mi>f</mi> <mrow> <msup> <mi>Au</mi> <mi>t</mi> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mfrac> <msup> <mi>u</mi> <mi>t</mi> </msup> <mrow> <mn>1</mn> <mo>-</mo> <mi>&eta;</mi> <mi>G</mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi> </mi> <msub> <mi>J</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
where, represents a dot product between elements, t represents the number of iterations, f is a blurred image, ATThe transpose of A η is a parameter, Grad J (u) represents J And (u) obtaining a final original image u by iterative solution.
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