Image restoration method for fitting a PSF

Abstract

The present application relates to a kind of image restoration methods of fitting PSF, including S1, extract actual image LSF, actual image LSF is converted into the linear combination of Gaussian second derivative;S2, according to the linear combination of Gaussian second derivative, actual line spread function is fitted and corrected;S3, using actual line spread function after fitting and correction, generate restoration image.The method of the present application extracts actual image line spread function, and it is modeled into the form of linear combination of a series of Gaussian second derivative;Then, based on the Gaussian second derivative model established, the LSF extracted from blurred image is fitted and corrected;Finally, blurred image is restored using PSF after fitting and correction, and finally clear image is obtained.Compared with the prior art image restoration method, the method of the present application can produce clearer restoration image when facing high blur degree original image.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of image restoration, and particularly relates to a PSF fitting image restoration method. BACKGROUND

[0002] In many special application fields, such as remote sensing image restoration, public security, biomedical imaging and the like, image restoration technology plays an important role. The purpose of image restoration is to restore a clear image from a blurred observation. Generally, a blurred image is caused by camera motion or lens defocus and the like. The ubiquitous image degradation often leads to difficulties in object recognition and scene interpretation, and therefore, a clear image needs to be restored. In order to obtain a clear image, it is necessary to analyze a point spread function (PSF) of the image. The PSF is also referred to as a blur kernel of the image, which plays an important role in describing overall imaging performance and evaluating imaging quality. High-precision on-orbit point spread function estimation can convert the blurred image restoration into a non-blind restoration problem. However, with the rapid development of information and communication technology, the causes of image blurring are becoming more and more diversified. The current PSF analysis method is mostly established on the basis of an ideal situation, and can only analyze a symmetric and regular point spread function curve, and cannot be applied to actual scenes. Therefore, the research on image restoration technology based on PSF analysis needs to be developed.

[0003] In recent years, image restoration based on imaging system characteristics and image characteristics to estimate the point spread function is a research hotspot in the field of image deblurring. Li et al. analyzed the PSF of a fluorescent three-dimensional microscopic image based on an improved Gibson-Lanni parameter model, and performed blind convolution restoration, thereby improving the accuracy of blurred image restoration. Liu et al. theoretically analyzed the PSF, modeled the PSF as a generalized Gaussian function, and simplified it into a single parameter model, thereby performing image restoration. Lee's team used a linear combination of Gaussian functions to approximate the PSF, thereby improving the speed and accuracy of image restoration. However, the above methods mostly only consider the influence of defocus, and are not suitable for high blurring degree situations. At the same time, the blur kernel modeling model is uniformly smooth, and the research on the blur model of the "non-smooth" phenomenon caused by multiple factors lacks in-depth research.

[0004] Therefore, there is an urgent need for an image restoration method which can obtain a clearer restored image when restoring a high blurring degree image. SUMMARY

[0005] Based on the above-mentioned shortcomings and deficiencies in the prior art, one of the purposes of the present application is to at least solve the above-mentioned problems in the prior art, in other words, one of the purposes of the present application is to provide a PSF fitting image restoration method which meets the aforementioned needs.

[0006] To achieve the above object, the present application adopts the following technical solutions:

[0007] An image restoration method for fitting PSF, comprising:

[0008] S1, extracting an actual image LSF, and converting the actual image LSF into a linear combination of Gaussian second derivatives;

[0009] S2, fitting and correcting the actual line spread function according to the linear combination of Gaussian second derivatives;

[0010] S3, generating a restored image using the fitted and corrected actual line spread function.

[0011] As a preferred solution, the extraction in step S1 uses an edge method.

[0012] As a preferred solution, step S1 comprises the following steps:

[0013] S11, extracting an average edge spread function of the actual image, and differentiating the average edge spread function to obtain an actual image LSF;

[0014] S12, modeling the actual image LSF as a linear combination of a series of Gaussian second derivatives.

[0015] As a further preferred solution, step S2 comprises the following steps:

[0016] S21, constructing a nulling filter, which is used to annihilate an asymmetric pulse sequence in the linear combination of Gaussian second derivatives;

[0017] S22, calculating a position parameter used for annihilation in step S21;

[0018] S23, calculating an amplitude parameter used for annihilation in step S21;

[0019] S24, fitting and correcting the actual line spread function using the position parameter and the amplitude parameter.

[0020] As a preferred solution, step S3 comprises the following steps:

[0021] S31, generating an image point spread function according to the fitted and corrected actual line spread function;

[0022] S32, iteratively generating a restored image according to the image point spread function.

[0023] As a further preferred solution, the iterative generation in step S32 uses a Richardson-Lucy algorithm.

[0024] As a further preferred solution, step S31 generates the actual line spread function as a one-dimensional line spread function of the image point spread function along the track and perpendicular direction.

[0025] Compared with the prior art, the present application has the following beneficial effects:

[0026] The method of the present application extracts the actual image line spread function (LSF) by using the knife-edge method, and models it into a form of linear combination of a series of Gaussian second derivatives (GSD); then, based on the established Gaussian second derivative model, the LSF extracted from the blurred image is fitted and corrected by using an improved null filter algorithm; finally, the blurred image is restored by using the fitted and corrected PSF, and a clear image is finally obtained. Compared with the image restoration method of the prior art, the method of the present application can produce a clearer restored image when facing a high blur degree original image. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 Fig. 1 shows a flow chart of an image restoration method of fitting PSF according to the present application;

[0028] Figure 2 Fig. 2 shows a schematic diagram of the actual image LSF extracted by step S1 of the embodiment of the present application;

[0029] Figure 3 Fig. 3 shows a schematic diagram of the corrected actual line spread function curve of step S2 of the embodiment of the present application. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0031] In the following description, a plurality of embodiments of the present application are provided, and different embodiments can be replaced or combined, so that the present application can be considered to include all possible combinations of the same and / or different embodiments described. Therefore, if one embodiment includes features A, B and C, and another embodiment includes features B and D, the present application should also be considered to include one or more embodiments of all other possible combinations of A, B, C and D, although the embodiment may not be explicitly described in the following content.

[0032] The following description provides examples, and is not intended to limit the scope, applicability or examples set forth in the claims. Alterations and changes in the function and arrangements of elements could be made without deviating from the scope of the application. Various examples could omit, substitute, or add various procedures or components as appropriate. For instance, the methods described could be performed in a different order than described, and various steps could be added, omitted, or combined. Also, features described with respect to some examples could be combined in other examples.

[0033] The present application provides a PSF fitting image restoration method, whose flow chart is shown as Figure 1 The present application provides a PSF fitting image restoration method, whose flow chart is shown as

[0034] S1, extracting an actual image LSF, and converting the actual image LSF into a linear combination of Gaussian second derivatives;

[0035] S2, fitting and correcting the actual line spread function according to the linear combination of Gaussian second derivatives;

[0036] S3, generating a restored image using the fitted and corrected actual line spread function.

[0037] One embodiment of the present application provides a specific implementation of the above step S1. In this embodiment, the extraction of step S1 is performed using the knife-edge method. Specifically, step S1 includes the following steps:

[0038] S11, extracting an average edge spread function of the actual image. The average edge spread function (ESF) of the image is obtained by least square fitting, averaging, etc., and is differentiated to obtain the actual image LSF. The actual image LSF extracted using the above method is shown as Figure 2

[0039] S12, modeling the actual image LSF as a linear combination of a series of Gaussian second derivatives:

[0040]

[0041] wherein the constant represents the one-dimensional length of the image; the variable t∈[0,T) represents the position variable; the constant represents the number of combined pulses, and the variable k=1,2,,K represents the serial number of the pulse; the unknown parameter t k represents the position of the kth pulse, arranged in ascending order, i.e., 0≤t1<t2<<t k <T. The Gaussian and its second derivative h k (t-t k ) are defined as follows: ​

[0042]

[0043] where unknown parameters are the amplitudes of the Gaussian components; unknown parameters are the amplitudes of the Gaussian second derivative components; h(t) is the Gaussian function, is its second derivative, which is as follows:

[0044]

[0045]

[0046] Accordingly, the LSF is expressed as:

[0047]

[0048] After modeling, the basis function and the spectral information of the modeled signal are obtained according to the linear combination of the series of Gaussian second derivatives. Let be the basis signal. The Fourier transform is performed on the signal x(t) and the basis signal h(t) respectively, and the results are as follows:

[0049]

[0050]

[0051] Let H(ω)≠0, and define:

[0052]

[0053] Discretize it: let m∈K represents the serial number of the signal frequency. Substitute it into equation (8) to obtain the discrete spectrum:

[0054]

[0055] One embodiment of the present application also provides a specific implementation of step S2, including the following steps:

[0056] S21, construct a zeroing filter, which is used to annihilate the asymmetric pulse sequence in the linear combination of the Gaussian second derivatives.

[0057] First, 2K+1 continuous samples p[n] are obtained from the FRI sampling structure. A zeroing filter is constructed:

[0058]

[0059] where represents the zero point of the zeroing filter, and the coefficient A[m] is obtained by convolving Y[m] (m=0, 1, 2K) with A[m].

[0060]

[0061] Thus, the annihilating filter The annihilating signal Y[m], i.e., A[m]*Y[m] = 0.

[0062] S22, solving equation (11), the position parameter Equation (11) can be written in the form of matrix-vector:

[0063]

[0064] According to the prior information A[0] = 1, the linear equation group (12) can be simplified as follows:

[0065] Yx = b (13)

[0066] Where,

[0067]

[0068] x = [A[1], A[2],..., A[2K]] T (15)

[0069] b = [-Y[0], -Y[1],..., -Y[2K-1], -Y[2K]] T (16)

[0070] The matrix Y is a Hankel matrix. According to its properties, when the measured value Y[m] is non-zero, Y is invertible, and at this time, equation (13) has a unique solution as:

[0071] x = Y -1 b (17)

[0072] In a noisy environment, the least square solution is generally used:

[0073] x = (Y T Y) -1 Y T b (18)

[0074] After obtaining the coefficients A[m] of the annihilating filter, the unknown parameter can be obtained simply by solving

[0075] Because so the position parameter

[0076]

[0077] ​S23, solving the amplitude parameter According to formula (9), a linear equation group is constructed as follows:

[0078] y = Br (20)

[0079] wherein,

[0080] y = [Y[1] Y[2]... Y[M]] T (21)

[0081] r = [c1 c2... c K d1 d2... d K ] T (22)

[0082]

[0083] Finally, the value of the amplitude parameter is obtained by solving the equation group (20) by the least square method:

[0084]

[0085]

[0086] S24, fitting and correcting the actual line spread function using the position parameter and the amplitude parameter. The parameter set is substituted into formula (1), and the fitting and corrected actual line spread function curve is obtained, as shown in Figure 3 :

[0087]

[0088] One embodiment of the present application also provides a specific implementation of step S3, including the following steps:

[0089] S31, generating an image point spread function (PSF) according to the fitting and corrected actual line spread function. The image in the present application is obtained by a push-broom TDI-CCD camera. For this kind of camera, the asymmetry between the longitudinal and vertical directions can be ignored, and therefore, the two-dimensional PSF can be decomposed into one-dimensional LSFs along the track and vertical directions, i.e.:

[0090] PSF(i,j) = LSF(i) x LSF(j) (27)

[0091] wherein, LSF(i) = LSF(j) is the fitting and corrected LSF obtained in step two.

[0092] S32, generating a restored image according to the image point spread function iteratively. Based on the LSF curve corrected by fitting in step 3.1, the blurred image is restored by using Richardson-Lucy (R-L) algorithm. The R-L algorithm is as follows:

[0093]

[0094] wherein the constant n represents the number of iterations, (i,j) is the image pixel point, f n+1 (i,j) and f n (i,j) are the restored image outputs after the n+1th and nth iterations respectively, h(i,j) is the system estimated PSF, h T (i,j) is the transpose of the PSF, the symbol * represents convolution operation, and g(i,j) is the blurred image. After the above step S32, the parameters are substituted into formula (28), and the restored image is obtained.

[0095] The method of the above embodiment firstly extracts the actual image line spread function (LSF) by using the knife-edge method, and models it into a linear combination of a series of Gaussian second derivatives (GSD); then, based on the established Gaussian second derivative model, the LSF extracted from the blurred image is corrected by fitting using the improved zero filter algorithm; finally, the blurred image is restored by using the corrected PSF, and a clear image is finally obtained. The method can restore a clear image from a blurred image. The simulation results show that the method of the above embodiment has good performance in terms of evaluation indexes such as RMSE, GMG, R-square, SSIM, etc.

[0096] The above-described embodiments are merely exemplary embodiments of the present disclosure, and cannot limit the scope of the present disclosure. That is, any equivalent changes and modifications made in accordance with the teachings of the present disclosure are still within the scope of the present disclosure. Other embodiments of the present disclosure will be readily apparent to those skilled in the art upon considering the specification and practicing the present disclosure herein. The present application is intended to cover any variations, uses, or adaptive changes to the present disclosure that follow the general principles of the present disclosure and include common knowledge or conventional technical means in the technical field not described in the present disclosure. The specification and examples are only considered as exemplary, and the scope and spirit of the present disclosure are defined by the claims.

Claims

1. An image restoration method for fitting a PSF, characterized in that, include: S1. Extract the actual image LSF and convert the actual image LSF into a linear combination of Gaussian second derivatives; S2. Fit and correct the actual line spread function based on the linear combination of the second derivatives of Gauss. S3. Generate the restored image using the fitted and corrected actual line spread function; The extraction in step S1 uses the edge-cutting method. Specifically, step S1 includes the following steps: S11. Extract the average edge spread function of the actual image, and differentiate the average edge spread function to obtain the actual image LSF; S12. The actual image LSF is modeled as a linear combination of a series of Gaussian second derivatives; Step S2 includes the following steps: S21. Construct a nullification filter, which is used to annihilate the asymmetric pulse sequence in the linear combination of the Gaussian second derivative; S22. Calculate the position parameters used for annihilation in step S21; S23. Calculate the amplitude parameters used for annihilation in step S21; S24. Use the position parameter and the amplitude parameter to fit and correct the actual line spread function; Step S3 includes the following steps: S31. Generate an image point spread function based on the fitted and corrected actual line spread function; S32. Generate the restored image iteratively based on the image point spread function.

2. The image restoration method for fitting PSF as described in claim 1, characterized in that, The iterative generation in step S32 uses the Richardson-Lucy algorithm.

3. The image restoration method for fitting PSF as described in claim 1, characterized in that, Step S31 generates the actual line spread function as a one-dimensional line spread function along the orbital and vertical directions of the image point spread function.

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