CN112927317A - Optical coherence tomography fast space self-adaptive deconvolution method - Google Patents

Optical coherence tomography fast space self-adaptive deconvolution method Download PDF

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CN112927317A
CN112927317A CN202110181508.6A CN202110181508A CN112927317A CN 112927317 A CN112927317 A CN 112927317A CN 202110181508 A CN202110181508 A CN 202110181508A CN 112927317 A CN112927317 A CN 112927317A
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CN112927317B (en
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任尚杰
杜艺娜
董峰
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Tianjin University
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Abstract

The invention provides a fast space self-adaptive deconvolution method for optical coherence tomography, which comprises the following steps: constructing a mathematical model for deconvolution of the OCT image, and discretizing the mathematical model to obtain the linear model; step two: constructing a least square form of a deconvolution optimization problem; obtaining initial estimation of imaging depth and a clear image by a Richardson-Lucy algorithm, and setting a maximum iteration time Tmax and an image residual error threshold tau; setting the estimated values of the imaging depth and the clear image as wt and It respectively in the iteration of the t step, and obtaining a solution for accelerating iterative optimization according to a Gauss-Newton iterative solution of the objective function; and (5) iterating the calculation until convergence.

Description

Optical coherence tomography fast space self-adaptive deconvolution method
Technical Field
The invention belongs to the technical field of optical coherence tomography, and relates to a method for estimating a point spread function of an imaging system and enhancing the resolution of an optical coherence tomography image by using a deconvolution method.
Background
Optical Coherence Tomography (OCT) is a new generation of biomedical imaging technology, which uses a michelson interferometer to detect an interference signal after interference between backscattered light in a biological tissue and reflected light from a reference arm, and then calculates a microscopic two-dimensional or three-dimensional structural image of the biological tissue from an interference pattern of the scattered light and the reference light. The imaging depth of the OCT can reach mm level, and the imaging resolution can reach mum level. Compared with the traditional medical imaging technologies which are commonly used clinically, such as X-ray computed tomography (X-CT), Magnetic Resonance Imaging (MRI), Ultrasonic Imaging (UI) and the like, the OCT imaging uses light waves as an energy source for imaging, and has the advantages of non-invasion, non-contact, no damage, high spatial resolution, low cost and the like. The OCT imaging has many advantages, so the development is rapid, the application field is wide, and the application prospect is wide. In addition to the medical field, the method is also applied to the fields of shape detection of precision mechanical devices, quality detection of semiconductor devices, material surface damage detection, crack detection of substances such as porcelain stones and the like, plant leaf and seed form, micro-organism internal structure imaging of micron order and the like.
Spatial resolution enhancement of OCT images is one of the hot spots in OCT research. The enhancement method of the OCT image can be classified into a hardware-based method and a digital-based method. Among the mathematical-based image enhancement methods, the deconvolution method is most commonly used. Deconvolution is a method to reduce ambiguity, and commonly used deconvolution methods are wiener filtering, Richardson-Lucy iterative deconvolution, and least squares deconvolution. Wiener et al, also known as minimum mean square error filtering, published by massachusetts institute of technology (MIT Press) in 1964 in a book entitled "Extrapolation, interpolation, and smoothing and engineering applications of stationary time series" (Extrapolation, interpolation, and smoothing of stationary time series with engineering applications). The goal is to find an estimate of the non-contaminated image, minimize the mean square error between them, and sharpen the blurred image while removing noise. The Richardson-Lucy iterative deconvolution reconstruction algorithm is an iterative algorithm used for image restoration under the Poisson noise background and is based on the maximum likelihood solution of Poisson statistical data. It aims to maximize the likelihood of restoring an image by using an expectation maximization algorithm (EM). The algorithm requires a good estimate of the process of image degradation to achieve accurate recovery. Fish et al succeeded in blindly deconvolving OCT images using Richardson-Lucy algorithm, first applied to OCT imaging, in Journal of The American Society of Optics-Optical Image Science and Vision, Vol.12, pages 58-65, published by Journal of The Optical Society of America A-Optics, Science and Vision, and Blind deconvolution with Richardson-Lucy algorithm, by Richardson-Lucy algorithm, et al, 1995. Ralston et al, 2005, IEEE Transactions on Image Processing 14, 1254, 1264, published under the heading Deconvolution method for eliminating lateral blur in optical coherence tomography (Deconvolution method for estimation of transverse blur in optical coherence tomography) proposes a regularized inverse Deconvolution algorithm using a Gaussian beam Deconvolution algorithm that reduces the lateral blur of OCT images and increases the lateral resolution of OCT images.
Methods for deblurring an image can be further classified into non-blind deconvolution and blind deconvolution, depending on whether the Point Spread Function (PSF) is known or not. In 1978, Trussell and Hunt, an article entitled "method for restoring blocks of spatially blurred images" (Image restoration of space-variant blurry by section methods), published by IEEE Transactions on Acoustics Speech & Signal Processing, volume 26, page 608 and 609, first proposed a method for restoring blocks of images using wiener filtering algorithm, which is an important method for performing spatially varying PSF non-blind deconvolution. The method mainly comprises the steps of dividing an image into subblocks, considering that PSF of each subblock image is space-invariant, deconvoluting each subblock by using a wiener filtering algorithm, and finally splicing the restored subblock blocks together to reconstruct the whole clear image. Liu et al 2011, in the article entitled "Automatic estimation of deconvolution defocused optical coherence tomography image point spread function based on information entropy" (Automatic estimation of point-spread-function for deconvolution defocused optical coherence tomography image point spread function), published in pages 18135-18148, propose an information entropy-based PSF Automatic estimation method to deconvolve the defocused area of an OCT image. They performed non-blind deconvolution operations on out-of-focus images using a set of gaussian PSFs of different spot sizes using an richardson-lucy iterative deconvolution algorithm. Podolean et al, 2013, in Applied Optics 52, 5663-5670, published under the article entitled "optical coherence tomography Image quality improvement based on Richardson-outi deconvolution algorithm" (Image quality improvement in optical coherence tomography using Lucy-Richardson deconvolution algorithm), used a solid phantom to evaluate the average PSF of the imaging system and an iterative Richardson-outi iterative deconvolution algorithm to improve the Image quality. Mohammadreza et al, 2017, in the Society of Optical instruments Engineers (Conference Series), an article entitled "Optical coherence tomography spatial variant deconvolution method based on total variation" (A spatial-variant deconvolution method based on total variation) published by Society of Optical Instrumentation Engineers (SPIE): Conference Series), propose a new OCT image spatial deconvolution method based on total variation. They use solid mimetics to estimate the point spread function of each subregion of the imaging system and then use the iterative deconvolution method of Richardson-Lucy, Hybr and gross variation to mitigate the blurring of spatial variation.
In addition, Wang et al, 2018, in the 40th International Annual institute of IEEE Medicine and biological Engineering (40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society), pages 1-4, an article entitled Super-Resolution in Optical Coherence Tomography (Super-Resolution in Optical Coherence Tomography), proposes a solution based on inverse problem solving, namely a deconvolution method and a cost function for Super-Resolution, wherein the deconvolution method can be implemented by solving a least squares method. They then minimize them using an alternate direction multiplier (ADMM) and a back-and-forth splitting (FBS) algorithm. In addition, the standard L1 regularization with soft threshold was also compared to TV regularization in the ADMM scheme.
However, there still exist many problems in the OCT image reconstruction of biological tissues at home and abroad at present: (1) OCT systems require a compromise between imaging depth and imaging resolution, limited by the physical properties of the excitation source itself. On the premise of ensuring higher imaging resolution, the imaging depth of OCT is usually less than 4mm and is influenced by sample tissues; (2) the PSF of a cross-sectional image obtained by an OCT system at an arbitrary depth is generally unknown, and the size thereof is affected by factors such as the imaging depth and the imaging position. The existing image reconstruction algorithm uses PSF with unchanged space, so that the accuracy of the reconstructed image is lower; (3) if the OCT image is large, the amount of calculation of the image deconvolution operation is large, the time consumption is long, and the requirement on the configuration performance of the computing device is high.
Disclosure of Invention
The invention aims to provide a quick space self-adaptive deconvolution method which can improve the resolution of a reconstructed image and increase the imaging depth. In order to eliminate the influence of prior information of imaging depth in a PSF model on the deconvolution effect of an OCT image, a mathematical model of the deconvolution problem of the OCT image is constructed based on a least square method, an alternative optimization image reconstruction algorithm for automatically estimating the imaging depth is introduced in the process of deconvolution reconstruction of the OCT image, an iterative solution of the constructed model is deduced by adopting an alternative optimization and Gaussian-Newton method, the imaging depth and a real image are estimated at the same time, and the rapid spatial adaptive deconvolution of the OCT image is realized. Aiming at the problems of large calculation amount and long time consumption of the algorithm, the invention provides a quick implementation method of blind area deconvolution based on convolution property and Fourier transform. The invention can improve the reconstruction quality of the OCT image in both simulation results and experimental results, and obviously improves the resolution of the OCT image. The technical scheme is as follows:
an optical coherence tomography fast space adaptive deconvolution method comprises the following steps:
the method comprises the following steps: constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where, is the convolution operator, o (x, y) is the observed OCT signal, ι (x, y) is the refractive index distribution function to be detected, (x, y) is the coordinates of the probe point, w is the depth of the probe point, and h (x, y, w) is the point spread function obtained based on the gaussian beam model:
Figure BDA0002941576520000031
discretizing the mathematical model to obtain the following linear model:
Figure BDA0002941576520000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002941576520000033
is the blurred image corresponding to the signal o (x, y),
Figure BDA0002941576520000034
a clear image corresponding to the refractive index function iota (x, y),
Figure BDA0002941576520000035
a linear matrix corresponding to the convolution kernel h (x, y, w) and the convolution operation,
Figure BDA0002941576520000036
representing that both sides of the symbol have an equivalence relationship.
Step two: constructing a least squares version of the deconvolution optimization problem:
Figure BDA0002941576520000037
wherein | O | count the luminance2Representing the two-norm of the vector O,
Figure BDA0002941576520000038
for a blurred image generated by discretization of the OCT signal,
Figure BDA0002941576520000039
for dispersion of refractive index profile function to be detectedThe obtained clear image is changed into a clear image,
Figure BDA0002941576520000041
for the convolution kernel matrix, w is the imaging depth,
Figure BDA0002941576520000042
and
Figure BDA0002941576520000043
regularization terms for I and w, respectively, and λ and μ are regularization parameters;
step three: and setting t to be 0, obtaining initial estimation w of imaging depth and clear image by Richardson-Lucy algorithmtAnd ItAnd setting the maximum iteration number TmaxAnd an image residual error threshold τ;
step four: setting the estimated values of the imaging depth and the clear image as w in the t-th iterationtAnd It(ii) a Fixed wtIn the second step
Figure BDA0002941576520000044
Is a constant, an estimate of I and
Figure BDA0002941576520000045
and independently, the optimization problem in the step two is simplified into the following form:
Figure BDA0002941576520000046
in the formula (I), the compound is shown in the specification,
Figure BDA0002941576520000047
when the imaging depth is wtThe convolution operator of the time-of-day,
Figure BDA0002941576520000048
selecting a Tikhonnv regularization form as a regularization item of the image in the t-th iteration, and obtaining a solution for accelerating iterative optimization according to a Gauss-Newton iterative solution form, wherein the solution is as follows:
Figure BDA0002941576520000049
wherein the content of the first and second substances,
Figure BDA00029415765200000410
represents the point spread function h (x, y,
Figure BDA00029415765200000411
) The corresponding n x n discretized image,
Figure BDA00029415765200000412
and
Figure BDA00029415765200000413
respectively representing Fourier change and inverse Fourier transform of the two-dimensional image;
step five: fixing It+1In the second step
Figure BDA00029415765200000414
Is a constant, an estimate of w
Figure BDA00029415765200000415
And independently, the optimization problem in the step two is simplified into the following form:
Figure BDA00029415765200000416
in the formula (I), the compound is shown in the specification,
Figure BDA00029415765200000417
using a Tikhronv regularization term, i.e.
Figure BDA00029415765200000418
wpIs a priori value of imaging depth;
the objective function w can be obtained according to the form of Gauss-Newton iterative solutiontThe gaussian-newton iterative solution of (a) is:
Figure BDA00029415765200000419
of formula (II) to'tAnd O ″)tSatisfy the requirement of
Figure BDA00029415765200000420
Figure BDA0002941576520000051
Step six: repeating the fourth step and the fifth step until the image residual error
Figure BDA0002941576520000052
Or the number of iterations t>Tmax。
The method provided by the invention improves the OCT image quality, obviously improves the contrast and resolution of the image, has stronger expression capability on details and smaller boundary loss; in addition, the alternating optimization algorithm provided by the invention can accurately estimate the imaging depth, further improve the accuracy of image reconstruction and reduce errors caused by imaging depth estimation errors; the operation time of the program is reduced, and the operation amount is reduced.
Drawings
FIG. 1 is a complete flow chart of the fast spatial adaptive deconvolution algorithm of the present invention;
FIG. 2 is a three representative simulation models of the present invention and shows the final imaging results using the Richardson-Lucy deconvolution method and the method of the present invention, the test method proposed by the present invention using a TV regularization term;
FIG. 3 is a time-averaged value before and after acceleration of deconvolution reconstruction of a simulation model of the present invention, wherein AO represents an alternating optimization algorithm before acceleration and AAO represents an alternating optimization algorithm after acceleration;
FIG. 4 is a diagram of the relative error of the estimated imaging depth of the present invention;
FIG. 5 shows the three OCT image deconvolution experimental results of the present invention, and shows the final imaging results using the Richardson-Lucy deconvolution method and the method of the present invention, which uses the TV regularization term.
FIG. 6 is a time-averaged value before and after acceleration of deconvolution reconstruction of OCT images of the invention.
Detailed Description
The optical coherence tomography fast space adaptive deconvolution method is described with reference to the attached drawings and embodiments.
Constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where, is the convolution operator, o (x, y) is the observed OCT signal, ι (x, y) is the refractive index distribution function to be detected, (x, y) is the coordinates of the probe point, w is the depth of the probe point, and h (x, y, w) is the point spread function obtained based on the gaussian beam model:
Figure BDA0002941576520000053
discretizing the analytic model to obtain the following linear model:
Figure BDA0002941576520000054
in the formula (I), the compound is shown in the specification,
Figure BDA0002941576520000055
is the blurred image corresponding to the signal o (x, y),
Figure BDA0002941576520000056
a clear image corresponding to the refractive index function iota (x, y),
Figure BDA0002941576520000061
is the convolution kernel h (x, y, w) and the linear matrix corresponding to the convolution operation.
Constructing a least squares version of the deconvolution problem:
Figure BDA0002941576520000062
wherein | O | count the luminance2Representing the two-norm of the vector O, is a blurred image generated by discretization of the OCT signal,
Figure BDA0002941576520000063
for a clear image obtained by discretizing the refractive index distribution function to be detected,
Figure BDA0002941576520000064
for the convolution kernel matrix, w is the imaging depth,
Figure BDA0002941576520000065
and
Figure BDA0002941576520000066
regularization terms for I and w, respectively, and λ and μ are regularization parameters.
And setting t to be 0, obtaining initial estimation w of imaging depth and clear image by Richardson-Lucy algorithmtAnd ItAnd setting the maximum iteration number TmaxAnd an image residual threshold τ.
Setting the estimated values of the imaging depth and the clear image as w in the t-th iterationtAnd It. Fixed wtIn the second step
Figure BDA0002941576520000067
Is a constant, an estimate of I and
Figure BDA0002941576520000068
and independently, the optimization problem in the step two is simplified into the following form:
Figure BDA0002941576520000069
in the formula (I), the compound is shown in the specification,
Figure BDA00029415765200000610
when the imaging depth is wtThe convolution operator of the time-of-day,
Figure BDA00029415765200000611
and selecting a Tikhonnv regularization form as a regularization item of the image in the t-th iteration, and using a reconstruction result of a Richardson-Lucy iterative deconvolution method as an initial value of a reconstructed image.
Obtained from the form of Gauss-Newton iterative solution, the objective function ItThe gaussian-newton iterative solution of (a) is:
Figure BDA00029415765200000612
from Lesion 1 (as demonstrated in the last part of the detailed description), the real matrix
Figure BDA00029415765200000613
I.e. presence matrix
Figure BDA00029415765200000614
Order:
Figure BDA00029415765200000615
then:
Figure BDA00029415765200000616
in the formula (I), the compound is shown in the specification,
Figure BDA00029415765200000617
the Tikhronv regularization term is usually chosen, i.e.
Figure BDA00029415765200000618
IpIs a prior value of the reconstructed image.
Let Ip＝ItThen, the final iterative solution of the gaussian-newton iterative method is:
Figure BDA0002941576520000071
from Lesion 2 (as demonstrated in the last part of the detailed description), it can be seen that for the convolution kernel matrix HwThe inverse operation can be converted into a simple calculation in the frequency domain by means of fourier transformation and inverse fourier transformation, so that the latter half of the above formula can be simplified to obtain an accelerated solution of the iterative optimization:
Figure BDA0002941576520000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002941576520000073
is the image h (x, y,
Figure BDA0002941576520000074
) The vector of (2).
Fixing It+1In the second step
Figure BDA0002941576520000075
Is a constant, an estimate of w
Figure BDA0002941576520000076
And independently, the optimization problem in the step two is simplified into the following form:
Figure BDA0002941576520000077
in the formula (I), the compound is shown in the specification,
Figure BDA0002941576520000078
the Tikhronv regularization term is usually chosen, i.e.
Figure BDA0002941576520000079
wpIs a priori the imaging depth.
The objective function w can be obtained according to the form of Gauss-Newton iterative solutiontThe gaussian-newton iterative solution of (a) is:
Figure BDA00029415765200000710
in the formula (I), the compound is shown in the specification,
Figure BDA00029415765200000711
Figure BDA00029415765200000712
step six: repeating the fourth step and the fifth step until the image residual error
Figure BDA00029415765200000713
Or the number of iterations t>Tmax。
Introduction 1 if
Figure BDA00029415765200000714
Presence of real numbers
Figure BDA00029415765200000715
And
Figure BDA00029415765200000716
order matrix
Figure BDA00029415765200000717
Prove 1 known H ═ HTAnd then:
Figure BDA00029415765200000718
performing a two-dimensional fourier transform on the PSF can obtain a formula of the form:
Figure BDA00029415765200000719
then:
Figure BDA0002941576520000081
namely:
Figure BDA0002941576520000082
and because:
Figure BDA0002941576520000083
therefore, the method comprises the following steps:
Figure BDA0002941576520000084
so that there are real numbers c and AcOrder matrix
Figure BDA0002941576520000085
Wherein:
Figure BDA0002941576520000086
the theory of leading 1 can be used for the evidence.
Introduction 2 if
Figure BDA0002941576520000087
Then
Figure BDA0002941576520000088
Prove 2 for a given PSF expression
Figure BDA0002941576520000089
The regularization parameter λ and the low resolution image O, the target image I, may be given by the following formula:
(Hw+λE)-1I＝O (4-8)
namely:
Figure BDA00029415765200000810
simultaneous fourier transformation of both sides of equation (4-43) yields:
Figure BDA0002941576520000091
by simple transformation it can be obtained:
Figure BDA0002941576520000092
and then carrying out inverse Fourier transform on the formula (4-45) to obtain an expression in the following form:
Figure BDA0002941576520000093
namely:
Figure BDA0002941576520000094
wherein the content of the first and second substances,
Figure BDA0002941576520000095
is a vector of the point spread function h (x, y, w).
So 2 can be introduced to ensure this.
The listed results comprise a simulation part and an experiment part, wherein the simulation model comprises a simulation tube, a Siemens Star diagram and an onion skin structure simulation diagram; the experimental data are OCT experimental images of the biological microstructure of the object to be detected, including in-vitro OCT images of fresh onions, in-vivo OCT images of human retina and human fingertip.
Fig. 2 shows the deconvolution imaging results of the three simulation models, respectively. As can be seen from the simulation results, the definition of the reconstructed image obtained by the reconstruction method based on regularization is obviously increased; compared with the reconstruction result of the Richardson-Lucy deconvolution method, the intensity and the contrast of the deconvolution image obtained by the method are higher, the reconstructed image is clearer, edges are hardly damaged, and obviously, the reconstruction method based on the regularization method provided by the invention has better effect;
FIG. 3 is a time-use average value before and after acceleration of deconvolution reconstruction of the simulation model of the present invention, from which it can be known that the acceleration algorithm can increase the overall operation speed of the algorithm, and the program operation time after acceleration is about one tenth of that before acceleration;
FIG. 4 is a diagram showing the relative error of the imaging depth estimation according to the present invention, wherein the relative error of the imaging depth estimation is 10-8The method has the advantages that the method is within the order of magnitude range and is a reasonable error range, and the result proves that the method is accurate and credible in the estimation of the imaging depth, so that the reconstruction error caused by the error in the estimation of the imaging depth can be reduced;
FIG. 5 shows the deconvolution experiment results of three OCT images according to the present invention. The reconstruction method still has a good reconstruction effect on OCT experimental data, and the improvement of the image resolution is obvious as seen from the arrow direction of a local enlarged image, a finer structure can be displayed, the brightness and the contrast of the image are higher, and the reconstruction method based on the regularization method provided by the invention has a good deconvolution reconstruction effect obviously.
FIG. 6 is a time-averaged value before and after acceleration of OCT image deconvolution reconstruction, from which it can be seen that the overall operation speed of the algorithm can be increased by the acceleration algorithm, and the program operation time after acceleration is about one tenth of that before acceleration;
the present invention is not limited to the disclosure of the embodiment and the drawings. It is intended that all equivalents and modifications which come within the spirit of the disclosure be protected by the present invention.

Claims (1)

1. An optical coherence tomography fast space adaptive deconvolution method comprises the following steps:
the method comprises the following steps: constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where, is the convolution operator, o (x, y) is the observed OCT signal, ι (x, y) is the refractive index distribution function to be detected, (x, y) is the coordinates of the probe point, w is the depth of the probe point, and h (x, y, w) is the point spread function obtained based on the gaussian beam model:
Figure FDA0002941576510000011
discretizing the mathematical model to obtain the following linear model:
Figure FDA0002941576510000012
in the formula (I), the compound is shown in the specification,
Figure FDA0002941576510000013
is the blurred image corresponding to the signal o (x, y),
Figure FDA0002941576510000014
a clear image corresponding to the refractive index function iota (x, y),
Figure FDA0002941576510000015
a linear matrix corresponding to the convolution kernel h (x, y, w) and the convolution operation,
Figure FDA0002941576510000016
representing that both sides of the symbol have an equivalence relationship.
Step two: constructing a least squares version of the deconvolution optimization problem:
Figure FDA0002941576510000017
wherein | O | count the luminance2Representing the two-norm of the vector O,
Figure FDA0002941576510000018
for a blurred image generated by discretization of the OCT signal,
Figure FDA0002941576510000019
for a clear image obtained by discretizing the refractive index distribution function to be detected,
Figure FDA00029415765100000110
for the convolution kernel matrix, w is the imaging depth,
Figure FDA00029415765100000111
and
Figure FDA00029415765100000112
regularization terms for I and w, respectively, and λ and μ are regularization parameters;
step three: and setting t to be 0, obtaining initial estimation w of imaging depth and clear image by Richardson-Lucy algorithmtAnd ItAnd setting the maximum iteration number TmaxAnd an image residual error threshold τ;
step four: setting the estimated values of the imaging depth and the clear image as w in the t-th iterationtAnd It(ii) a Fixed wtIn the second step
Figure FDA00029415765100000113
Is a constant, an estimate of I and
Figure FDA00029415765100000114
and independently, the optimization problem in the step two is simplified into the following form:
Figure FDA00029415765100000115
in the formula (I), the compound is shown in the specification,
Figure FDA00029415765100000116
when the imaging depth is wtThe convolution operator of the time-of-day,
Figure FDA00029415765100000117
selecting a Tikhonnv regularization form as a regularization item of the image in the t-th iteration, and obtaining a solution for accelerating iterative optimization according to a Gauss-Newton iterative solution form, wherein the solution is as follows:
Figure FDA0002941576510000021
wherein the content of the first and second substances,
Figure FDA0002941576510000022
representing point spread function
Figure FDA0002941576510000023
The corresponding n x n discretized image,
Figure FDA0002941576510000024
and
Figure FDA0002941576510000025
respectively representing Fourier change and inverse Fourier transform of the two-dimensional image;
step five: fixing It+1In the second step
Figure FDA0002941576510000026
Is a constant, an estimate of w
Figure FDA0002941576510000027
And independently, the optimization problem in the step two is simplified into the following form:
Figure FDA0002941576510000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002941576510000029
using a Tikhronv regularization term, i.e.
Figure FDA00029415765100000210
wpIs a priori value of imaging depth;
the objective function w can be obtained according to the form of Gauss-Newton iterative solutiontThe gaussian-newton iterative solution of (a) is:
Figure FDA00029415765100000211
of formula (II) to'tAnd O "tSatisfy the requirement of
Figure FDA00029415765100000212
Figure FDA00029415765100000213
Step six: repeating the fourth step and the fifth step until the image residual error
Figure FDA00029415765100000214
Or the number of iterations t>Tmax。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116843788A (en) * 2023-08-31 2023-10-03 清华大学 Limited angle tomography method and device

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009095296A1 (en) * 2008-01-29 2009-08-06 Bergen Teknologioverforing As Constrained iterative blind deconvolution
CN103761712A (en) * 2014-01-21 2014-04-30 太原理工大学 Image blind convolution method based on adaptive optical system point spread function reconstruction
US20140176937A1 (en) * 2011-08-18 2014-06-26 Tiegen Liu Distributed disturbance sensing device and the related demodulation method based on polarization sensitive optical frequency domain reflectometry
CN109919844A (en) * 2019-02-28 2019-06-21 河南师范大学 A kind of high-resolution electricity tomography distribution of conductivity method for reconstructing
CN111476733A (en) * 2020-04-07 2020-07-31 浙江大学 Microscope image deconvolution acceleration algorithm based on unmatched operators

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009095296A1 (en) * 2008-01-29 2009-08-06 Bergen Teknologioverforing As Constrained iterative blind deconvolution
US20140176937A1 (en) * 2011-08-18 2014-06-26 Tiegen Liu Distributed disturbance sensing device and the related demodulation method based on polarization sensitive optical frequency domain reflectometry
CN103761712A (en) * 2014-01-21 2014-04-30 太原理工大学 Image blind convolution method based on adaptive optical system point spread function reconstruction
CN109919844A (en) * 2019-02-28 2019-06-21 河南师范大学 A kind of high-resolution electricity tomography distribution of conductivity method for reconstructing
CN111476733A (en) * 2020-04-07 2020-07-31 浙江大学 Microscope image deconvolution acceleration algorithm based on unmatched operators

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张丽娟;杨进华;苏伟;姜成昊;王晓坤;谭芳: "基于改进的期望值最大化自适应光学图像多帧迭代去卷积算法", 兵工学报, vol. 35, no. 11, 31 December 2014 (2014-12-31) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116843788A (en) * 2023-08-31 2023-10-03 清华大学 Limited angle tomography method and device
CN116843788B (en) * 2023-08-31 2023-11-28 清华大学 Limited angle tomography method and device

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