CN112927317B - Optical coherence tomography rapid space self-adaptive deconvolution method - Google Patents
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Abstract
The invention provides a rapid space self-adaptive deconvolution method for optical coherence tomography, which comprises the following steps: constructing a mathematical model of the OCT image deconvolution, and discretizing the mathematical model to obtain the linear model; step two: constructing a least square form of deconvolution optimization problem; obtaining initial estimation of imaging depth and a clear image by using a Lechadson-dew algorithm, and setting a maximum iteration number Tmax and an image residual error threshold tau; in the iteration of the step t, the estimated values of the imaging depth and the clear image are respectively wt and It, and a solution for accelerating iteration optimization is obtained according to a Gaussian-Newton iteration solution of the objective function; and (5) iterating the calculation until convergence.
Description
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 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 that uses a michelson interferometer to detect interference signals after back-scattered light in biological tissue interferes with reflected light from a reference arm, and further calculates microscopic two-dimensional or three-dimensional structural images of the biological tissue from the interference patterns of the scattered light and the reference light. The imaging depth of OCT can be on the order of mm and the imaging resolution can be on the order of μm. Compared with the clinical common medical imaging technology, the method has the advantages of non-invasive, non-contact, no damage, high spatial resolution, low cost and the like, and the OCT imaging uses light waves as an imaging energy source for continuous traditional medical urban and rural areas such as X-ray computed tomography (X-CT), magnetic Resonance Imaging (MRI), ultrasonic Imaging (UI) and the like. OCT imaging has many advantages, so that the OCT imaging has rapid development, wide application field and wide application prospect. The method is also applied to the fields of shape detection of precision mechanical devices, quality detection of semiconductor devices, material surface damage detection, detection of cracks of substances such as porcelain and precious stone, imaging of plant leaves, seed morphology and micro-scale microscopic organism internal structures, and the like.
Spatial resolution enhancement of OCT images is one of the hot spots of OCT studies. Enhancement methods of OCT images can be classified into two types, hardware-based methods and digital-based methods. Among the mathematical-based image enhancement methods, the deconvolution method is most commonly used. Deconvolution is a method for reducing ambiguity, and common deconvolution methods are wiener filtering, richardson-Lucy iterative deconvolution and least squares deconvolution. Wiener filtering deblurring algorithm was proposed by n.wiener et al in 1964 in the book entitled "smooth time series Extrapolation, interpolation and smoothing and engineering application" (extraction, interpolation, and smoothing of stationary time series with engineering applications) published by the university of hemp and university Press (MIT Press), also known as minimum mean square error filtering. The goal is to find an estimate of the uncontaminated 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 for image recovery in a poisson noise background and is a maximum likelihood solution based on poisson statistics. It aims to maximize the likelihood of recovering an image by using a expectation maximization algorithm (EM). The algorithm requires a good estimate of the process of image degradation to achieve accurate recovery. Fish et al 1995 in journal of the United states society of optics, optical image science and Vision (Journal of The Optical Society of America A-Optics Image Science and Vision), volume 12, pages 58-65, blind deconvolution with the Lechadson-Louis algorithm (Blind deconvolution by means of the Richardson-Lucy algorithm), successfully applied the Richardson-Lucy algorithm to OCT imaging. In IEEE image processing J.No. (IEEE Transactions on Image Processing) volume 14, pages 1254-1264, published article entitled "deconvolution method for removing lateral blur in optical coherence tomography" (Deconvolution methods for mitigation of transverse blurring in optical coherence tomography), ralston et al 2005, a regularized inversion deconvolution algorithm is presented that uses a Gaussian beam deconvolution algorithm that reduces the lateral blur of an OCT image and improves the lateral resolution of an OCT image.
The image deblurring method can be further classified into a non-blind deconvolution method and a blind deconvolution method according to whether a Point Spread Function (PSF) is known. In 1978, trussel and Hunt, volume 26 of IEEE acoustic, speech and signal processing assembly (IEEE Transactions on Acoustics Speech & Signal Processing), pages 608-609, entitled "method for block recovery of spatially blurred images" (Image restoration of space-variant blurs by sectioned methods), first proposed a method for block recovery of images using wiener filtering algorithm, which is an important method for performing spatially varying PSF blind deconvolution. Dividing an image into sub-blocks, considering that the PSF of each sub-block image is unchanged in space, deconvolving each sub-block by using a wiener filtering algorithm, and finally splicing the restored sub-image blocks together to reconstruct a whole clear image. Liu et al 2011, volume 19, pages 18135-18148, published under the heading of automatic estimation of the information entropy-based deconvolution out-of-focus optical coherence tomography image point spread function (Automatic estimation of point-spin-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based Approx) propose an information entropy-based PSF automatic estimation method for deconvolving out-of-focus regions of OCT images. They performed a non-blind deconvolution of the defocused image using a set of gaussian PSFs of different spot sizes using a richardson-dew iterative deconvolution algorithm. In volume 52, applied Optics, pages 5663-5670, published under the article "optical coherence tomography image quality improvement based on the richardson-dew deconvolution algorithm" (Image quality improvement in optical coherence tomography using Lucy-Richardson deconvolution algorithm), podoleanu et al 2013, a solid replica was used to evaluate the average PSF of the imaging system and an iterative richardson-dew iterative deconvolution algorithm was used to improve the image quality. A new total variation-based OCT image space deconvolution method is proposed in Mohammadrza et al 2017, entitled "total variation-based optical coherence tomography space variation deconvolution method" (A space-variant deconvolution method based on total variation for optical coherence tomography images) published in conference series (Society of optical Engineers of Photo-Optical Instrumentation Engineers (SPIE): conference Series). They use solid simulations to estimate the point spread functions of the various subregions of the imaging system and then use the iterative deconvolution method of Richardson-Lucy, hybrid, and total variation to mitigate the blurring of the spatial variation.
In addition, Q.Wang et al 2018, published in International annual institute of IEEE medicine and biology at 40 (40 th Annual International Conference of the IEEE Engineering in Medicine and Biology Society) pages 1-4 entitled Super resolution in optical coherence tomography (Super-Resolution in Optical Coherence Tomography), propose a solution based on inverse problem solving, namely a cost function for deconvolution method and Super resolution, wherein the deconvolution method can be implemented by solving the least squares method. They then used an alternate direction multiplier (ADMM) and front-to-back split (FBS) algorithm to minimize it. Furthermore, the standard L1 regularization with soft threshold is also compared to TV regularization in ADMM schemes.
However, at present, when the OCT image reconstruction is carried out on biological tissues at home and abroad, a plurality of problems still exist: (1) OCT systems require a compromise between imaging depth and imaging resolution, limited by the physical nature 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 its size is affected by factors such as imaging depth, imaging position, and the like. The existing image reconstruction algorithm uses a PSF with unchanged space, and the accuracy of the reconstructed image is lower; (3) If the OCT image is large, the calculation amount of the image deconvolution operation is large, the time consumption is long, and the configuration performance requirement on the computing device is high.
Disclosure of Invention
The invention aims to provide a rapid space self-adaptive deconvolution method capable of improving the resolution of a reconstructed image and increasing the imaging depth. In order to eliminate the influence of priori 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 alternate optimization image reconstruction algorithm for automatically estimating the imaging depth is introduced in the deconvolution reconstruction process of the OCT image, and an iterative solution of the constructed model is deduced by adopting an alternate optimization method and a Gaussian-Newton method, and meanwhile, the imaging depth and a real image are estimated, so that the rapid spatial self-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 blind area deconvolution rapid implementation method based on convolution properties and Fourier transformation. The invention can improve the reconstruction quality of the OCT image in both the simulation result and the experimental result, and obviously improves the resolution of the OCT image. The technical proposal is as follows:
an optical coherence tomography rapid spatially adaptive deconvolution method comprises the following steps:
step one: constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where x is a convolution operator, o (x, y) is an observed OCT signal, iota (x, y) is a refractive index distribution function to be detected, (x, y) is coordinates of a detection point, w is a depth of the detection point, and h (x, y, w) is a point spread function obtained based on a gaussian beam model:
discretizing the mathematical model to obtain the following linear model:
in the method, in the process of the invention,for blurred images corresponding to the signals o (x, y),/>for a sharp image corresponding to the refractive index function iota (x, y), +.>Is a linear matrix corresponding to convolution kernel h (x, y, w) and convolution operation, ++>Representing that the symbols have an equivalence relation on both sides.
Step two: constructing a least square form of deconvolution optimization problem:
in the formula, O is 2 Representing the two norms of the vector O,for blurred images generated by the discretization of OCT signals,for a clear image discretized by the refractive index profile function to be detected>For the convolution kernel matrix, w is the imaging depth, < +.>And->Regularization terms for I and w, respectively, lambda and mu being regularization parameters;
step three: let t=0, obtain initial estimate w of imaging depth and sharp image from the richardson-dew algorithm t And I t And setting the maximum iteration times T max An image residual threshold τ;
step four: let the estimated values of imaging depth and clear image in the iteration of step t be w respectively t And I t The method comprises the steps of carrying out a first treatment on the surface of the Fix w t Then in step twoIs constant, the estimated value of I is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,is imaged with depth w t Convolution operator of time, ++>For regularization item about the image in the t-th iteration, selecting a Tikhnonv regularization form, and obtaining a solution for accelerating iteration optimization according to the form of Gaussian-Newton iteration solution, wherein the solution comprises the following steps of:
wherein,represents the point spread function h (x, y, < ->) Corresponding nxn discretized image, < >>And->Respectively representing the Fourier transform and the inverse Fourier transform of the two-dimensional image;
step five: fixing I t+1 Then in step twoIs constant, the estimated value of w is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,selecting Tikhnonv regularization term, i.e.>w p A priori value for imaging depth;
from the form of a Gaussian-Newton iterative solution, the objective function w t Is:
wherein O 'is' t And O' t Satisfy the following requirements
Step six: repeating the fourth and fifth steps until the graphImage residual errorOr the number of iterations t>T max 。
The method provided by the invention improves the OCT image quality, obviously improves the contrast and resolution of the image, and has stronger expressive power 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 spatially adaptive deconvolution algorithm of the present invention;
FIG. 2 is a graph of three exemplary simulation models of the present invention and shows the final imaging results using the Lechadson-Louis deconvolution method and the method of the present invention, the test method of the present invention using the TV regularization term;
FIG. 3 is a time average 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 graph of relative error in estimating imaging depth in accordance with the present invention;
fig. 5 is a graph showing the results of three OCT image deconvolution experiments of the present invention, and gives the final imaging results using the richardson-dew deconvolution method and the method of the present invention, which uses the TV regularization term.
Fig. 6 shows the time average before and after acceleration of the deconvolution reconstruction of OCT images according to the present invention.
Detailed Description
The fast spatially adaptive deconvolution method of optical coherence tomography of the present invention is described with reference to the accompanying drawings and examples.
Constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where x is a convolution operator, o (x, y) is an observed OCT signal, iota (x, y) is a refractive index distribution function to be detected, (x, y) is coordinates of a detection point, w is a depth of the detection point, and h (x, y, w) is a point spread function obtained based on a gaussian beam model:
discretizing the analytical model can obtain the following linear model:
in the method, in the process of the invention,for blurred images corresponding to the signal o (x, y,)>For a sharp image corresponding to the refractive index function iota (x, y), +.>Is a linear matrix corresponding to convolution kernel h (x, y, w) and convolution operation.
Constructing a least squares version of the deconvolution problem:
in the formula, O is 2 The two norms representing the vector O, which are blurred images generated by discretization of the OCT signal,for a clear image discretized by the refractive index profile function to be detected>For the convolution kernel matrix, w is the imaging depth,and->Regularization terms for I and w, respectively, λ and μ are regularization parameters.
Let t=0, obtain initial estimate w of imaging depth and sharp image from the richardson-dew algorithm t And I t And setting the maximum iteration times T max An image residual threshold τ.
Let the estimated values of imaging depth and clear image in the iteration of step t be w respectively t And I t . Fix w t Then in step twoIs constant, the estimated value of I is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,is imaged with depth w t Convolution operator of time, ++>And (3) selecting a Tikhnonv regularization form for regularization items about the image in the t-th iteration, and using a result of the reconstruction by using a Lechadson-dew iteration deconvolution method as an initial value of the reconstructed image.
From the form of Gaussian-Newton iterative solution, the objective function I t Is:
from the quotients 1 (demonstrated in the last part of the implementation method), it can be seen that the real matrixI.e. presence matrix->And (3) making:
then:
in the method, in the process of the invention,tikhnonv regularization term is usually chosen, i.e.)>I p For reconstructing a priori values of the image.
Let I p ＝I t The final iteration solution of the gauss-newton iteration method is:
as can be seen from the quotients 2 (which are proved in the last part of the implementation method), for the convolution kernel matrix H w The inverse operation can be converted into simple calculation in the frequency domain through fourier transformation and inverse fourier transformation, so that the latter half of the above formula can be simplified to obtain an accelerated iterative optimized solution:
in the method, in the process of the invention,image h (x, y, < > for PSF>) Is a vector of (a).
Fixing I t+1 Then in step twoIs constant, the estimated value of w is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,tikhnonv regularization term is usually chosen, i.e.)>w p Is an a priori value of the imaging depth.
From the form of a Gaussian-Newton iterative solution, the objective function w t Is:
in the method, in the process of the invention,
step six: repeating the fourth step and the fifth step until the residual error of the imageOr the number of iterations t>T max 。
Lemma 1 ifThere is real->And->Let matrix
Proof 1 known h=h T Then:
performing two-dimensional Fourier transform on PSF can obtain the following formula:
then:
namely:
again because:
therefore:
there are real numbers c and A c Ream matrixWherein:
and the quotation mark 1 is obtained.
2 cases of quotationThen->
Proof 2 for a given PSF expressionRegularization parameter λ and low resolution image O, target image I may be given by:
(H w +λE) -1 I＝O (4-8)
namely:
the simultaneous fourier transform of both sides of equation (4-43) yields:
by simple transformation, it can be obtained:
and then carrying out Fourier inverse transformation on the formula (4-45) to obtain the expression in the following form:
namely:
wherein,is a vector of the point spread function h (x, y, w).
So, the theory 2 is proved.
The listed results comprise two parts of simulation and experiment, 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 biological microstructures of objects to be detected, including in-vitro OCT images of fresh onions, in-vivo OCT images of human retina and human fingertip.
The deconvolution imaging results of the three simulation models are given in fig. 2, respectively. As can be seen from the simulation result, the definition of the reconstructed image obtained by the regularized reconstruction method is obviously increased; compared with the reconstruction result of the Ichadson-dew deconvolution method, the deconvolution method has the advantages that the intensity and the contrast of the obtained deconvolution image are higher, the reconstructed image is clearer, the edge is hardly damaged, and obviously, the reconstruction method based on the regularization method provided by the invention has better effect;
FIG. 3 is a graph showing the average time before and after the deconvolution reconstruction acceleration of the simulation model, wherein the acceleration algorithm can improve the overall running speed of the algorithm, and the running time of the program after the acceleration is about one tenth of that before the acceleration;
FIG. 4 shows the relative error of the estimated imaging depth of the present invention, which is shown as 10 -8 In the range of the order of magnitude, the reasonable error range is achieved, and the result proves that the imaging depth estimation method is accurate and reliable in imaging depth estimation, and can reduce reconstruction errors caused by imaging depth estimation errors;
fig. 5 shows the results of deconvolution experiments of three OCT images according to the present invention. The invention has good reconstruction effect on OCT experimental data, and the arrow direction of the local enlarged image can be used for obviously improving the resolution of the image, displaying finer structure and higher brightness and contrast of the image, and obviously the reconstruction method based on the regularization method has good deconvolution reconstruction effect.
FIG. 6 is a graph showing the average time before and after the OCT image deconvolution reconstruction acceleration, wherein the acceleration algorithm can improve the overall running speed of the algorithm, and the running time of the program after acceleration is about one tenth of that before acceleration;
the invention is not limited to the embodiments and the disclosure of the drawings. All equivalents and modifications that come within the spirit of the disclosure are within the scope of the invention.
Claims (1)
1. An optical coherence tomography rapid spatially adaptive deconvolution method comprises the following steps:
step one: constructing a mathematical model of the deconvolution of the OCT image:
o(x,y)＝h(x,y,w)*ι(x,y)
where x is a convolution operator, o (x, y) is an observed OCT signal, iota (x, y) is a refractive index distribution function to be detected, (x, y) is coordinates of a detection point, w is a depth of the detection point, and h (x, y, w) is a point spread function obtained based on a gaussian beam model:
discretizing the mathematical model to obtain the following linear model:
in the method, in the process of the invention,for blurred images corresponding to the signal o (x, y,)>For a sharp image corresponding to the refractive index function iota (x, y), +.>Is a linear matrix corresponding to convolution kernel h (x, y, w) and convolution operation, ++>Representing that the two sides of the symbol have equivalent relations;
step two: constructing a least square form of deconvolution optimization problem:
in the formula, O is 2 Representing the two norms of the vector O,for blurred images generated by the discretization of OCT signals,for a clear image discretized by the refractive index profile function to be detected>For the convolution kernel matrix, w is the imaging depth, < +.>And->Regularization terms for I and w, respectively, lambda and mu being regularization parameters;
step three: let t=0, obtain initial estimate w of imaging depth and sharp image from the richardson-dew algorithm t And I t And setting the maximum iteration times T max An image residual threshold τ;
step four: let the estimated values of imaging depth and clear image in the iteration of step t be w respectively t And I t The method comprises the steps of carrying out a first treatment on the surface of the Fix w t Then in step twoIs constant, the estimated value of I is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,is imaged with depth w t Convolution operator of time, ++>For regularization item about the image in the t-th iteration, selecting a Tikhnonv regularization form, and obtaining a solution for accelerating iteration optimization according to the form of Gaussian-Newton iteration solution, wherein the solution comprises the following steps of:
wherein,representing the point spread function +.>Corresponding nxn discretized image, < >>And->Respectively representing the Fourier transform and the inverse Fourier transform of the two-dimensional image;
step five: fixing I t+1 Then in step twoIs constant, the estimated value of w is equal to +.>Irrespective, the optimization problem in step two is reduced to the following form:
in the method, in the process of the invention,selecting Tikhnonv regularization term, i.e.>w p A priori value for imaging depth;
from the form of a Gaussian-Newton iterative solution, the objective function w t Is:
wherein O 'is' t And O' t Satisfy the following requirements
Step six: repeating the fourth step and the fifth step until the residual error of the imageOr the number of iterations t>T max 。
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