CN113670961A - A gamma photon multiple scattering correction method based on spatial distribution fitting - Google Patents

A gamma photon multiple scattering correction method based on spatial distribution fitting Download PDF

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CN113670961A
CN113670961A CN202110957666.6A CN202110957666A CN113670961A CN 113670961 A CN113670961 A CN 113670961A CN 202110957666 A CN202110957666 A CN 202110957666A CN 113670961 A CN113670961 A CN 113670961A
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范兼睿
刘小姣
徐风友
汪玥
张昕婷
沈高青
李志林
曹盼
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Nanjing University of Aeronautics and Astronautics
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Abstract

本发明公开了一种基于空间分布拟合的γ光子多次散射校正方法，该方法通过把γ光子多次散射看作γ光子多个单次散射的叠加，将γ光子采样数据按LoR在Root中的保存方式进行投影，分别对离散的γ光子单次散射分布和多次散射分布进行函数拟合，确定核函数的表达形式，计算探测系统中每个探测器对记录的γ光子多次散射数目，最后，将多次散射的γ光子从原始γ光子数据中剔除。本方法有效解决了由于散射的γ光子造成重建图像出现的星状辐射伪影、边缘模糊等图像失真情况，从而达到了γ光子多次散射校正的目的，并且提高了γ光子多次散射识别准确性。

Figure 202110957666

The invention discloses a gamma photon multiple scattering correction method based on spatial distribution fitting. The method treats the gamma photon multiple scattering as the superposition of the gamma photon multiple single scattering, and converts the gamma photon sampling data in the Root according to LoR. Project the storage method in the γ photon, and perform function fitting on the discrete γ photon single scattering distribution and multiple scattering distribution respectively, determine the expression form of the kernel function, and calculate the multiple scattering of the recorded γ photons by each detector in the detection system. The number, and finally, of multiply scattered gamma photons is eliminated from the raw gamma photon data. The method effectively solves the image distortion such as star radiation artifacts and edge blurring in the reconstructed image caused by scattered γ photons, thereby achieving the purpose of γ photon multiple scattering correction and improving the accuracy of γ photon multiple scattering identification. sex.

Figure 202110957666

Description

Gamma photon multiple scattering correction method based on space distribution fitting
Technical Field
The invention relates to the field of gamma photon three-dimensional imaging, in particular to a gamma photon multiple scattering correction method based on space distribution fitting.
Background
When the gamma photon three-dimensional imaging technology is applied to the detection of defects of an inner cavity structure and an inner wall of an industrial complex part, because the industrial complex part is made of metal and alloy with high density, when gamma photons penetrate through a detection object and are recorded by a detection system, the gamma photons can generate scattering events under the influence of Compton scattering effect, Rayleigh scattering effect and the like. Some gamma photons undergo multiple scattering events during the penetration of the complex and are recorded by the detector, referred to as gamma photon multiple scattering events. The gamma photon scattering event changes the motion track and the carried energy of gamma photons, so that LoR recorded by a gamma photon detection system contains error information of positron annihilation positions, the number of the scattered gamma photons accounts for 30% -50% of all gamma photons, and the scattered gamma photons can cause image distortion problems such as edge blurring and star artifacts of reconstructed images, thereby reducing the detection resolution. Therefore, gamma photon scattering correction is necessary to obtain a gamma photon three-dimensional imaging detection technology with high resolution.
The existing gamma photon scattering correction methods are mainly classified into four types: energy window identification, iterative scattering compensation, convolution processing, Monte Carlo simulation, and the like. The energy window segmentation and calibration coefficients of the energy window identification method need to be artificially selected and determined in a simulation mode, so that the discrimination efficiency is reduced; the scattering compensation iterative method can only play a role in scattering compensation for low-proportion gamma photon scattering events; the convolution processing method only has obvious scattering correction effect on the detection experiment of the even distribution of the nuclide space; the Monte Carlo simulation method has high accuracy and good effect, but needs to predict each experimental parameter in the detection process in advance, which cannot be guaranteed in the actual detection application.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems existing in gamma photon multiple scattering correction, the invention provides a gamma photon multiple scattering correction method based on gamma photon Compton scattering distribution theory, which considers gamma photon multiple scattering distribution as convolution of gamma photon single scattering distribution function and multiple scattering Gaussian kernel function, the difference between the variance of the gamma photon single scattering Gaussian distribution and the gamma photon multiple scattering distribution is a fixed value, gamma photon sampling data is projected according to the storage mode of LoR in Root, the function fitting is respectively carried out on the discrete gamma photon single scattering distribution and the multiple scattering distribution, the expression form of the kernel function is determined, the gamma photon multiple scattering number recorded by each detector in a detection system is calculated, finally the gamma photon multiple scattering is removed from the original gamma photon data, and the aim of gamma photon multiple scattering correction is achieved, the accuracy of gamma photon multiple scattering identification is improved.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a gamma photon multiple scattering correction method based on space distribution fitting specifically comprises the following steps:
step 1: under a three-dimensional data acquisition mode, a gamma photon multiple scattering correction mathematical model is established based on gamma photon pairs which are recorded by a detector pair A, B and generate multiple scattering coincidence events;
step 2: transforming XYZ projection of the space three-dimensional coordinate system into a two-dimensional coordinate system L theta after LoR data recombination to obtain a gamma photon multiple scattering distribution Gaussian kernel function;
and step 3: the number of gamma photon pairs recorded by detector pair A, B that have multiple scatter coincidence events occurring is calculated.
In the three-dimensional data acquisition mode, a gamma photon multiple scattering correction mathematical model is established based on gamma photon pairs recorded by the detector pair A, B and subjected to multiple scattering coincidence events:
step 1-1: transforming the spatial coordinate system XYZ into a polar coordinate system
Figure BSA0000250409330000021
Order to
Figure BSA0000250409330000022
As a function of the spatial distribution of the nuclides,
Figure BSA0000250409330000031
is the attenuation coefficient;
step 1-2: each gamma photon scattering event belongs to mutually independent events, so the probability density of multiple scattering can be completely calculated according to the mode of independent events, and I isS(A, B) is a gamma photon single scattering distribution function, KM(x, y, z) is a Gaussian kernel function of the multiple scattering probability distribution of gamma photons, and the calculation formula is as follows:
Figure BSA0000250409330000032
step 1-3: gamma photon multiple scattering distribution IM(A, B) is regarded as the convolution of a gamma photon single scattering distribution function and a multiple scattering Gaussian kernel function, and the calculation formula is as follows:
Figure BSA0000250409330000033
where V is the gamma photon detection space.
The calculation steps of transforming the XYZ projection of the space three-dimensional coordinate system to the two-dimensional coordinate system L theta after LoR data recombination and the Gaussian kernel function of gamma photon multiple scattering distribution are as follows:
step 2-1: calculating a Gaussian fitting coefficient delta, wherein the calculation formula is as follows:
Figure BSA0000250409330000034
wherein deltaMIs a Gaussian function coefficient, delta, of the spatial distribution fitting gamma photon multiple scatteringSIs a Gaussian function coefficient of space distribution fitting gamma photon single scattering;
step 2-2: and (3) calculating a gamma photon multiple scattering distribution Gaussian kernel function, wherein the calculation formula is as follows:
Figure BSA0000250409330000035
where a is the gaussian fit coefficient.
The calculation of the number of pairs of gamma photons recorded by the detector pair A, B for which multiple scatter coincidence events occur is as follows:
step 3-1: substituting equation (4) into equation (2), the number of gamma photon pairs recorded by detector pair A, B for which multiple scatter coincidence events occur is as follows:
Figure BSA0000250409330000041
has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
(1) the invention provides a gamma photon multiple scattering correction method based on space distribution fitting aiming at the gamma photon multiple scattering problem and based on the gamma photon space distribution fitting theory;
(2) the gamma photon physical detection system firstly carries out single scattering correction on the collected gamma photon data, then carries out three-dimensional image reconstruction on the gamma photon data subjected to the single scattering correction, compares gamma photon single scattering distribution under the same experimental condition, determines gamma photon multiple scattering distribution and further determines a Gaussian fitting coefficient;
(3) the gamma photon single scattering correction method based on the trajectory mapping can effectively solve the image distortion conditions such as star radiation artifact, edge blurring and the like of a reconstructed image caused by scattered gamma photons, and improves the gamma photon multiple scattering identification accuracy.
Generally speaking, the gamma photon multiple scattering is regarded as superposition of multiple single scattering of gamma photons, gamma photon sampling data is projected according to a storage mode of LoR in Root, function fitting is respectively carried out on discrete gamma photon single scattering distribution and multiple scattering distribution, an expression form of a kernel function is determined, the multiple scattering number of gamma photons recorded by each detector in a detection system is calculated, finally, the multiple scattering gamma photons are removed from original gamma photon data, the purpose of gamma photon multiple scattering correction is achieved, and the gamma photon multiple scattering identification accuracy is improved.
Drawings
FIG. 1 is a schematic diagram of multiple scattering in a gamma photon three-dimensional data acquisition mode;
FIG. 2 is a schematic diagram of a gamma photon multiple scattering correction method based on spatial distribution fitting;
fig. 3 is a detection object taking an industrial hydraulic part as an example;
FIG. 4 is a reconstructed image of gamma photons containing scatter;
fig. 5 is a gamma photon reconstructed image after multiple scatter correction.
Detailed Description
The technical solution of the present invention will be further described with reference to the accompanying drawings and embodiments.
As shown in fig. 1, it is a schematic view of multiple scattering of gamma photons in a gamma photon three-dimensional data acquisition mode by the gamma photon multiple scattering correction method based on spatial distribution fitting of the present invention, and specifically includes the following steps:
step 1: under a three-dimensional data acquisition mode, a gamma photon multiple scattering correction mathematical model is established based on gamma photon pairs which are recorded by a detector pair A, B and generate multiple scattering coincidence events;
step 2: transforming XYZ projection of the space three-dimensional coordinate system into a two-dimensional coordinate system L theta after LoR data recombination to obtain a gamma photon multiple scattering distribution Gaussian kernel function;
and step 3: the number of gamma photon pairs recorded by detector pair A, B that have multiple scatter coincidence events occurring is calculated.
In the three-dimensional data acquisition mode, a gamma photon multiple scattering correction mathematical model is established based on gamma photon pairs recorded by the detector pair A, B and subjected to multiple scattering coincidence events:
step 1-1: transforming the spatial coordinate system XYZ into a polar coordinate system
Figure BSA0000250409330000051
Order to
Figure BSA0000250409330000052
As a function of the spatial distribution of the nuclides,
Figure BSA0000250409330000053
is the attenuation coefficient;
step 1-2: each gamma photon scattering event belongs to mutually independent events, so the probability density of multiple scattering can be completely calculated according to the mode of independent events, and I isS(A, B) is a gamma photon single scattering distribution function, KM(x, y, z) is a Gaussian kernel function of the multiple scattering probability distribution of gamma photons, and the calculation formula is as follows:
Figure BSA0000250409330000054
step 1-3: gamma photon multiple scattering distribution IM(A, B) is regarded as the convolution of a gamma photon single scattering distribution function and a multiple scattering Gaussian kernel function, and the calculation formula is as follows:
Figure BSA0000250409330000061
where V is the gamma photon detection space.
As shown in fig. 2, the computation steps of transforming XYZ, a spatial three-dimensional coordinate system to L θ, γ -photon multiple scattering distribution gaussian kernel function after the reconstruction of the LoR data are as follows:
step 2-1: calculating a Gaussian fitting coefficient delta, wherein the calculation formula is as follows:
Figure BSA0000250409330000062
wherein deltaMIs a Gaussian function coefficient, delta, of the spatial distribution fitting gamma photon multiple scatteringSIs a Gaussian function coefficient of space distribution fitting gamma photon single scattering;
step 2-2: and (3) calculating a gamma photon multiple scattering distribution Gaussian kernel function, wherein the calculation formula is as follows:
Figure BSA0000250409330000063
where a is the gaussian fit coefficient.
The calculation of the number of pairs of gamma photons recorded by the detector pair A, B for which multiple scatter coincidence events occur is as follows:
step 3-1: substituting equation (4) into equation (2), the number of gamma photon pairs recorded by detector pair A, B for which multiple scatter coincidence events occur is as follows:
Figure BSA0000250409330000064
for better illustration, as shown in fig. 3, the detection object is an industrial hydraulic part, for example, gamma photon three-dimensional imaging detection is performed on the cylinder body structure of the hydraulic part and the shape of a piston rod nut, the inner diameter of the cylinder body of the hydraulic part is 63mm, the outer diameter of the cylinder body of the hydraulic part is 73mm, the material is alloy steel, firstly hydraulic oil with the activity of 0.85mCi and marked with nuclide 18F is injected into a hydraulic part through a hydraulic hole, the hydraulic part is kept inverted to ensure that the piston rod nut of the cylinder body is immersed in the hydraulic oil marked with the nuclide, the hydraulic part is placed in a gamma photon detection system, the time window of the gamma photon detection system is set to be 1ns, the energy window is 434KeV-587KeV, the gamma photon acquisition time is 5s, image reconstruction is performed on the gamma photon data before and after scattering correction by iterating four times by using an OSEM algorithm, the subset is divided into 4 hydraulic oil, because the piston rod nut of the cylinder body is immersed in the hydraulic oil, the nut imaging area in the gamma photon three-dimensional reconstruction image can be covered by the nuclide distribution area, so the cross section shape of the nut in the gamma photon two-dimensional slice image is selected for analysis, as shown in figure 4, the gamma photon reconstruction image containing scattering is shown, as the gamma photon containing scattering is included in the image reconstruction process, star-shaped artifacts appear on the edge of the hydraulic part cylinder body and the edge of the piston rod nut, the edge profile of the nut is implicitly distinguished, and the shape of the nut cannot be determined, as shown in figure 5, the gamma photon reconstruction image after multiple scattering correction based on space distribution fitting is shown, after the interference of the gamma photon of single scattering is eliminated, the edge of the hydraulic part cylinder body and the edge of the piston rod nut become clear, as the piston rod nut does not generate the gamma photon, the cross section where the piston rod nut is positioned is imaged into a black image, after the interference of the gamma photon of multiple scattering is eliminated, compared with the imaging result of fig. 4, the edge artifact disappears, and the black area in the cross-sectional image where the piston rod nut is located is enlarged, so that the effectiveness of the gamma photon multiple scattering correction method based on spatial distribution fitting provided by the invention can be seen.
According to the invention, gamma photon multiple scattering is regarded as superposition of multiple single scattering of gamma photon, gamma photon sampling data is projected according to a storage mode of LoR in Root, function fitting is respectively carried out on discrete gamma photon single scattering distribution and multiple scattering distribution, the expression form of a kernel function is determined, the multiple scattering number of gamma photon recorded by each detector in a detection system is calculated, finally, the multiple scattering gamma photon is removed from the original gamma photon data, the purpose of gamma photon multiple scattering correction is achieved, and the accuracy of gamma photon multiple scattering identification is improved
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Details not described in the present application are well within the skill of those in the art.

Claims (4)

1.一种基于空间分布拟合的γ光子多次散射校正方法，具体包括以下步骤：1. A gamma photon multiple scattering correction method based on spatial distribution fitting, specifically comprising the following steps: 步骤1：在三维数据采集模式下，基于探测器对A、B记录的发生多次散射符合事件的γ光子对，建立γ光子多次散射校正数学模型；Step 1: In the three-dimensional data acquisition mode, based on the γ photon pairs with multiple scattering coincidence events recorded by the detector pairs A and B, establish a γ photon multiple scattering correction mathematical model; 步骤2：将空间三维坐标系XYZ投影变换到LoR数据重组后的二维坐标系Lθ，得出γ光子多次散射分布高斯核函数；Step 2: Transform the spatial three-dimensional coordinate system XYZ to the two-dimensional coordinate system Lθ after the LoR data recombination, and obtain the Gaussian kernel function of the γ photon multiple scattering distribution; 步骤3：计算探测器对A、B记录的发生多次散射符合事件的γ光子对数目。Step 3: Calculate the number of γ-photon pairs with multiple scattering coincidence events recorded by the detector pair A and B. 2.根据权利要求1所述的基于空间分布拟合的γ光子多次散射校正方法，其特征在于：在三维数据采集模式下，基于探测器对A、B记录的发生多次散射符合事件的γ光子对，γ光子多次散射校正数学模型的建立步骤如下：2. The gamma photon multiple scattering correction method based on spatial distribution fitting according to claim 1, characterized in that: in the three-dimensional data acquisition mode, based on the occurrence of multiple scattering events recorded by detectors A and B, For γ photon pairs, the steps for establishing the mathematical model of γ photon multiple scattering correction are as follows: 步骤1-1：将空间坐标系XYZ变换为极坐标系
Figure FSA0000250409320000011
令
Figure FSA0000250409320000012
为核素空间分布函数，
Figure FSA0000250409320000013
为衰减系数；Step 1-1: Transform the spatial coordinate system XYZ into a polar coordinate system
Figure FSA0000250409320000011
make
Figure FSA0000250409320000012
is the nuclide spatial distribution function,
Figure FSA0000250409320000013
is the attenuation coefficient; 步骤1-2：每次γ光子散射事件属于互相独立事件，因此多次散射的概率密度完全可以按照独立事件的方式进行计算，令IS(A，B)为γ光子单次散射分布函数，KM(x，y，z)为γ光子多次散射概率分布高斯核函数，其计算公式如下：Step 1-2: Each γ photon scattering event is an independent event, so the probability density of multiple scattering can be calculated in the way of independent events. Let I S (A, B) be the γ photon single scattering distribution function, K M (x, y, z) is the Gaussian kernel function of the multiple scattering probability distribution of γ photons, and its calculation formula is as follows:
Figure FSA0000250409320000014
Figure FSA0000250409320000014
 步骤1-3：γ光子多次散射分布IM(A，B)看作是γ光子单次散射分布函数和多次散射高斯核函数的卷积，其计算公式如下：Step 1-3: The γ photon multiple scattering distribution I M (A, B) is regarded as the convolution of the γ photon single scattering distribution function and the multiple scattering Gaussian kernel function, and the calculation formula is as follows:
Figure FSA0000250409320000015
Figure FSA0000250409320000015
 其中V是γ光子探测空间。where V is the gamma photon detection space. 3.根据权利要求1所述的基于空间分布拟合的γ光子多次散射校正方法，其特征在于：将空间三维坐标系XYZ投影变换到LoR数据重组后的二维坐标系Lθ，γ光子多次散射分布高斯核函数的计算步骤如下：3. The gamma photon multiple scattering correction method based on spatial distribution fitting according to claim 1, is characterized in that: the spatial three-dimensional coordinate system XYZ is projected and transformed to the two-dimensional coordinate system Lθ after LoR data reorganization, and the gamma photon is many. The calculation steps of the Gaussian kernel function of the subscattering distribution are as follows: 步骤2-1：计算高斯拟合系数δ，其计算公式如下：Step 2-1: Calculate the Gaussian fitting coefficient δ, and its calculation formula is as follows:
Figure FSA0000250409320000021
Figure FSA0000250409320000021
 其中δM是空间分布拟合γ光子多次散射的高斯函数系数，δS是空间分布拟合γ光子单次散射的高斯函数系数；where δ M is the Gaussian function coefficient of the spatial distribution fitting the multiple scattering of γ photons, and δ S is the Gaussian function coefficient of the spatial distribution fitting the single scattering of γ photons; 步骤2-2：计算γ光子多次散射分布高斯核函数，其计算公式如下：Step 2-2: Calculate the Gaussian kernel function of the γ photon multiple scattering distribution, the calculation formula is as follows:
Figure FSA0000250409320000022
Figure FSA0000250409320000022
 其中A是高斯拟合系数。where A is the Gaussian fitting coefficient. 4.根据权利要求1所述的基于轨迹映射的γ光子单次散射校正方法，其特征在于：探测器对A、B记录的发生多次散射符合事件的γ光子对数目的计算过程如下：4. the γ photon single scattering correction method based on trajectory mapping according to claim 1, is characterized in that: the calculation process of the number of γ photon pairs that the detector records to A, B and the occurrence of multiple scattering coincidence events is as follows: 步骤3-1：将公式(4)代入公式(2)，探测器对A、B记录的发生多次散射符合事件的γ光子对数目如下：Step 3-1: Substitute formula (4) into formula (2), the number of γ photon pairs with multiple scattering coincidence events recorded by the detector pair A and B is as follows:
Figure FSA0000250409320000023
Figure FSA0000250409320000023
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