CN113670961A - Gamma photon multiple scattering correction method based on space distribution fitting - Google Patents
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Abstract
The invention discloses a gamma photon multiple scattering correction method based on space distribution fitting, which comprises the steps of regarding gamma photon multiple scattering as superposition of multiple single scattering of gamma photons, projecting gamma photon sampling data according to a storage mode of LoR in Root, respectively carrying out function fitting on discrete gamma photon single scattering distribution and multiple scattering distribution, determining an expression form of a kernel function, calculating the multiple scattering number of gamma photons recorded by each detector in a detection system, and finally removing the multiple scattering gamma photons from original gamma photon data. The method effectively solves the image distortion conditions of star radiation artifacts, edge blurring and the like of the reconstructed image caused by the scattered gamma photons, thereby achieving the purpose of gamma photon multiple scattering correction and improving the gamma photon multiple scattering identification accuracy.
Description
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
Order to
As a function of the spatial distribution of the nuclides,
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:
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:
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:
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:
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:
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
Order to
As a function of the spatial distribution of the nuclides,
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:
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:
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:
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:
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:
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. 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.
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 gamma photon pair recorded by the detector pair A, B and having multiple scattering coincidence events, the gamma photon multiple scattering correction mathematical model is established as follows:
step 1-1: transforming the spatial coordinate system XYZ into a polar coordinate system
Order to
As a function of the spatial distribution of the nuclides,
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:
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:
where V is the gamma photon detection space.
3. The gamma photon multiple scattering correction method based on spatial distribution fitting according to claim 1, characterized in that: 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:
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:
where a is the gaussian fit coefficient.
4. The trajectory mapping-based gamma photon single scatter correction method of claim 1, wherein: 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:
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