Multi-energy CT scattering correction method and device based on Boltzmann transport equation

Abstract

This application relates to the field of radiation imaging technology, and in particular to a multi-energy CT scattering correction method and apparatus based on the Boltzmann transport equation. The method includes: preprocessing the initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object to obtain initial corrected multi-energy projection data; performing material density conversion on the initial corrected multi-energy projection data to obtain material density distribution data; discretizing and labeling the actual scanning energy spectrum of the object during the multi-energy CT scanning process to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation; calculating the multi-energy scattering signal data of the object; and using the multi-energy scattering signal data to obtain the actual multi-energy projection data. This solves the problems in related technologies, such as insufficient scattering correction leading to distortion of material density obtained from material decomposition, and the need for multiple scattering estimates under different X-ray source conditions due to the multi-energy spectrum, resulting in a lengthy and complex processing procedure.

Description

Technical Field

[0001] This application relates to the field of radiation imaging technology, and in particular to a multi-energy CT scattering correction method and device based on the Boltzmann transport equation. Background Technology

[0002] Computed tomography (CT) is a commonly used non-destructive testing technique that can obtain information about the internal structure of the object being examined without damaging it. ME-CBCT (Multi-Energy Cone Beam Computed Tomography) is one such technique.

[0003] It is a type of CT that has developed rapidly in recent years. Compared with traditional single-energy CBCT, it can provide stronger material discrimination and more material structure information, and has been widely used in medical diagnosis and security inspection.

[0004] In related technologies, Monte Carlo simulations of the multi-energy CBCT scanning process can be performed based on Beer's law and Compton scattering formula, combined with a database of physical parameters such as the attenuation coefficient and scattering factor of the material, to obtain the corresponding scattering signal and thus achieve scattering correction. Alternatively, considering the low-frequency nature of the scattering signal, the frequency domain distribution of the scattering signal in the image can be modeled to construct a scattering kernel, which can then be combined with an iterative algorithm to achieve scattering correction. Another approach is to use actual or simulated data, with images containing scattering as the training set and images without scattering as labels, to train a relevant network using deep learning techniques to obtain the corresponding scattering signal, thereby achieving scattering correction and reducing scattering artifacts.

[0005] However, in related technologies, since the material decomposition counting used in energy spectrum imaging is very sensitive to the energy spectrum, some simple descattering methods, even if they can remove most of the scattering, will lead to serious distortion of the obtained material density. Furthermore, due to the multi-energy spectrum, multiple scattering estimates need to be performed under different X-ray source conditions, making the processing lengthy and complex, and urgently needing improvement. Summary of the Invention

[0006] This application provides a multi-energy CT scattering correction method and device based on the Boltzmann transport equation to solve the problems in related technologies, such as the fact that material decomposition is very sensitive to the energy spectrum, and that some simple descattering methods, even if they can remove most of the scattering, will lead to serious distortion of the material density obtained by material decomposition. Furthermore, due to the multi-energy spectrum, multiple scattering estimates need to be performed under different X-ray source conditions, which makes the processing process lengthy and complicated.

[0007] The first aspect of this application provides a multi-energy CT scattering correction method based on the Boltzmann transport equation, comprising the following steps: preprocessing the initial multi-energy projection data to be corrected obtained after multi-energy computed tomography (CT) scanning of an object to obtain preprocessed initial corrected multi-energy projection data; performing material density conversion on the initial corrected multi-energy projection data to obtain material density distribution data after material density conversion; discretizing and labeling the actual scanning energy spectrum of the object during the multi-energy CT scanning process to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum; calculating the multi-energy scattering signal data of the object in the multi-energy CT scan based on the final scattering signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the material density distribution data; and using the multi-energy scattering signal data to perform scattering correction on the initial multi-energy projection data to obtain the actual multi-energy projection data of the object after scattering correction.

[0008] Optionally, in one embodiment of this application, before calculating the multi-energy scattering signal data of the object in multi-energy CT scanning based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the matter density distribution data, the method further includes: constructing a static Boltzmann transport equation during the multi-energy CT scanning process; obtaining the photon flux integral expression and photon flux differential expression of the photon flux, and the photon source term integral expression and photon source term differential expression of the photon flux and photon source term in the static Boltzmann transport equation during the multi-energy CT scanning process; and obtaining the discrete expression of the photon flux and the photon source term based on the photon flux integral expression, the photon flux differential expression, the photon source term integral expression, and the photon source term differential expression. The photon source term is discretely expressed; based on the photon flux integral expression, the photon flux differential expression, the photon source term integral expression, and the photon source term differential expression, an initial scattered signal intensity equation is generated for the scattered signal during the multi-energy CT scan; the initial scattered signal intensity equation is discretized using the photon flux discrete expression and the photon source term discrete expression to obtain the final scattered signal intensity equation after discretization of the initial scattered signal intensity equation; based on the photon flux discrete expression, the photon source term discrete expression, and the final scattered signal intensity equation, at least one labeled dimension of the static Boltzmann transport equation is determined; based on the photon flux discrete expression, the photon source term discrete expression, the final scattered signal intensity equation, and the at least one labeled dimension, a labeled Boltzmann transport equation is constructed.

[0009] Optionally, in one embodiment of this application, the step of discretizing and tagging the actual scan energy spectrum of the object during multi-energy CT scanning, and determining the energy spectrum matrix in the pre-constructed tagged Boltzmann transport equation based on the discretized and tagged actual scan energy spectrum, includes: determining whether the number of discretized and tagged actual scan energy spectra is greater than half the number of preset discrete energy groups; if the number of discretized and tagged actual scan energy spectra is greater than half the number of preset discrete energy groups, then based on the preset discrete energy groups... The number of columns determines the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation, wherein the energy spectrum matrix is ​​an identity matrix; if the number of actual scanned energy spectra after discretization and labeling is less than or equal to half the number of preset discrete energy groups, then the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation are determined based on the number of actual scanned energy spectra after discretization and labeling, wherein each column vector in the energy spectrum matrix is ​​the energy spectrum vector of each actual scanned energy spectrum after discretization and labeling.

[0010] Optionally, in one embodiment of this application, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as:

[0011]

[0012] in, Let be the magnitude of the angular flux of a photon with voxel i, energy group g, emission direction m, tag l, and scattering order n at position i; For voxel i w′ The average linear decay coefficient at position i over the energy group g, where i w′ The voxel number where path w′ is located; w′ is a vector. The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; The intensity of a photon source at position i, with energy group g, emission direction m, tag l, and scattering order n+1; μ s；i,g′→g,m′→m Let i be a voxel at position i, with a discrete angle m′ and energy group g′. Let g′ be the scattering cross section of a photon with a discrete angle m and energy group g. Let be the angular flux of a photon at position i, energy group g′, emission direction m′, tag l, and scattering order n. Let i be the position of voxel i, energy group g, and emission direction m (this direction m is determined by...) The direction determines the intensity of the photon source labeled l and with a scattering order of k. d Let d be the area of ​​pixel d, and θ be... The angle E between the vector and the normal vector of pixel d g Let D(E) be the average energy of energy group g. g ) for the detector at energy E g Lower detector gain, Let be the spatial position vector of voxel i. Let be the spatial position vector of the detector pixel d, where i is the discrete voxel index, identifying the discrete spatial position; g is the energy group index, identifying the position of different discrete energy groups; m is the discrete solid angle index, identifying different spatial directions; l is the tag index, used to identify photons from different energy spectra; k is the scattering order, which exists as a summation variable in the formula; N is the total number of discretized voxels; G is the number of discretized energy groups; K is the highest scattering order selected for calculation; n is the scattering order (i.e., the photon was scattered n times); n+1 is the scattering order (i.e., the photon was scattered n+1 times).

[0013] Optionally, in one embodiment of this application, the expression for the final scattered signal intensity equation may be, but is not limited to, as:

[0014]

[0015] A second aspect of this application provides a multi-energy CT scattering correction device based on the Boltzmann transport equation, comprising: a preprocessing module for preprocessing initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object, to obtain preprocessed initial corrected multi-energy projection data; a material density conversion module for converting the initial corrected multi-energy projection data into material density data to obtain material density distribution data after material density conversion; and an energy spectrum discrete labeling module for marking the actual energy distribution of the object during the multi-energy CT scanning process. The actual scanning energy spectrum is discretized and labeled to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum; a calculation module is used to calculate the multi-energy scattering signal data of the object in multi-energy CT scanning based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the material density distribution data; a scattering correction module is used to perform scattering correction on the initial multi-energy projection data using the multi-energy scattering signal data to obtain the actual multi-energy projection data of the object after scattering correction.

[0016] Optionally, in one embodiment of this application, it further includes: a first construction module, used to construct a static Boltzmann transport equation during the multi-energy CT scan process before calculating the multi-energy scattering signal data of the object in the multi-energy CT scan based on the final scattering signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the matter density distribution data; a first acquisition module, used to acquire the photon flux integral expression and photon flux differential expression of the photon flux, and the photon source term integral expression and photon source term differential expression of the photon flux and photon source term in the static Boltzmann transport equation during the multi-energy CT scan process; a second acquisition module, used to acquire the discrete expression of the photon flux and the photon source term based on the photon flux integral expression, the photon flux differential expression, the photon source term integral expression, and the photon source term differential expression. The system comprises: a discrete expression of the photon source term; a generation module, used to generate an initial scattered signal intensity equation for the scattered signal during the multi-energy CT scan based on the integral expression of the photon flux, the differential expression of the photon flux, the integral expression of the photon source term, and the differential expression of the photon source term; a correction module, used to discretize the initial scattered signal intensity equation using the discrete expression of the photon flux and the discrete expression of the photon source term to obtain a final scattered signal intensity equation after discretization of the initial scattered signal intensity equation; a determination module, used to determine at least one label dimension of the static Boltzmann transport equation based on the discrete expression of the photon flux, the discrete expression of the photon source term, and the final scattered signal intensity equation; and a second construction module, used to construct a labeled Boltzmann transport equation based on the discrete expression of the photon flux, the discrete expression of the photon source term, the final scattered signal intensity equation, and the at least one label dimension.

[0017] Optionally, in one embodiment of this application, the energy spectrum discretization and labeling module includes: a judgment unit, configured to determine whether the number of actual scanned energy spectra after discretization and labeling is greater than half of the number of preset discrete energy groups; a first determination unit, configured to determine the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the number of preset discrete energy groups when the number of actual scanned energy spectra after discretization and labeling is greater than half of the number of preset discrete energy groups, wherein the energy spectrum matrix is ​​an identity matrix; and a second determination unit, configured to determine the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the number of actual scanned energy spectra after discretization and labeling when the number of actual scanned energy spectra after discretization and labeling is less than or equal to half of the number of preset discrete energy groups, wherein each column vector in the energy spectrum matrix is ​​the energy spectrum vector of each actual scanned energy spectrum after discretization and labeling.

[0018] Optionally, in one embodiment of this application, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as:

[0019]

[0020] in, Let be the magnitude of the angular flux of a photon with voxel i, energy group g, emission direction m, tag l, and scattering order n at position i; For voxel i w′ The average linear decay coefficient at position i over the energy group g, where i w′ The voxel number where path w′ is located; w′ is a vector. The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; The intensity of a photon source at position i, with energy group g, emission direction m, tag l, and scattering order n+1; μ s；i,g′→g,m′→m Let i be a voxel at position i, with a discrete angle m′ and energy group g′. Let g′ be the scattering cross section of a photon with a discrete angle m and energy group g. Let be the angular flux of a photon at position i, energy group g′, emission direction m′, tag l, and scattering order n. Let i be the position of voxel i, energy group g, and emission direction m (this direction m is determined by...) The direction determines the intensity of the photon source labeled l and with a scattering order of k. d Let d be the area of ​​pixel d, and θ be... The angle E between the vector and the normal vector of pixel d g Let D(E) be the average energy of energy group g. g ) for the detector at energy E g Lower detector gain, Let be the spatial position vector of voxel i. Let be the spatial position vector of the detector pixel d, where i is the discrete voxel index, identifying the discrete spatial position; g is the energy group index, identifying the position of different discrete energy groups; m is the discrete solid angle index, identifying different spatial directions; l is the tag index, used to identify photons from different energy spectra; k is the scattering order, which exists as a summation variable in the formula; N is the total number of discretized voxels; G is the number of discretized energy groups; K is the highest scattering order selected for calculation; n is the scattering order (i.e., the photon was scattered n times); n+1 is the scattering order (i.e., the photon was scattered n+1 times).

[0021] Optionally, in one embodiment of this application, the expression for the final scattered signal intensity equation may be, but is not limited to, as:

[0022]

[0023] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the multi-energy CT scattering correction method based on the Boltzmann transport equation as described in the above embodiments.

[0024] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-energy CT scattering correction method based on the Boltzmann transport equation.

[0025] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, implements the above-described multi-energy CT scattering correction method based on the Boltzmann transport equation.

[0026] This application embodiment first preprocesses the initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object, thereby obtaining the preprocessed initial corrected multi-energy projection number and performing material density conversion to obtain the object's material density distribution data. Then, the multi-energy spectrum data is discretized and labeled to obtain the energy spectrum matrix. Then, combining the material density distribution data and the energy spectrum matrix, the multi-energy scattering signal data of the object in multi-energy CT scanning is calculated using a pre-constructed labeled Boltzmann transport equation. The initial multi-energy projection data is then scattered and corrected using the multi-energy scattering signal data to obtain the scattering-corrected actual multi-energy projection data. The multi-energy scattering signal data is calculated based on the pre-constructed labeled Boltzmann transport equation. By discretizing the phase space, the equation is transformed into an analytical solution, resulting in superior parallelism in the program, thereby improving the calculation speed and portability. For the scattering correction requirements in multi-energy CT, an additional label dimension is introduced to achieve vectorization of the energy group space, thereby reducing the amount of computation and enabling the acquisition of scattering signals under multiple energy spectra in a single calculation. This solves the problems in related technologies, such as the fact that material decomposition is very sensitive to the energy spectrum, and that some simple descattering methods, even if they can remove most of the scattering, will lead to serious distortion of the material density obtained by material decomposition. Furthermore, due to the multi-energy spectrum, multiple scattering estimates need to be performed under different X-ray source conditions, which makes the processing lengthy and complicated.

[0027] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0028] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0029] Figure 1 This is a flowchart of a multi-energy CT scattering correction method based on the Boltzmann transport equation provided in an embodiment of this application;

[0030] Figures 2(a)-2(d) This is a schematic diagram comparing the scattering estimation results provided according to an embodiment of this application with those obtained using the Monte Carlo method with the Geant4 tool;

[0031] Figure 3 This is a schematic diagram comparing images of projections acquired on a multi-energy CT scanner before and after scattering correction, as well as fan beam standard values, according to an embodiment of this application.

[0032] Figure 4 This is a flowchart illustrating the working principle of a multi-energy CT scattering correction method based on the Boltzmann transport equation according to an embodiment of this application;

[0033] Figure 5 This is a block diagram of a multi-energy CT scattering correction device based on the Boltzmann transport equation provided in an embodiment of this application;

[0034] Figure 6 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0035] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0036] The following describes a multi-energy CT scattering correction method and apparatus based on the Boltzmann transport equation, according to embodiments of this application, with reference to the accompanying drawings. Addressing the issues mentioned in the background art, where material decomposition is highly sensitive to the energy spectrum, some simple descattering methods, even if they remove most of the scattering, can lead to severe distortion of the material density obtained from material decomposition. Furthermore, due to the multi-energy spectrum, multiple scattering estimates need to be performed under different X-ray source conditions, resulting in a lengthy and complex processing procedure. This application provides a multi-energy CT scattering correction method based on the Boltzmann transport equation. In this method, the initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object can be preprocessed to obtain the preprocessed initial corrected multi-energy projection data, and then material density conversion can be performed to obtain the material density. The material density distribution data of the object is obtained, and then the multi-energy spectrum data is discretized and labeled to obtain the energy spectrum matrix. Combining the material density distribution data and the energy spectrum matrix, a pre-constructed labeled Boltzmann transport equation is used to calculate the multi-energy scattering signal data of the object in multi-energy CT scanning. The initial multi-energy projection data is then corrected using the multi-energy scattering signal data to obtain the corrected actual multi-energy projection data. The multi-energy scattering signal data is calculated based on the pre-constructed labeled Boltzmann transport equation. By discretizing the phase space, the equation is transformed into an analytical solution, resulting in superior parallelism and improved computational speed and portability. For the scattering correction requirements in multi-energy CT, an additional label dimension is introduced to vectorize the energy group space, thereby reducing the computational load and enabling the acquisition of scattering signals under multiple energy spectra in a single calculation. This solves the problems in related technologies, such as the fact that material decomposition is very sensitive to the energy spectrum, and that some simple descattering methods, even if they can remove most of the scattering, will lead to serious distortion of the material density obtained by material decomposition. Furthermore, due to the multi-energy spectrum, multiple scattering estimates need to be performed under different X-ray source conditions, which makes the processing lengthy and complicated.

[0037] Specifically, Figure 1 This is a flowchart of a multi-energy CT scattering correction method based on the Boltzmann transport equation provided in an embodiment of this application.

[0038] like Figure 1 As shown, the multi-energy CT scattering correction method based on the Boltzmann transport equation includes the following steps:

[0039] In step S101, the initial multi-energy projection data to be corrected obtained after the object is scanned by multi-energy CT is preprocessed to obtain the initial corrected multi-energy projection data after the initial multi-energy projection data to be corrected is preprocessed.

[0040] As one possible implementation method, embodiments of this application can acquire multiple energy spectra of an object during the scanning process and initial multi-energy projection data under each energy spectrum through multi-energy CT scanning. Then, embodiments of this application preprocess the initial multi-energy projection data, such as coarse scattering correction and hardening correction, etc. This application does not impose specific limitations, thereby obtaining the initial corrected multi-energy projection data after the initial projection data preprocessing.

[0041] For example, embodiments of this application can utilize multiple energy spectra S obtained from an object through multi-energy CT scanning. l ,l=1,2,…,L and initial multi-energy projection data P under each energy spectrum l (N D Given that l = 1, 2, 3, ..., L, let P = [P1, P2, ..., P...]. L ](N D ×L), and coarse scattering correction and hardening correction are performed in the projection domain to obtain the preprocessed initial corrected multi-energy projection data P. f .

[0042] For example, this application's embodiments employ a three-dimensional rectangular coordinate system. In terms of voxel discretization, the object is discretized into 16×16×16 uniformly sized cubic units. Regarding solid angles, following a discretization method similar to latitude and longitude in geography, the 4π solid angle is divided into 16 longitudes and 9 latitudes at intervals of π / 8, resulting in a total of 114 discrete angles. In terms of energy, the energy spectrum from 0 to E is used to further divide the solid angles. max The range is approximately uniformly divided into 8 energy groups.

[0043] Therefore, in this embodiment, two sets of initial multi-energy projection data of an object can be obtained through multi-energy CT scanning, which can be, but are not limited to, represented as p1 and p2. Then, coarse scattering correction and hardening correction processing are performed on the initial multi-energy projection data to obtain pre-processed initial corrected multi-energy projection data, which can be, but are not limited to, represented as...

[0044] In step S102, the initial corrected multi-energy projection data is converted to material density to obtain the material density distribution data after the initial corrected multi-energy projection data is converted to material density.

[0045] For example, embodiments of this application can use multiple energy spectra S l ,l=1,2,…,L and initial corrected multi-energy projection data P f This application does not impose specific limitations on the conversion of material density, such as material decomposition or pre-reconstruction, to obtain the material density distribution data ρ of the object. l The density distribution data of the material, l = 1, 2, ..., L, can be used as input to a pre-constructed labeled Boltzmann transport equation.

[0046] In some embodiments, the present application can perform material decomposition based on the initial corrected multi-energy projection data to directly obtain multi-material density projection data and reconstruct the material density distribution data of the object during the multi-energy CT scanning process.

[0047] For example, embodiments of this application can be based on initial calibrated multi-energy projection data. By performing material decomposition to obtain multi-material density projection data, and then reconstructing it, two types of material density distribution data can be obtained, which can be, but are not limited to, represented as ρ1 and ρ2.

[0048] In some embodiments, the present application can perform material decomposition based on initial corrected multi-energy projection data to obtain a virtual mono-energy reconstructed image, and then convert the HU value data into material density distribution data of the object during the multi-energy CT scanning process based on the material conversion curve.

[0049] For example, embodiments of this application may first be based on initial calibrated multi-energy projection data. The material is decomposed to obtain multi-material density projection data, which is then weighted and summed to obtain virtual monoenergetic projection data. Three-dimensional reconstruction is then performed to obtain a virtual monoenergetic reconstruction image. Through the material conversion curve, two material density distribution data are obtained, which can be, but are not limited to, represented as ρ1 and ρ2.

[0050] In some embodiments, the present application can perform pre-reconstruction based on initial corrected projection data at a certain energy to obtain a three-dimensional reconstructed image, and then convert the HU value data into material density distribution data of the object during the multi-energy CT scanning process based on the material conversion curve.

[0051] For example, embodiments of this application can be based on initial corrected projection data at a certain energy level. A three-dimensional reconstructed image is obtained by performing a pre-reconstruction, and then two material density distribution data are obtained through the material conversion curve, which can be, but are not limited to, represented as ρ1 and ρ2.

[0052] Optionally, in one embodiment of this application, before calculating the multi-energy scattering signal data of an object in a multi-energy CT scan based on the final scattered signal intensity equation, energy spectrum matrix, and matter density distribution data in the pre-constructed labeled Boltzmann transport equation, the method further includes: constructing a static Boltzmann transport equation during the multi-energy CT scan process; obtaining the photon flux integral expression and photon flux differential expression of the photon flux, and the photon source term integral expression and photon source term differential expression of the photon flux and photon source term in the static Boltzmann transport equation during the multi-energy CT scan process; and obtaining the discrete expression of the photon flux based on the photon flux integral expression, photon flux differential expression, photon source term integral expression, and photon source term differential expression. Discrete expression of the photon source term; based on the integral expression, differential expression, integral expression, and differential expression of the photon source term, generate the initial scattered signal intensity equation for the scattered signal during multi-energy CT scanning; discretize the initial scattered signal intensity equation using the discrete expressions of photon flux and photon source term to obtain the final scattered signal intensity equation after discretization; determine at least one label dimension of the static Boltzmann transport equation based on the discrete expressions of photon flux, photon source term, and the final scattered signal intensity equation; construct a labeled Boltzmann transport equation based on the discrete expressions of photon flux, photon source term, the final scattered signal intensity equation, and at least one label dimension. The expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as follows:

[0053]

[0054] in, Let be the magnitude of the angular flux of a photon with voxel i, energy group g, emission direction m, tag l, and scattering order n at position i; For voxel i w′ The average linear decay coefficient at position i over the energy group g, where i w′ The voxel number where path w′ is located; w′ is a vector. The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; The intensity of a photon source at position i, with energy group g, emission direction m, tag l, and scattering order n+1; μ s；i,g′→g,m′→m Let i be a voxel at position i, with a discrete angle m′ and energy group g′. Let g′ be the scattering cross section of a photon with a discrete angle m and energy group g. Let be the angular flux of a photon at position i, energy group g′, emission direction m′, tag l, and scattering order n. Let i be the position of voxel i, energy group g, and emission direction m (this direction m is determined by...) The direction determines the intensity of the photon source labeled l and with a scattering order of k. d Let d be the area of ​​pixel d, and θ be... The angle E between the vector and the normal vector of pixel d g Let D(E) be the average energy of energy group g. g ) for the detector at energy E g Lower detector gain, Let be the spatial position vector of voxel i. Let be the spatial position vector of the detector pixel d, where i is the discrete voxel index, identifying the discrete spatial position; g is the energy group index, identifying the position of different discrete energy groups; m is the discrete solid angle index, identifying different spatial directions; l is the tag index, used to identify photons from different energy spectra; k is the scattering order, which exists as a summation variable in the formula; N is the total number of discretized voxels; G is the number of discretized energy groups; K is the highest scattering order selected for calculation; n is the scattering order (i.e., the photon was scattered n times); n+1 is the scattering order (i.e., the photon was scattered n+1 times).

[0055] Those skilled in the art will understand that the embodiments of this application can be based on the Boltzmann transport equation concerning the transport and scattering of photons in CT scans. Considering the very short interaction time between photons and matter, the relaxation time is ignored in the model, and the system is assumed to reach static equilibrium instantaneously. Based on the above description, the embodiments of this application can construct a static Boltzmann transport equation in the process of multi-energy CT scanning, which can be, but is not limited to, expressed as:

[0056]

[0057] in, This represents the position vector of a photon in three-dimensional space. The vector represents the direction of motion of the photon in three-dimensional space; E represents the energy carried by the photon. Indicates in Position, direction of movement The flux of photons carrying energy E; Indicates in Position, direction of movement The number of newly generated photons carrying energy E; Indicates in In terms of position, for a photon with energy E, the linear attenuation coefficient of the material; Indicates in Positionally, the direction of movement is A photon carrying energy E' interacts with matter and is scattered into a new direction of motion. The proportion of newly generated photons carrying energy E; Emax This represents the highest energy of a photon in a CT system, equivalent to the maximum photon energy emitted by the X-ray source.

[0058] Furthermore, embodiments of this application can obtain the photon flux integral expression and photon flux differential expression of photon flux and the photon source term integral expression and photon source term differential expression of photon flux and photon source term in the static Boltzmann transport equation during multi-energy CT scanning. Then, the discrete expression of photon flux, the discrete expression of photon source term, and the initial scattered signal intensity equation of the scattered signal are determined. The initial scattered signal intensity equation is then discretized using the discrete expression of photon flux and the discrete expression of photon source term to obtain the final scattered signal intensity equation after discretization, thereby constructing the Boltzmann transport equation.

[0059] For example, in this embodiment of the application, based on the physical process during CT scanning, the iterative source method is used to decouple equation (1). Considering the process of photon transport and scattering inside an object, the iterative source method is used to perform multi-order expansion of photon flux and photon source terms according to the number of photon scatterings, thereby obtaining the photon flux integral expression and photon flux differential expression, and the photon source term integral expression and photon source term differential expression, which can be, but are not limited to, expressed as:

[0060]

[0061] Where, φ (n) S is the photon flux term composed of photons scattered n times. (n) Let the photon scattering source term consist of photons scattered n times. This decouples the integral and differential terms, and the following relationship exists between the photon flux and the photon source term at each order:

[0062]

[0063] Additionally, it should be noted that in this embodiment, photons are emitted from the object and enter the detector for recording. During this stage, no photon scattering occurs, and the photon flux φ received by the detector is... D It can be expressed as, but is not limited to:

[0064]

[0065] Where u and w are both integral variables, and at this time, the energy deposition signal I received by the detector is... scatter That is, the initial scattered signal intensity equation can be expressed, but is not limited to, as:

[0066]

[0067] in, Let D(E) be the unit normal vector of the detector plane, and let D(E) be the energy response of the detector. Ideally, the detector can completely deposit energy for any energy photon, i.e., D(E) = 1.

[0068] Furthermore, embodiments of this application can select a suitable discretization scheme for the degenerate equation after decoupling the above integral and differential equations, and discretize the phase space. Discretization is performed to enable computer computation. Spatially, the object is discretized into N ordered voxels. In terms of energy, from 0 to E max The continuous energy is divided into G energy groups (E g Regarding solid angles, the 4π solid angle is discretized into M discrete spatial angles. This yields the discrete expression for photon flux and the discrete expression for photon source terms, which can be, but are not limited to, expressed as:

[0069]

[0070] Based on this, in the embodiments of this application, equations (7) and (8) can be written in matrix form, which can be, but are not limited to, expressed as:

[0071] Ф (n) =TS (n) ,S (n-1) =CФ (n)

[0072] (9)

[0073] After discretization, the final scattered signal intensity equation after discretization of the initial scattered signal intensity equation can be expressed, but is not limited to, as:

[0074]

[0075] Based on this, in the embodiments of this application, equation (10) can be written in matrix form, which can be, but is not limited to, expressed as:

[0076]

[0077] Furthermore, in this embodiment, based on the discrete expression of photon flux, the discrete expression of photon source terms, and the final scattered signal intensity equation, at least one label dimension is introduced into the phase space through a discrete phase space solution method (assuming L labels are introduced, this application does not impose a specific limitation). The phase space is then transformed from... Expand to The introduced label dimension is independent of the actual physical process. Based on this, for different labels l, the matrices F, T, C, D are completely identical, meaning they can be represented, but are not limited to, as:

[0078]

[0079] Furthermore, in the embodiments of this application, equation (12) can be reduced, and it can be expressed, but is not limited to, as follows:

[0080]

[0081] in, Let l be a matrix independent of l.

[0082] In this embodiment, only T, C, and D need to be calculated once in actual calculations. Adding the L dimension only increases the computational cost by 2K(L-1) sparse matrix multiplications, which is negligible compared to the computational cost of T, C, and D. The computational cost of calculations involving exponential operations in T and D matrix solving, and the tracking of intravoxel lengths, is far greater than the aforementioned sparse matrix multiplications. In other words, introducing the label dimension in this embodiment only increases the computational cost slightly, but makes it possible to simultaneously calculate scattering images under multiple different energy spectra. For multiple X-ray energy spectra... 1,2,…,L, denoted Calculate F, T, C, D, and thus obtain Scattering image Where I = [I1, I2, ..., I L ], I is of size N D ×L, N D I represents the number of pixels in the detector. l l = 1, 2, ..., L, and its size is N. D ×1.

[0083] In particular, in embodiments of this application, when L≥G or it is uncertain whether a new energy spectrum scan will be used subsequently, R can be constructed. G Given a basis for a space, we can take a set of basis vectors as an orthonormal basis E = [E1, E2, ..., E...]. G E is a G×G diagonal matrix, thus enabling the calculation of a set of basis scattering images. Among them, I E Size N D ×G. Therefore, for any energy spectrum... The corresponding scattering image can be easily obtained from the embodiments of this application. In this case, since the photoelectric effect and Compton effect are considered in the equation, the energy of the photon will only gradually decrease and not increase. Let energy group 1 be the highest energy group and energy group G be the lowest energy group, then for the fundamental energy spectrum E... i(That is, the energy spectrum with only group i having values), only the photon behavior of the low-energy energy groups of i, i + 1, i + 2,..., G - 1, G needs to be considered, without considering the behavior of the high-energy energy groups of 1, 2,..., i - 1. This enables the small amount of computation introduced by increasing the label dimension to be further reduced by half, and enables the judgment condition L ≥ G proposed above to be further corrected to L >= G / 2.

[0084] The above analysis shows that in the embodiment of the present application, if L < G / 2, the original energy spectrum is directly discretized and labeled by energy groups, introducing L labels; if L >= G / 2, the above energy spectrum basis vector method is introduced, introducing G labels, thereby enabling the optimization of the calculation speed.

[0085] Thereby constructing a Boltzmann transport equation with labels, which can be but is not limited to being expressed as:

[0086]

[0087] In step S103, the actual scan energy spectrum of the object during the multi-energy CT scan is discretized and labeled, so as to determine the energy spectrum matrix in the pre-constructed Boltzmann transport equation with labels based on the discretized and labeled actual scan energy spectrum.

[0088] As a possible implementation, the embodiment of the present application can discretize the actual scan energy spectrum of the object during the multi-energy CT scan into multiple energy spectrum vectors, and then combine the label dimension to obtain the energy spectrum matrix.

[0089] Optionally, in an embodiment of the present application, discretizing and labeling the actual scan energy spectrum of the object during the multi-energy CT scan to determine the energy spectrum matrix in the pre-constructed Boltzmann transport equation with labels based on the discretized and labeled actual scan energy spectrum includes: determining whether the number of the discretized and labeled actual scan energy spectra is greater than half of the number of preset discrete energy groups; if the number of the discretized and labeled actual scan energy spectra is greater than half of the number of preset discrete energy groups, determining the dimension and value of the energy spectrum matrix in the pre-constructed Boltzmann transport equation with labels based on the number of preset discrete energy groups, where the energy spectrum matrix is an identity matrix; if the number of the discretized and labeled actual scan energy spectra is less than or equal to half of the number of preset discrete energy groups, determining the dimension and value of the energy spectrum matrix in the pre-constructed Boltzmann transport equation with labels based on the number of the discretized and labeled actual scan energy spectra, where each column vector in the energy spectrum matrix is the energy spectrum vector of each discretized and labeled actual scan energy spectrum.

[0090] As one possible implementation, embodiments of this application can determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation by judging whether the number of actual scanned energy spectra after discretization and labeling is greater than half of a certain number of discrete energy groups. Specifically, embodiments of this application can determine the dimension and value of the energy spectrum matrix based on the number of discrete energy groups when the number of actual scanned energy spectra after discretization and labeling is greater than half of the preset number of discrete energy groups, wherein the energy spectrum matrix is ​​an identity matrix; when the number of actual scanned energy spectra after discretization and labeling is less than or equal to half of the preset number of discrete energy groups, the dimension and value of the energy spectrum matrix can be determined based on the number of actual scanned energy spectra after discretization and labeling, wherein each column vector in the energy spectrum matrix is ​​the energy spectrum vector after discretization of each actual scanned energy spectrum after discretization and labeling. The certain number of discrete energy groups can be set by those skilled in the art according to actual circumstances, and this application does not impose specific limitations.

[0091] For example, in the embodiments of this application, L different initial energy spectra S are actually used in the multi-energy CT scanning process. l The data is then discretized and sampled into a certain number of scattering energy spectra, such as G specific scattering energy spectra. Obtain the matrix If L <= G / 2, then the energy spectrum matrix is ​​determined to be S with dimensions G×L; if L > G / 2, then the energy spectrum matrix is ​​determined to be the identity matrix E with dimensions G×G.

[0092] In step S104, based on the final scattered signal intensity equation, energy spectrum matrix, and matter density distribution data in the pre-constructed tagged Boltzmann transport equation, the multi-energy scattered signal data of the object in multi-energy CT scanning is calculated. The expression for the final scattered signal intensity equation can be, but is not limited to, as follows:

[0093]

[0094] It is understood that the inputs to the pre-constructed labeled Boltzmann transport equation in the embodiments of this application may include, but are not limited to, material density distribution data, geometric parameters, and discretization parameters, etc., and this application does not impose specific limitations. Among them, geometric parameters may include, but are not limited to, source-detector distance, detector size, detector offset, etc., and this application does not impose specific limitations; discretization parameters may include, but are not limited to, the number of voxels N, the number of discrete angles M, the number of energy groups G, etc., and this application does not impose specific limitations.

[0095] Additionally, it should be noted that in the embodiments of this application, the calculation of the pre-constructed labeled Boltzmann transport equations is implemented by computer programming and uses GPUs for parallel acceleration calculations. The specific settings can be made by those skilled in the art according to the actual situation, and this application does not impose any specific limitations.

[0096] In some embodiments, the present application can use material density distribution data and energy spectrum matrix as inputs to a pre-constructed labeled Boltzmann transport equation to calculate the multi-energy scattering signal data of the object. The main steps in calculating the multi-energy scattering signal data of the object in the present application can be as follows: First, determine whether the number of actual scanned energy spectra after discretization and labeling during multi-energy CT scanning is greater than half the number of a certain number of discrete energy groups. If the number of actual scanned energy spectra after discretization and labeling is greater than half the number of a certain number of discrete energy groups, combine the energy spectrum matrix and material density distribution data, and calculate the scattering signal intensity using the final scattering signal intensity equation in the pre-constructed labeled Boltzmann transport equation. Multiplying this scattering signal intensity with the energy spectrum vector yields the multi-energy scattering signal data. If the number of actual scanned energy spectra after discretization and labeling is less than or equal to half the number of preset discrete energy groups, combine the energy spectrum matrix and material density distribution data, and calculate the scattering signal intensity using the final scattering signal intensity equation in the pre-constructed labeled Boltzmann transport equation, thus obtaining the multi-energy scattering signal data.

[0097] For example, in the embodiments of this application, L different initial energy spectra are input during the multi-energy CT scan. The data is then discretized and sampled into a certain number of scattering energy spectra, such as G specific scattering energy spectra. Obtain the matrix If L <= G / 2, the scattered signal intensity obtained according to the final scattered signal intensity equation can be expressed as, but is not limited to, as follows: Multi-energy scattering signal data can be, but is not limited to, represented as: If L > G / 2, the scattered signal intensity obtained according to the final scattered signal intensity equation can be, but is not limited to, expressed as I. E Then, multi-energy scattering signal data can be represented, but is not limited to, as...

[0098] The expression for the final scattered signal intensity equation can be, but is not limited to, as follows:

[0099]

[0100] For example, embodiments of this application can obtain the attenuation coefficient distribution μ based on material density distribution data. t and linear scattering coefficient distribution μ s The value of L is set to 2, and then input into the Boltzmann transport equation implemented by the computer to obtain the scattered signal intensity through a single calculation. The multi-energy scattering signal data is as follows:

[0101] In step S105, the initial multi-energy projection data is scattered and corrected using multi-energy scattering signal data to obtain the actual multi-energy projection data of the object after scattering correction.

[0102] As one possible approach, embodiments of this application can utilize multi-energy scattering signal data to scatter and correct the initial multi-energy projection data, thereby obtaining the scatter-corrected actual multi-energy projection data.

[0103] For example, in embodiments of this application, appropriate scattering correction coefficients e1 and e2 can be selected first to obtain the actual multi-energy projection data after scattering correction. The scattering correction process is complete. The calculation results are as follows: Figure 2(a)-Figure 3 As shown.

[0104] The working principle of the multi-energy CT scattering correction method based on the Boltzmann transport equation proposed in this application will be introduced below with reference to an embodiment.

[0105] Figure 4 This is a flowchart illustrating the working principle of a multi-energy CT scattering correction method based on the Boltzmann transport equation according to an embodiment of this application.

[0106] Step S401: Data preprocessing.

[0107] In this embodiment of the application, the initial multi-energy projection data (p1, p2, ..., p) of the object can be used. n Coarse scattering correction and hardening correction are performed to obtain preprocessed initial corrected multi-energy projection data.

[0108] Step S402: Material density conversion.

[0109] In this embodiment, the initial calibrated multi-energy projection data can be used. This application does not impose specific limitations on the process of converting material density, such as material decomposition or pre-reconstruction, to obtain the material density distribution data (ρ1, ρ2, ... ρ) of the object. n ).

[0110] Step S403: Energy spectrum discretization and labeling.

[0111] In this application, the embodiments can be based on actual scanned energy spectrum data. The energy spectrum is discretized using discretization parameters and labeled with a label dimension to obtain the energy spectrum matrix (E or S).

[0112] Step S404: Solve the pre-constructed labeled Boltzmann transport equations.

[0113] In this application, the embodiments can be based on the material density distribution data (ρ1, ρ2, ... ρ n The multi-energy scattering signal data is solved using a pre-constructed labeled Boltzmann transport equation, taking into account the energy spectrum matrix (E or S), geometric parameters, and discretization parameters.

[0114] Step S405: Scattering correction.

[0115] In this embodiment, the initial multi-energy projection data (p1, p2, ..., p) can be used as the basis for the implementation of the application. n Multi-energy scattering signal data By combining the scattering correction coefficients, scattering correction is performed, thereby obtaining the actual multi-energy projection data after scattering correction.

[0116] According to the multi-energy CT scattering correction method based on the Boltzmann transport equation proposed in this application, the initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object can be preprocessed to obtain the preprocessed initial corrected multi-energy projection number. Material density conversion is then performed to obtain the material density distribution data of the object. Then, the multi-energy spectrum data is discretized and labeled to obtain the energy spectrum matrix. Then, the material density distribution data and the energy spectrum matrix are combined, and the multi-energy scattering signal data of the object in multi-energy CT scanning is calculated using the pre-constructed labeled Boltzmann transport equation. The initial multi-energy projection data is then scattered and corrected using the multi-energy scattering signal data to obtain the actual multi-energy projection data after scattering correction. The multi-energy scattering signal data is calculated based on the pre-constructed labeled Boltzmann transport equation. By discretizing the phase space, the equation is transformed into an analytical solution, which gives the program superior parallelism, thereby improving the calculation speed and portability. To address the scattering correction requirements in multi-energy CT, an additional label dimension is introduced to vectorize the energy group space, thereby reducing computational load and enabling the acquisition of scattering signals under multiple energy spectra in a single calculation. This solves the problems in related technologies, such as the fact that material decomposition is highly sensitive to the energy spectrum, and that even simple descattering methods, while removing most scattering, lead to severe distortion of the material density obtained from material decomposition; and the lengthy and complex processing required for multiple scattering estimates under different X-ray source conditions due to the multi-energy spectrum.

[0117] Next, referring to the accompanying drawings, a multi-energy CT scattering correction device based on the Boltzmann transport equation is described according to an embodiment of this application.

[0118] Figure 5 This is a block diagram of a multi-energy CT scattering correction device based on the Boltzmann transport equation provided in an embodiment of this application.

[0119] like Figure 5As shown, the multi-energy CT scattering correction device 50 based on the Boltzmann transport equation includes: a preprocessing module 100, a material density conversion module 200, an energy spectrum discrete labeling module 300, a calculation module 400, and a scattering correction module 500.

[0120] The preprocessing module 100 is used to preprocess the initial multi-energy projection data to be corrected obtained after the object is scanned by multi-energy CT, so as to obtain the initial corrected multi-energy projection data after the initial multi-energy projection data to be corrected is preprocessed.

[0121] The material density conversion module 200 is used to convert the initial corrected multi-energy projection data into material density data to obtain the material density distribution data of the object.

[0122] The energy spectrum discretization and labeling module 300 is used to discretize and label the actual scanning energy spectrum of an object during multi-energy CT scanning, so as to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum.

[0123] The calculation module 400 is used to calculate the multi-energy scattering signal data of an object in a multi-energy CT scan based on the final scattered signal intensity equation, energy spectrum matrix and material density distribution data in the pre-constructed labeled Boltzmann transport equation.

[0124] The scattering correction module 500 is used to perform scattering correction on the initial multi-energy projection data using multi-energy scattering signal data, so as to obtain the actual multi-energy projection data of the object after scattering correction.

[0125] Optionally, in one embodiment of this application, it further includes: a first construction module, a first acquisition module, a second acquisition module, a generation module, a correction module, a determination module, and a second construction module.

[0126] The first building module is used to construct the static Boltzmann transport equation during the multi-energy CT scan process before calculating the multi-energy scattering signal data of the object in the multi-energy CT scan based on the final scattered signal intensity equation, energy spectrum matrix and material density distribution data in the pre-built labeled Boltzmann transport equation.

[0127] The first acquisition module is used to acquire the photon flux integral expression and photon flux differential expression of the photon flux and the photon source term integral expression and photon source term differential expression of the photon flux and photon source term in the static Boltzmann transport equation during multi-energy CT scanning.

[0128] The second acquisition module is used to acquire the discrete expression of photon flux and the discrete expression of photon source terms based on the integral expression of photon flux, the differential expression of photon flux, the integral expression of photon source terms, and the differential expression of photon source terms.

[0129] The generation module is used to generate the initial scattering signal intensity equation for the scattering signal during multi-energy CT scanning based on the integral expression of photon flux, the differential expression of photon flux, the integral expression of photon source term, and the differential expression of photon source term.

[0130] The correction module is used to discretize the initial scattering signal intensity equation using the discrete expression of photon flux and the discrete expression of photon source term, so as to obtain the final scattering signal intensity equation after discretization of the initial scattering signal intensity equation.

[0131] The determination module is used to determine at least one label dimension of the static Boltzmann transport equation based on the discrete expression of photon flux, the discrete expression of photon source terms, and the final scattered signal intensity equation.

[0132] The second building module is used to construct the labeled Boltzmann transport equation based on the discrete expression of photon flux, the discrete expression of photon source term, the final scattered signal intensity equation, and at least one label dimension.

[0133] Optionally, in one embodiment of this application, the energy spectrum discrete labeling module 300 includes: a judgment unit, a first determination unit, and a second determination unit.

[0134] The judgment unit is used to determine whether the number of actual scanned energy spectra after discretization and labeling is greater than half of the preset number of discrete energy groups.

[0135] The first determining unit is used to determine the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the number of preset discrete energy groups when the number of actual scanned energy spectra after discretization and labeling is greater than half of the preset number of discrete energy groups. The energy spectrum matrix is ​​an identity matrix.

[0136] The second determining unit is used to determine the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the number of actual scanned energy spectra after discretization and labeling, when the number of actual scanned energy spectra after discretization and labeling is less than or equal to half of the preset number of discrete energy groups. Each column vector in the energy spectrum matrix is ​​the energy spectrum vector of each actual scanned energy spectrum after discretization and labeling.

[0137] Optionally, in one embodiment of this application, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as follows:

[0138]

[0139] in, Let be the magnitude of the angular flux of a photon with voxel i, energy group g, emission direction m, tag l, and scattering order n at position i; For voxel i w′ The average linear decay coefficient at position i over the energy group g, where i w′ The voxel number where path w′ is located; w′ is a vector. The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; The intensity of a photon source at position i, with energy group g, emission direction m, tag l, and scattering order n+1; μ s；i,g′→g,m′→m Let i be a voxel at position i, with a discrete angle m′ and energy group g′. Let g′ be the scattering cross section of a photon with a discrete angle m and energy group g. Let be the angular flux of a photon at position i, energy group g′, emission direction m′, tag l, and scattering order n. Let i be the position of voxel i, energy group g, and emission direction m (this direction m is determined by...) The direction determines the intensity of the photon source labeled l and with a scattering order of k. d Let d be the area of ​​pixel d, and θ be... The angle E between the vector and the normal vector of pixel d g Let D(E) be the average energy of energy group g. g ) for the detector at energy E g Lower detector gain, Let be the spatial position vector of voxel i. Let be the spatial position vector of the detector pixel d, where i is the discrete voxel index, identifying the discrete spatial position; g is the energy group index, identifying the position of different discrete energy groups; m is the discrete solid angle index, identifying different spatial directions; l is the tag index, used to identify photons from different energy spectra; k is the scattering order, which exists as a summation variable in the formula; N is the total number of discretized voxels; G is the number of discretized energy groups; K is the highest scattering order selected for calculation; n is the scattering order (i.e., the photon was scattered n times); n+1 is the scattering order (i.e., the photon was scattered n+1 times).

[0140] Optionally, in one embodiment of this application, the expression for the final scattered signal intensity equation may be, but is not limited to, as follows:

[0141]

[0142] It should be noted that the foregoing explanation of the embodiment of the multi-energy CT scattering correction method based on the Boltzmann transport equation also applies to the multi-energy CT scattering correction device based on the Boltzmann transport equation in this embodiment, and will not be repeated here.

[0143] According to the multi-energy CT scattering correction device based on the Boltzmann transport equation proposed in this application, the initial multi-energy projection data to be corrected obtained after multi-energy CT scanning of an object can be preprocessed to obtain the preprocessed initial corrected multi-energy projection number. Material density conversion is then performed to obtain the material density distribution data of the object. Then, the multi-energy spectrum data is discretized and labeled to obtain the energy spectrum matrix. Then, the material density distribution data and the energy spectrum matrix are combined, and the multi-energy scattering signal data of the object in multi-energy CT scanning is calculated using the pre-constructed labeled Boltzmann transport equation. The initial multi-energy projection data is then scattered and corrected using the multi-energy scattering signal data to obtain the actual multi-energy projection data after scattering correction. The multi-energy scattering signal data is calculated based on the pre-constructed labeled Boltzmann transport equation. By discretizing the phase space, the equation is transformed into an analytical solution, which gives the program superior parallelism, thereby improving the calculation speed and portability. To address the scattering correction requirements in multi-energy CT, an additional label dimension is introduced to vectorize the energy group space, thereby reducing computational load and enabling the acquisition of scattering signals under multiple energy spectra in a single calculation. This solves the problems in related technologies, such as the fact that material decomposition is highly sensitive to the energy spectrum, and that even simple descattering methods, while removing most scattering, lead to severe distortion of the material density obtained from material decomposition; and the lengthy and complex processing required for multiple scattering estimates under different X-ray source conditions due to the multi-energy spectrum.

[0144] Figure 6 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. The electronic device may include:

[0145] The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0146] When the processor 602 executes the program, it implements the multi-energy CT scattering correction method based on the Boltzmann transport equation provided in the above embodiments.

[0147] Furthermore, electronic devices also include:

[0148] Communication interface 603 is used for communication between memory 601 and processor 602.

[0149] The memory 601 is used to store computer programs that can run on the processor 602.

[0150] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0151] If the memory 601, processor 602, and communication interface 603 are implemented independently, then the communication interface 603, memory 601, and processor 602 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0152] Optionally, in a specific implementation, if the memory 601, processor 602, and communication interface 603 are integrated on a single chip, then the memory 601, processor 602, and communication interface 603 can communicate with each other through an internal interface.

[0153] The processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0154] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-energy CT scattering correction method based on the Boltzmann transport equation.

[0155] This application also provides a computer program product, including a computer program that, when executed, implements the above-described multi-energy CT scattering correction method based on the Boltzmann transport equation.

[0156] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0157] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0158] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0159] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). In addition, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically by optically scanning paper or other media, then editing, interpreting or otherwise processing them as necessary, and then storing them in computer memory.

[0160] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0161] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium. When executed, the program includes one or a combination of the steps of the method embodiments.

[0162] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0163] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A multi-energy CT scattering correction method based on the Boltzmann transport equation, characterized in that, Includes the following steps: The initial multi-energy projection data to be corrected obtained after the object is scanned by multi-energy computed tomography (CT) is preprocessed to obtain the initial corrected multi-energy projection data after the initial multi-energy projection data to be corrected is preprocessed. The initial corrected multi-energy projection data is subjected to material density conversion to obtain the material density distribution data after the initial corrected multi-energy projection data is converted. The actual scanning energy spectrum of the object during multi-energy CT scanning is discretized and labeled, so as to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum; Based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the material density distribution data, the multi-energy scattered signal data of the object in multi-energy CT scanning is calculated. The initial multi-energy projection data is corrected by using the multi-energy scattering signal data to obtain the actual multi-energy projection data of the object after scattering correction. The expression for the pre-constructed labeled Boltzmann transport equation is as follows: ， in, voxels Location, energy group Launch direction is , tag as And the scattering order is The magnitude of the angular flux of photons; voxels Location relative to energy group The average linear attenuation coefficient within the range, where for The voxel number where the path is located; For vectors The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; voxels Location, energy group Launch direction is , tag as And the scattering order is The intensity of the photon source; voxels Position, direction of movement Discrete angle and energy group are Photon scattering is in the direction of motion Discrete angle and energy group are The scattering cross section of photons; voxels Location, energy group Launch direction is , tag as And the scattering order is The magnitude of the angular flux of photons, voxels Location, energy group Launch direction is , Direction from Direction determines, label as And the scattering order is The intensity of the photon source, For pixels area, for Vectors and pixels The angle between the normal vectors, For the group The average energy, For the detector in energy Lower detector gain, voxels The spatial location vector, For detector pixels The spatial location vector, These are discrete voxel subscripts, used to identify locations in discrete space; These are subscripts for energy groups, used to identify the positions of different discrete energy groups; Labels and subscripts are used to identify photons from different energy spectra; The scattering order exists as a summation variable in the formula; The total number of discretized voxels; The number of discretized energy groups. To select the highest scattering order for calculation; The scattering order is the number of times the photon is scattered. This represents the scattering order, meaning the photon was scattered n+1 times. This is the expression for the final scattered signal intensity equation.

2. The method according to claim 1, characterized in that, Before calculating the multi-energy scattering signal data of the object in multi-energy CT scanning based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the matter density distribution data, the method further includes: Construct the static Boltzmann transport equation for the object during multi-energy CT scanning; During the multi-energy CT scan, the photon flux integral expression and photon flux differential expression of the photon flux and the photon source term are obtained in the static Boltzmann transport equation; Based on the integral expression of photon flux, the differential expression of photon flux, the integral expression of photon source term, and the differential expression of photon source term, the discrete expression of photon flux and the discrete expression of photon source term are obtained. Based on the integral expression of photon flux, the differential expression of photon flux, the integral expression of photon source term, and the differential expression of photon source term, the initial scattering signal intensity equation of the scattering signal during the multi-energy CT scan is generated; The initial scattering signal intensity equation is discretized using the discrete expression of photon flux and the discrete expression of photon source term to obtain the final scattering signal intensity equation after discretization of the initial scattering signal intensity equation; Based on the discrete expression of photon flux, the discrete expression of photon source term, and the final scattered signal intensity equation, at least one label dimension of the static Boltzmann transport equation is determined. Based on the discrete expression of photon flux, the discrete expression of photon source term, the final scattered signal intensity equation, and the at least one labeled dimension, a labeled Boltzmann transport equation is constructed.

3. The method according to claim 1, characterized in that, The discretization and labeling of the actual scan energy spectrum of the object during multi-energy CT scanning, and the determination of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scan energy spectrum, include: Determine whether the number of actual scanned energy spectra after discretization and tagging is greater than half of the preset number of discrete energy groups; If the number of actual scanned energy spectra after discretization and tagging is greater than half of the number of preset discrete energy groups, then the dimension and value of the energy spectrum matrix in the pre-constructed tagged Boltzmann transport equation are determined based on the number of preset discrete energy groups, wherein the energy spectrum matrix is ​​an identity matrix. If the number of actual scanned energy spectra after discretization and tagging is less than or equal to half the number of preset discrete energy groups, then the dimension and value of the energy spectrum matrix in the pre-constructed tagged Boltzmann transport equation are determined based on the number of actual scanned energy spectra after discretization and tagging, wherein each column vector in the energy spectrum matrix is ​​the energy spectrum vector of each actual scanned energy spectrum after discretization and tagging.

4. A multi-energy CT scattering correction device based on the Boltzmann transport equation, characterized in that, include: The preprocessing module is used to preprocess the initial multi-energy projection data to be corrected obtained after the object is scanned by multi-energy CT, so as to obtain the initial corrected multi-energy projection data after the initial multi-energy projection data to be corrected is preprocessed. The material density conversion module is used to convert the initial corrected multi-energy projection data into material density to obtain the material density distribution data after the initial corrected multi-energy projection data is converted into material density. The energy spectrum discretization and labeling module is used to discretize and label the actual scanning energy spectrum of the object during multi-energy CT scanning, so as to determine the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum. The calculation module is used to calculate the multi-energy scattering signal data of the object in multi-energy CT scanning based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the material density distribution data. A scattering correction module is used to perform scattering correction on the initial multi-energy projection data using the multi-energy scattering signal data, so as to obtain the actual multi-energy projection data of the object after scattering correction. The expression for the pre-constructed labeled Boltzmann transport equation is as follows: ， in, voxels Location, energy group Launch direction is , tag as And the scattering order is The magnitude of the angular flux of photons; voxels Location relative to energy group The average linear attenuation coefficient within the range, where for The voxel number where the path is located; For vectors The path represents the path through each voxel, and the path length in each voxel exists as an accumulated variable; voxels Location, energy group Launch direction is , tag as And the scattering order is The intensity of the photon source; voxels Position, direction of movement Discrete angle and energy group are Photon scattering is in the direction of motion. Discrete angle and energy group are The scattering cross section of photons; voxels Location, energy group Launch direction is , tag as And the scattering order is The magnitude of the angular flux of photons, voxels Location, energy group Launch direction is , Direction from The direction determines, and the label is And the scattering order is The intensity of the photon source, For pixels area, for Vectors and pixels The angle between the normal vectors, For the group The average energy, For the detector in energy Lower detector gain, voxels The spatial location vector, For detector pixels The spatial location vector, These are discrete voxel subscripts, used to identify locations in discrete space; These are subscripts for energy groups, used to identify the positions of different discrete energy groups; Labels and subscripts are used to identify photons from different energy spectra; The scattering order exists as a summation variable in the formula; The total number of discretized voxels; The number of discretized energy groups. To select the highest scattering order for calculation; The scattering order is the number of times the photon is scattered. This represents the scattering order, meaning the photon was scattered n+1 times. This is the expression for the final scattered signal intensity equation.

5. The apparatus according to claim 4, characterized in that, Also includes: The first construction module is used to construct the static Boltzmann transport equation during the multi-energy CT scan process before calculating the multi-energy scattering signal data of the object in the multi-energy CT scan based on the final scattered signal intensity equation in the pre-constructed labeled Boltzmann transport equation, the energy spectrum matrix, and the material density distribution data. The first acquisition module is used to acquire the photon flux integral expression and photon flux differential expression of the photon flux and the photon source term of the photon source term in the static Boltzmann transport equation during the multi-energy CT scan process. The second acquisition module is used to acquire the discrete expression of the photon flux and the discrete expression of the photon source term based on the integral expression of the photon flux, the differential expression of the photon flux, the integral expression of the photon source term, and the differential expression of the photon source term; The generation module is used to generate the initial scattering signal intensity equation of the scattering signal during the multi-energy CT scan based on the photon flux integral expression, the photon flux differential expression, the photon source term integral expression, and the photon source term differential expression. The correction module is used to discretize the initial scattering signal intensity equation using the discrete expression of the photon flux and the discrete expression of the photon source term, so as to obtain the final scattering signal intensity equation after discretization of the initial scattering signal intensity equation; The determination module is used to determine at least one label dimension of the static Boltzmann transport equation based on the discrete expression of photon flux, the discrete expression of photon source terms, and the final scattered signal intensity equation. The second construction module is used to construct the labeled Boltzmann transport equation based on the discrete expression of photon flux, the discrete expression of photon source term, the final scattered signal intensity equation, and the at least one label dimension.

6. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the multi-energy CT scattering correction method based on the Boltzmann transport equation as described in any one of claims 1-3.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the multi-energy CT scattering correction method based on the Boltzmann transport equation as described in any one of claims 1-3.

8. A computer program product, characterized in that, Includes a computer program, which, when executed, is used to implement the multi-energy CT scattering correction method based on the Boltzmann transport equation as described in any one of claims 1-3.

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