Multi-energy CT scatter correction method and apparatus based on boltzmann transport equation

Abstract

A multi-energy CT scatter correction method and apparatus based on a Boltzmann transport equation. The method comprises: preprocessing initial multi-energy projection data to be corrected of an object obtained after multi-energy CT scanning, to acquire 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 an actual scanning energy spectrum of the object during the multi-energy CT scanning, and determining an energy spectrum matrix in a pre-constructed labeled Boltzmann transport equation; calculating multi-energy scatter signal data of the object during the multi-energy CT scanning; and using the multi-energy scatter signal data to perform scatter correction on the initial multi-energy projection data to obtain actual multi-energy projection data.

Description

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

[0001] Cross-references to related applications

[0002] This invention claims priority to Chinese patent application number 202510049214.6, filed by Tsinghua University on January 13, 2025, entitled "Multi-energy CT scattering correction method and device based on Boltzmann transport equation". Technical Field

[0003] This invention 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. Background Technology

[0004] 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.

[0005] 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.

[0006] 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.

[0007] 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

[0008] This invention 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 is a lengthy and complex process.

[0009] A first aspect of this invention provides a multi-energy CT scattering correction method based on the Boltzmann transport equation, comprising the following steps: preprocessing 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 a pre-constructed labeled Boltzmann transport equation based on the discretized and labeled actual scanning energy spectrum; calculating 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.

[0010] Optionally, in one embodiment of the present invention, 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.

[0011] Optionally, in one embodiment of the present invention, 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.

[0012] Optionally, in one embodiment of the present invention, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as follows:

[0013] 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 the photon source at position i, energy group g, emission direction m, tag l, and scattering order n+1; μs; i,g′→g,m′→m is the scattering cross section of the photon at position i, motion direction m′ discrete angle, and energy group g′, which is the photon at position i, motion direction m discrete angle, 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).

[0014] Optionally, in one embodiment of the present invention, the expression for the final scattered signal intensity equation may be, but is not limited to, the following:

[0015] A second aspect of the present invention 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 discretization labeling module for marking the actual energy distribution of the object during multi-energy CT scanning. 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 the present invention, it further includes: a first construction module, configured 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, configured 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; and a second acquisition module, configured 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 the present invention, 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 the present invention, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as follows:

[0019] 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 the photon source at position i, energy group g, emission direction m, tag l, and scattering order n+1; μs; i,g′→g,m′→m is the scattering cross section of the photon at position i, motion direction m′ discrete angle, and energy group g′, which is the photon at position i, motion direction m discrete angle, 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).

[0020] Optionally, in one embodiment of the present invention, the expression for the final scattered signal intensity equation may be, but is not limited to, the following:

[0021] A third aspect of the present invention 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.

[0022] A fourth aspect of the present invention 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.

[0023] A fifth aspect of the present invention 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.

[0024] This invention 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 numbers 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. 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 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 in the program, thereby improving 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.

[0025] Additional aspects and advantages of the invention 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 the invention. Attached Figure Description

[0026] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0027] Figure 1 is a flowchart of a multi-energy CT scattering correction method based on the Boltzmann transport equation according to an embodiment of the present invention;

[0028] Figures 2(a)-2(d) are schematic diagrams comparing the scattering estimation results provided by an embodiment of the present invention with those of the Monte Carlo method using the Geant4 tool;

[0029] Figure 3 is a schematic diagram comparing the images of the projection acquired on a multi-energy CT before and after scattering correction, and the standard value of the fan beam, according to an embodiment of the present invention.

[0030] Figure 4 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 the present invention.

[0031] Figure 5 is a block diagram of a multi-energy CT scattering correction device based on the Boltzmann transport equation provided in an embodiment of the present invention.

[0032] Figure 6 is a schematic diagram of the structure of an electronic device provided according to an embodiment of the present invention. Detailed Implementation

[0033] Embodiments of the present invention are described in detail below, examples of which are illustrated 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 the present invention, and should not be construed as limiting the present invention.

[0034] The following describes, with reference to the accompanying drawings, a multi-energy CT scattering correction method and apparatus based on the Boltzmann transport equation according to embodiments of the present invention. Addressing the issues mentioned in the background art, such as the high sensitivity of material decomposition to the energy spectrum, where simple descattering methods, even if capable of removing most scattering, lead to severe distortion of the material density obtained from material decomposition, and the lengthy and complex process of multiple scattering estimates under different X-ray source conditions due to the multi-energy spectrum, the present invention 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.

[0035] Specifically, Figure 1 is a flowchart of a multi-energy CT scattering correction method based on the Boltzmann transport equation provided in an embodiment of the present invention.

[0036] As shown in Figure 1, the multi-energy CT scattering correction method based on the Boltzmann transport equation includes the following steps:

[0037] 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.

[0038] As one possible implementation method, embodiments of the present invention 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 the present invention preprocess the initial multi-energy projection data, such as coarse scattering correction and hardening correction, etc. The present invention does not impose specific limitations, thereby obtaining the initial corrected multi-energy projection data after the initial projection data preprocessing.

[0039] For example, embodiments of the present invention 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 .

[0040] For example, embodiments of the present invention employ a three-dimensional rectangular coordinate system. In terms of voxel discretization, the object is discretized into 16×16×16 uniformly sized cubic units. In terms of 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.

[0041] Furthermore, embodiments of the present invention can obtain two sets of initial multi-energy projection data of an object 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...

[0042] 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.

[0043] For example, embodiments of the present invention can use multiple energy spectra S l ,l=1,2,…,L and initial corrected multi-energy projection data P f This invention performs material density conversion, such as material decomposition and pre-reconstruction, without specific limitations, 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.

[0044] In some embodiments, the present invention can perform material decomposition based on 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.

[0045] For example, embodiments of the present invention can be based on initial corrected 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.

[0046] In some embodiments, the present invention 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.

[0047] For example, embodiments of the present invention can 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.

[0048] In some embodiments, the present invention 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.

[0049] For example, embodiments of the present invention 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.

[0050] Optionally, in one embodiment of the present invention, before calculating the multi-energy scattering signal data of an object in multi-energy CT scanning 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 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 based on the photon flux integral expression, photon flux differential expression, photon source term integral expression, and photon source term differential expression. The photon source term is discretely expressed; based on the photon flux integral expression, photon flux differential expression, photon source term integral expression, and photon source term differential expression, an initial scattered signal intensity equation is generated for the scattered signal during multi-energy CT scanning; 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 at least one labeled dimension, a labeled Boltzmann transport equation is constructed.

[0051] The pre-constructed, labeled Boltzmann transport equation can be, but is not limited to, expressed as:

[0052] 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 the photon source at position i, energy group g, emission direction m, tag l, and scattering order n+1; μs; i,g′→g,m′→m is the scattering cross section of the photon at position i, motion direction m′ discrete angle, and energy group g′, which is the photon at position i, motion direction m discrete angle, 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).

[0053] Those skilled in the art will understand that embodiments of the present invention can be based on the Boltzmann transport equation concerning photon transport and scattering in CT scans. Considering the extremely short interaction time between photons and matter, the relaxation time is ignored in the model, assuming the system instantaneously reaches static equilibrium. Based on the above description, embodiments of the present invention can construct a static Boltzmann transport equation during multi-energy CT scanning, which can be, but is not limited to, expressed as:

[0054] 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 carried photons with energy E; E max This represents the highest energy of a photon in a CT system, equivalent to the maximum photon energy emitted by the X-ray source.

[0055] Furthermore, embodiments of the present invention 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.

[0056] For example, in this embodiment of the invention, based on the physical process during CT scanning, the iterative source method is used to decompose and 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:

[0057] 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:

[0058] Additionally, it should be noted that in this embodiment of the invention, photons are emitted from the object and enter the detector to be recorded. 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:

[0059] Where u and w are both integral variables, the initial scattering signal intensity equation of the energy deposition signal Iscatter received by the detector, i.e., the scattering signal, can be expressed, but is not limited to, as:

[0060] 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.

[0061] Furthermore, embodiments of the present invention 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:

[0062] Based on this, in embodiments of the present invention, equations (7) and (8) can be written in matrix form, which can be, but is not limited to, expressed as: Ф (n) =TS (n) ,S (n-1) =CФ (n) (9)

[0063] 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:

[0064] Based on this, in the embodiments of the present invention, equation (10) can be written in matrix form, which can be, but is not limited to, expressed as:

[0065] Furthermore, in this embodiment of the invention, 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 invention does not impose specific limitations). 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:

[0066] Furthermore, in embodiments of the present invention, equation (12) can be reduced, and it can be, but is not limited to, expressed as:

[0067] in, Let l be a matrix independent of l.

[0068] Among them, in the actual calculation of the embodiments of the present invention, it is only necessary to calculate T, C, and D once. Adding the L dimension only increases the computational complexity of 2K(L - 1) sparse matrix multiplications, and this part of the computational complexity is very small compared to the computational complexity of T, C, and D. For example, the exponential operations contained in the solution of the T and D matrices, as well as the tracking of the length within the voxel, these computational complexities are much greater than the aforementioned sparse matrix multiplications. That is to say, introducing the label dimension in the embodiments of the present invention only increases a tiny amount of computational complexity, but makes it possible to calculate scattering images under multiple different energy spectra simultaneously. For multiple X-ray energy spectra Denote Calculate F, T, C, and D, so as to obtain Scattering image Among them, I = [I1, I2,..., I L , the size of I is N d ×L, N D is the number of detector pixels, I l , l = 1, 2,.., L, and its size is N D ×1.

[0069] Particularly, in the embodiments of the present invention, when L≥G or it is uncertain whether new energy spectrum scanning will be adopted subsequently, a set of bases in the R G space can be constructed. Without loss of generality, a set of basis vectors is taken as the unit orthogonal basis E = [E1, E2,..., E G , E is a G×G diagonal matrix, so as to be able to calculate a set of basis scattering images Among them, the size of I E is N D ×G. Thus, for any energy spectrum The embodiments of the present invention can easily obtain the corresponding scattering image 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 will not increase. Let energy group 1 be the highest energy group and energy group G be the lowest energy group. Then for the basis energy spectrum E i (that is, the energy spectrum with only the value of energy group i), only the photon behaviors of the low-energy energy groups i, i + 1, i + 2…, G-1, G need to be considered, and the behaviors of the high-energy energy groups 1, 2,…, i-1 do not need to be considered. This makes the tiny computational complexity introduced by increasing the label dimension be further reduced by half, which makes the judgment condition L≥G proposed above can be further modified to L>=G / 2.

[0070] The above analysis shows that in the embodiments of the present invention, if L < G / 2, directly perform energy group discretization and labeling on the original energy spectrum, introducing L labels; if L>=G / 2, introduce the above energy spectrum basis vector method, introducing G labels, and then the calculation speed can be optimized.

[0071] Thus, the labeled Boltzmann transport equation can be constructed, which can be, but is not limited to, expressed as:

[0072] In step S103, the actual scanning energy spectrum of the object during the multi-energy CT scanning process 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.

[0073] As one possible implementation, embodiments of the present invention can discretize the actual scanning energy spectrum of an object during multi-energy CT scanning into multiple energy spectrum vectors, and then combine them with the label dimension to obtain an energy spectrum matrix.

[0074] Optionally, in one embodiment of the present invention, the actual scanning energy spectrum of an object during multi-energy CT scanning 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. This includes: determining whether the number of discretized and labeled actual scanning energy spectra is greater than half of the number of preset discrete energy groups; if the number of discretized and labeled actual scanning energy spectra is greater than half of the number of preset discrete energy groups, then determining 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, wherein the energy spectrum matrix is ​​an identity matrix; if the number of discretized and labeled actual scanning energy spectra is less than or equal to half of the number of preset discrete energy groups, then determining the dimension and value of the energy spectrum matrix in the pre-constructed labeled Boltzmann transport equation based on the number of discretized and labeled actual scanning energy spectra, wherein each column vector in the energy spectrum matrix is ​​the energy spectrum vector of each discretized and labeled actual scanning energy spectrum.

[0075] As one possible implementation, embodiments of the present invention 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, in embodiments of the present invention, 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 dimension and value of the energy spectrum matrix can be determined based on the certain 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 conditions, and the present invention does not impose specific limitations.

[0076] For example, in this embodiment of the invention, 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.

[0077] 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:

[0078] It is understood that the inputs to the pre-constructed labeled Boltzmann transport equation in this embodiment of the invention may include, but are not limited to, material density distribution data, geometric parameters, and discretization parameters, etc., and this invention does not impose specific limitations. Specifically, geometric parameters may include, but are not limited to, source-detector distance, detector size, detector offset, etc., and this invention 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 invention does not impose specific limitations.

[0079] Additionally, it should be noted that in the embodiments of the present invention, 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 configured by those skilled in the art according to the actual situation, and the present invention does not impose any specific limitations.

[0080] In some embodiments, the present invention 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 an object. The main steps in calculating the multi-energy scattering signal data of an object in the present invention are 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.

[0081] For example, in this embodiment of the invention, L different initial energy spectra are actually used 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...

[0082] The expression for the final scattered signal intensity equation can be, but is not limited to, as follows:

[0083] For example, embodiments of the present invention 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:

[0084] 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.

[0085] As one possible implementation, embodiments of the present invention can use 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.

[0086] For example, in embodiments of the present invention, 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 shown in Figures 2(a)-3.

[0087] The working principle of the multi-energy CT scattering correction method based on the Boltzmann transport equation proposed in this invention will be introduced below with reference to an embodiment.

[0088] Figure 4 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 the present invention.

[0089] Step S401: Data preprocessing.

[0090] In this embodiment of the invention, 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.

[0091] Step S402: Material density conversion.

[0092] In this embodiment of the invention, the initial corrected multi-energy projection data can be used. This invention does not impose specific limitations on the conversion of material density, such as material decomposition and pre-reconstruction, to obtain the material density distribution data (ρ1, ρ2, ... ρ) of the object. n ).

[0093] Step S403: Energy spectrum discretization and labeling.

[0094] In particular, embodiments of the present invention 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).

[0095] Step S404: Solve the pre-constructed labeled Boltzmann transport equations.

[0096] In this embodiment of the invention, the density distribution data (ρ) can be used as a basis. 11,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.

[0097] Step S405: Scattering correction.

[0098] In this embodiment of the invention, the initial multi-energy projection data (p1, p2, ..., p) can be used as the basis for the invention. 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.

[0099] The multi-energy CT scattering correction method based on the Boltzmann transport equation proposed in this invention 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, combined with 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. 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.

[0100] Next, referring to the accompanying drawings, a multi-energy CT scattering correction device based on the Boltzmann transport equation proposed according to an embodiment of the present invention is described.

[0101] Figure 5 is a block diagram of a multi-energy CT scattering correction device based on the Boltzmann transport equation provided in an embodiment of the present invention.

[0102] As shown in Figure 5, 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.

[0103] 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.

[0104] 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.

[0105] 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.

[0106] 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.

[0107] 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.

[0108] Optionally, in one embodiment of the present invention, 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.

[0109] 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.

[0110] 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.

[0111] 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.

[0112] 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.

[0113] 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.

[0114] 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.

[0115] 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 labeled dimension.

[0116] Optionally, in one embodiment of the present invention, the energy spectrum discrete labeling module 300 includes: a judgment unit, a first determination unit, and a second determination unit.

[0117] 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.

[0118] 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.

[0119] 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.

[0120] Optionally, in one embodiment of the present invention, the expression of the pre-constructed labeled Boltzmann transport equation may be, but is not limited to, as follows:

[0121] 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 the photon source at position i, energy group g, emission direction m, tag l, and scattering order n+1; μs; i,g′→g,m′→m is the scattering cross section of the photon at position i, motion direction m′ discrete angle, and energy group g′, which is the photon at position i, motion direction m discrete angle, 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).

[0122] Optionally, in one embodiment of the present invention, the expression for the final scattered signal intensity equation may be, but is not limited to, as follows:

[0123] 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.

[0124] The multi-energy CT scattering correction device based on the Boltzmann transport equation proposed in this embodiment of the invention can first preprocess 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 material density distribution data of the object. Then, the multi-energy spectrum data is discretized and labeled to obtain the energy spectrum matrix. Then, combined with 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, and the initial multi-energy projection data is 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, 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.

[0125] Figure 6 is a schematic diagram of the structure of an electronic device provided according to an embodiment of the present invention. The electronic device may include:

[0126] The memory 601, the processor 602, and the computer program stored on the memory 601 and capable of running on the processor 602.

[0127] 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.

[0128] Furthermore, electronic devices also include:

[0129] Communication interface 603 is used for communication between memory 601 and processor 602.

[0130] The memory 601 is used to store computer programs that can run on the processor 602.

[0131] The memory 601 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0132] If the memory 601, processor 602, and communication interface 603 are implemented independently, they can be interconnected via a bus to communicate with each other. 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. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, only one thick line is used in Figure 6, but this does not indicate that there is only one bus or one type of bus.

[0133] 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.

[0134] Processor 602 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention.

[0135] This invention 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.

[0136] This invention 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.

[0137] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. 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.

[0138] 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 indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0139] Any process or method description 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 preferred embodiments of the invention 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 will be understood by those skilled in the art to which embodiments of the invention pertain.

[0140] 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.

[0141] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented in 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.

[0142] 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.

[0143] Furthermore, the functional units in the various embodiments of the present invention 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.

[0144] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

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 scattered and corrected using the multi-energy scattering signal data to obtain the actual multi-energy projection data of the object after scattering correction.

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. The method according to claim 1, characterized in that, The expression for the pre-constructed labeled Boltzmann transport equation is as follows: 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 the photon source at position i, energy group g, emission direction m, tag l, and scattering order n+1; μs; i,g′→g,m′→m is the scattering cross section of the photon at position i, motion direction m′ discrete angle, and energy group g′, which is the photon at position i, motion direction m discrete angle, 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).

5. The method according to claim 1, characterized in that, The expression for the final scattered signal intensity equation is as follows:

6. 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. The 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.

7. The apparatus according to claim 6, 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.

8. 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 1-5.

9. 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 1-5.

10. 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 1-5.

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