A substance identification method
By employing a dual-effect model and an adaptive parameter-adjusted material decomposition method, combined with a photon counting detector, more accurate estimation of electron density and effective atomic number was achieved. This solved the problems of high noise and low accuracy in material decomposition and identification in CT technology, and improved the accuracy of material identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- INST OF HIGH ENERGY PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2023-02-27
- Publication Date
- 2026-04-24
AI Technical Summary
Existing CT technology suffers from problems such as high noise, low accuracy, complex calculations, and inability to select an effective model for unknown samples in material decomposition and atomic number identification, resulting in inaccurate material identification.
A matter decomposition method based on a dual-effect model is adopted. Through polynomial combination and image domain constraints, combined with adaptive parameter adjustment, the electron density and effective atomic number are estimated. Data of different energies are collected using a photon counting detector for matter decomposition and identification.
It improves the accuracy of substance decomposition and the precision of substance identification, especially the identification precision of elements with low atomic numbers, and solves the problems of high noise and poor model adaptability in existing technologies.
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Figure CN116183647B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of energy spectrum CT image processing, and specifically relates to a method for substance identification. Background Technology
[0002] CT technology has been widely used in various fields, but currently it mainly focuses on obtaining three-dimensional structural information of the interior of objects. Material decomposition and effective atomic number identification are important directions for the development of CT, and there are clear needs in medical diagnosis, security inspection and other research.
[0003] The linear attenuation coefficient of CT reconstruction is a physical quantity related to X-ray energy, material density, and atomic number. Therefore, different substances may exhibit the same linear attenuation coefficient value due to their different material density and atomic number. By acquiring two or more sets of X-rays with different energies, the density and atomic number distribution of different substances can be reconstructed separately, eliminating the ambiguity that may exist in ordinary CT images and realizing the identification of substances.
[0004] In current X-ray instruments, to acquire attenuation data for multiple X-ray energies, dual-source, dual-detector imaging structures or instantaneous switching of tube voltages are commonly used. These imaging methods suffer from poor spectral resolution, leading to excessive noise during reconstruction, and can only achieve dual-energy imaging. A novel photon-counting detector X-ray imaging method is proposed. The photon-counting detector uses an energy identification device to compare photon energy with a set threshold, counting photons exceeding the threshold to obtain the number of photons in different energy ranges. Compared to energy integration detectors, photon-counting detectors can eliminate dark current noise and improve the signal-to-noise ratio of the image by setting an appropriate threshold. Furthermore, photon-counting detectors allow for the free setting of multiple thresholds and do not suffer from phase matching issues.
[0005] The linear attenuation coefficient obtained by CT is a physical quantity related to radiation energy, material density, and atomic number. Ordinary CT cannot distinguish the differences in attenuation caused by atomic number and density. In 1976, R. Alvarez et al. first proposed dual-energy CT, which, by acquiring the attenuation intensity of two sets of radiation at different energies passing through material, can reconstruct the density distribution of different materials, thus achieving material decomposition. The linear attenuation coefficient of matter... It is a function of photon energy E and position r, and can be expanded into a linear combination of i basis functions:
[0006]
[0007] when The mass decay coefficient of the base material is represented by the decomposition coefficient. This represents the density distribution of each base material. If the coefficients represent the contributions of the Compton effect and the photoelectric effect, then the decomposition coefficients are... This will represent the cross-section of these effects. The key to the decomposition of matter lies in solving for the decomposition coefficients. .
[0008] Currently, material decomposition algorithms can be divided into three categories: preprocessing algorithms, post-processing algorithms, and iterative algorithms. Post-processing algorithms first reconstruct cross-sectional images for each energy region, and then decompose the reconstructed CT images. The disadvantages of this algorithm are strong hardening artifacts and low accuracy. Iterative algorithms directly solve for the spatial distribution of basis functions through nonlinear optimization, obtaining energy-independent CT images, suppressing hardening artifacts, and improving image quality. However, these algorithms suffer from computational complexity, implementation difficulties, and slow computation speed. Preprocessing algorithms decompose materials in the projection domain and reconstruct them using the decomposed projection images. This method can accurately simulate the hardening of the X-ray spectrum penetrating the object to eliminate hardening and obtain better image quality, but this type of algorithm requires the same X-ray path to be acquired in all energy regions. Different atomic number estimation models exist for different research objects, making different assumptions about the parameter m. However, in actual detection, for unknown samples, it is impossible to selectively choose a suitable and effective atomic number estimation model, which affects the accuracy of material identification.
[0009] Inspired by the empirical cupping correction (ECC) method, Stenner et al. proposed the empirical dual energy calibration (EDEC) method. This method solves for the decomposition coefficients by performing a polynomial combination of multi-energy projection data in the projection domain and constraining the combined polynomial image in the image domain. Obtained through the decomposition of substances It can estimate the effective atomic number, thereby enabling substance identification. Summary of the Invention
[0010] To address the aforementioned technical problems, this invention proposes a substance identification method. This method can be calibrated using two or more substances, improving the accuracy of substance decomposition. Based on dual-effect substance decomposition, this method can estimate electron density and obtain a more accurate physical model for atomic number estimation through an adaptive parameter determination method, thus improving the accuracy of substance identification. This invention proposes a substance identification method consisting of two parts: empirical dual-effect substance decomposition and adaptive atomic number estimation. The substance decomposition determines the polynomial coefficients by performing polynomial combination on the projected data and constraining it in the image domain. Calibration using multiple standard phantoms improves the accuracy of empirical substance decomposition. This method can estimate electron density and effective atomic number. Through an adaptive effective atomic number estimation model, a more accurate effective atomic number estimate can be achieved, improving the accuracy of substance identification. This invention combines photon counting spectroscopy (PDS) with data from different X-ray energies, allowing for complete matching and the use of preprocessing algorithms for substance decomposition.
[0011] To achieve the above objectives, the present invention adopts the following technical solution:
[0012] A method for identifying substances includes the following steps:
[0013] Step (1) Perform empirical dual-effect substance decomposition. By calibrating multiple standard phantoms, the projection data is combined in a polynomial and constrained in the image domain to determine the decomposition parameters and estimate the electron density.
[0014] Step (2) Estimate the effective atomic number. By calibrating the known standard phantom, establish an adaptive effective atomic number estimation model to estimate the effective atomic number of the imaging material.
[0015] Further, step (1) includes:
[0016] In energy-spectral CT, the linear attenuation coefficient is expanded into a linear combination of multiple basis functions:
[0017]
[0018] Wherein, basis functions It is energy-related, the decomposition coefficient The spatial distribution of the basis functions is position-dependent, and E represents the ray energy. is the pixel position of the image matrix, and I represents the number of basis functions.
[0019] Further, step (1) includes:
[0020] The basis functions are the relationship between the total photoelectric absorption cross section and the Compton scattering cross section of the photoelectric effect and energy. This decomposition is a two-effect decomposition.
[0021] The interactions between X-rays with energies less than 511 keV and matter include the photoelectric effect and Compton scattering:
[0022]
[0023] in, This represents the total photoelectric absorption cross section of the photoelectric effect. The Compton scattering cross section, The total photon interaction cross section;
[0024] The total photoelectric absorption cross section of the photoelectric effect is:
[0025]
[0026] in, E is the atomic number, and E is the radiation energy. It is a constant;
[0027] The Compton scattering cross section is:
[0028]
[0029] in, It is a constant. Representing energy-related quantities:
[0030] (5)
[0031]
[0032] The linear decay coefficient of a substance is expanded as follows:
[0033]
[0034] in, Denotes Avogadro's constant. Indicates the effective atomic number, Represents the effective atomic number raised to the power of m. Indicates atomic mass, It represents electron density.
[0035] Furthermore, the decomposition of the substance in step (1) includes solving for the decomposition coefficients. The attenuation of rays passing through matter is expressed as a weighted average of the attenuation at different energies:
[0036]
[0037] in, This represents the minimum energy of a ray. Indicates the maximum energy of the radiation;
[0038] in, Line integral representing the decomposition coefficients:
[0039]
[0040] in, Represents X-ray spectrum, Indicates the detector response, Represents a two-dimensional random transformation operator;
[0041] For the matter decomposition in the projection domain, the first step is to solve for the ray... The line integral of the corresponding decomposition coefficients Then, the decomposition coefficients are solved using a linear CT reconstruction algorithm. The relationship between attenuated projection and decomposition coefficient line integral is established using higher-order polynomials:
[0042]
[0043] in, Let represent the coefficients of the polynomial corresponding to the i-th basis function, where , This represents the maximum order of the polynomial. Indicates the first The logarithmic decay of each energy region, where J represents the number of energy regions. It is a cumulative multiplication operation;
[0044] The reconstruction of the line integral of the decomposed coefficients is as follows:
[0045]
[0046] The coefficients of the polynomial are estimated by least-squares fitting of measurements on multiple standard motifs:
[0047]
[0048] in, Represents the set of polynomial coefficients. These are the pixel positions in the image matrix; This is a standard template.
[0049] Furthermore, in the aforementioned dual-effect decomposition, the effective atomic number and electron density of the calibration material are used as prior knowledge, and the standard template... for:
[0050]
[0051]
[0052] Where m represents a parameter in the photoelectric effect. and Let represent the electron density and effective atomic number of the i-th constituent material of the standard motif, respectively. The decomposition parameters and the electron density can be determined through empirical double-effect decomposition.
[0053] In obtaining the combination of the electron density and effective atomic number of the analyte and electron density Then, the effective atomic number values of the unknown sample are obtained through an atomic number estimation model. It represents the product of electron density and effective atomic number raised to the power of m.
[0054] Furthermore, in CT applications such as medical diagnosis, biological research, and security inspection, the parameter m in the photoelectric effect takes a value between 3 and 4. By using the linear decay coefficient, electron density, and atomic number of a substance, the m value corresponding to different substances at different energies can be calculated, and the m value can be obtained. The discrete function is obtained through fitting. A continuous function.
[0055] Furthermore, the parameter m is adaptively adjusted, and different parameters m are calculated for different substances, and the electron density is obtained through substance decomposition. and Then, the parameter m of the unknown sample is estimated by fitting a power function, thereby estimating the effective atomic number:
[0056]
[0057] Beneficial effects:
[0058] This invention proposes a substance identification method that improves the accuracy of empirical substance decomposition through calibration using multiple standard phantoms. Based on a two-effect model, this method proposes an adaptive two-effect substance decomposition algorithm to obtain more accurate estimates of atomic number and electron density, thereby improving the precision of substance identification and solving the problem of inaccurate identification of elements with low atomic numbers in previous substance decomposition methods. Attached Figure Description
[0059] Figure 1 The diagram shows the imaging results of the material identification method of the present invention; wherein, (a) is the imaging result of the standard phantom, (b) is the imaging result of the test phantom, (c) is the electron density image obtained by quantitative analysis of material decomposition, and (d) is the effective atomic number image obtained by quantitative analysis of material decomposition. Detailed Implementation
[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0061] The linear attenuation coefficient is a physical quantity related to X-ray energy, matter density, and atomic number. In energy-spectral CT, the linear attenuation coefficient can be expanded into a linear combination of multiple basis functions:
[0062]
[0063] Wherein, basis functions It is energy-related, the decomposition coefficient It is position-dependent, and the most common set of basis functions is the relationship between the photoelectric effect and the Compton scattering cross section as a function of energy, also known as the "double-effect decomposition". Here, E is the ray energy. I represents the pixel position of the image matrix, and I represents the number of basis functions.
[0064] The interaction between X-rays with energies less than 511 keV and matter is mainly due to the photoelectric effect and Compton scattering.
[0065]
[0066] in, This represents the total photoelectric absorption cross section of the photoelectric effect. The Compton scattering cross section, This represents the total photon interaction cross section.
[0067] The total photoelectric absorption cross section of the photoelectric effect is:
[0068]
[0069] in, E is the atomic number, and E is the radiation energy. It is a constant.
[0070] The Compton scattering cross section is:
[0071]
[0072] in, It is a constant. Representing energy-related quantities:
[0073]
[0074]
[0075] Therefore, the linear decay coefficient of a substance can be expanded as follows:
[0076]
[0077] in, Represents Avogadro's constant. Indicates the effective atomic number, Indicates atomic mass, It represents electron density.
[0078] The key to the decomposition of matter lies in solving the decomposition coefficient. The attenuation of rays passing through matter can be expressed as a weighted average of the attenuation at different energies:
[0079]
[0080] This represents the minimum energy of a ray. This indicates the maximum energy of the radiation.
[0081] in, Line integral representing the decomposition coefficients:
[0082]
[0083] in, Represents X-ray spectrum, Indicates the detector response, To represent a two-dimensional random transformation operator, for the matter decomposition in the projective domain, it is first required that the ray... corresponding Then, the decomposition coefficients are obtained using linear CT reconstruction algorithms (such as filtered back projection, iterative reconstruction, etc.). The relationship between the attenuation projection and the line integral of the decomposition coefficients is established using higher-order polynomials:
[0084]
[0085] in, Let represent the coefficients of the polynomial corresponding to the i-th basis function, where , This represents the maximum order of the polynomial. Indicates the first The logarithmic decay of each energy region, where J represents the number of energy regions. It is a cumulative multiplication operation;
[0086] The reconstruction of the line integral of the decomposed coefficients is as follows:
[0087]
[0088] The coefficients of the polynomial are estimated by least-squares fitting of measurements on multiple standard motifs:
[0089]
[0090] in, Represents the set of polynomial coefficients. It represents the pixel position of the image matrix.
[0091] In the dual-effect decomposition, the effective atomic number and electron density of the calibrated material are used as prior knowledge, and the standard template... for:
[0092]
[0093]
[0094] Where m represents a parameter in the photoelectric effect. and These represent the electron density and effective atomic number of the i-th constituent material of the standard motif, respectively.
[0095] In obtaining the combination of the electron density and effective atomic number of the analyte and electron density Then, the effective atomic number values of the unknown samples are obtained through the effective atomic number estimation model.
[0096] In CT applications such as medical diagnosis, biological research, and security inspection, the parameter 'm' in the photoelectric effect takes a value between 3 and 4, and is a value related to energy and effective atomic number. Based on the linear decay coefficient and a given substance (with electron density and effective atomic number known a priori), the corresponding 'm' values for different substances at different energies can be obtained, and m can be derived. The discrete function is obtained through fitting. A continuous function.
[0097] At different energies, the parameter m exhibits a power-law variation with the effective atomic number. Therefore, this invention proposes an adaptive method for adjusting the parameter m, calculating different parameters m for different substances, thereby making the estimation model of the effective atomic number more accurate. This is achieved by obtaining the electron density through substance decomposition. and Then, the parameter m of the unknown sample is estimated by power function fitting, thereby achieving the estimation of the effective atomic number:
[0098]
[0099] Application example:
[0100] The test experiment used 10mm φ Cylindrical carbon (C), water, and aluminum (Al) phantoms of 100 μm were used as calibration materials for a 10 mm diameter phantom. 100m cylindrical polymethyl methacrylate (PMMA), polytetrafluoroethylene (Teflon), and polyvinyl chloride (PVC) phantoms were used for material decomposition and effective atomic number quantification. The highest imaging voltage was 120kVp, and the two thresholds of the photon counting detector were set to 45keV and 75keV, respectively, thus obtaining data in two energy regions: 45-75keV and 75-120keV.
[0101] Figure 1 The imaging results for the standard motif, the test motif, the electron density, and the effective atomic number are displayed. Figure 1 (a) in the image represents the imaging result of the standard phantom. Figure 1 (b) in the image shows the imaging results of the test phantom. Figure 1 Image (c) in the image is an electron density image obtained quantitatively through the decomposition of substances. Figure 1 In the figure (d), the effective atomic number image is obtained through quantitative analysis of the substance decomposition. Table 1 shows the quantitative results and errors of effective atomic number and electron density. It can be seen that the quantitative results of this invention have a quantitative error of less than 5% for substances with low atomic number (PMMA, Teflon) and substances with medium atomic number (PVC), which can effectively identify substances.
[0102] Table 1. Quantitative results and percentage error of effective atomic number and electron density.
[0103]
[0104] This invention proposes a substance identification method that improves the accuracy of substance decomposition through calibration with multiple standard phantoms. This invention can use two or more calibration materials to estimate electron density and effective atomic number. This invention proposes an adaptive effective atomic number estimation model, further improving the accuracy of substance identification. This invention can achieve relatively accurate estimation of electron density and effective atomic number for different types of substances; it can be applied to, but is not limited to, various dual-energy CT and spectral CT devices; and is suitable for medical imaging applications, security inspection applications, and non-destructive testing applications.
[0105] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for identifying substances, characterized in that, Includes the following steps: Step (1) involves performing empirical dual-effect substance decomposition. This is achieved by calibrating multiple standard phantoms, performing polynomial combinations on the projection data, and constraining the data in the image domain to determine the decomposition parameters and estimate the electron density. The substance decomposition includes solving for the decomposition coefficients. The attenuation of rays passing through matter is expressed as a weighted average of attenuations at different energies; for the matter decomposition in the projected domain, the ray attenuation is first solved. The line integral of the corresponding decomposition coefficients Then, the decomposition coefficients are solved using a linear CT reconstruction algorithm. The relationship between decaying projection and decomposition coefficient line integral is established using higher-order polynomials. The line integrals of the decomposition coefficients are reconstructed; the coefficients of the polynomial are estimated by least-squares fitting through measurements of multiple standard motifs; in the empirical dual-effect substance decomposition, the effective atomic number and electron density of the standard motifs are used as prior knowledge to obtain the standard template. ; The formula for reconstructing the line integral of the decomposed coefficients is: （11） in, The line integral representing the decomposition coefficients of the reconstruction. The line integral representing the decomposition coefficients. This represents the two-dimensional random transformation operator. Let represent the coefficients of the polynomial corresponding to the i-th basis function, where , This represents the maximum order of the polynomial. Indicates the first The logarithmic decay of each energy region, where J represents the number of energy regions. It is a cumulative multiplication operation; The coefficients of the polynomial are estimated by least-squares fitting of measurements on multiple standard motifs, as shown in the formula: （12） in, Represents the set of polynomial coefficients. These are the pixel positions in the image matrix; Standard Template for: ； （13） Where m represents a parameter in the photoelectric effect. and Let represent the electron density and effective atomic number of the i-th constituent material of the standard motif, respectively. The decomposition parameters and electron density are determined by empirical double-effect material decomposition. Step (2) involves estimating the effective atomic number. An adaptive effective atomic number estimation model is established through the calibration of a known standard phantom to estimate the effective atomic number of the imaging material. This process involves obtaining a combination of the electron density and effective atomic number of the analyte. and electron density Then, the effective atomic number values of the unknown samples were obtained through an effective atomic number estimation model. This represents the product of electron density and effective atomic number raised to the power of m. Using the linear decay coefficient, electron density, and effective atomic number of a substance, the values of parameter m for different substances at different energies are calculated, and m is obtained. The discrete function is obtained through fitting. A continuous function; the parameter m is adaptively adjusted, with different parameters m calculated for different substances, and the electron density is obtained through substance decomposition. and Then, the parameter m of the unknown sample is estimated by fitting a power function, thereby realizing the estimation of the effective atomic number; In medical diagnosis, biological research, and CT security inspection applications, the parameter m in the photoelectric effect takes a value between 3 and 4.
2. The substance identification method according to claim 1, characterized in that, Step (1) includes: In energy-spectral CT, the linear attenuation coefficient is expanded into a linear combination of multiple basis functions: （1） Wherein, basis functions It is energy-related, the decomposition coefficient The spatial distribution of the basis functions is position-dependent, and E represents the ray energy. is the pixel position of the image matrix, and I represents the number of basis functions.
3. The substance identification method according to claim 2, characterized in that, Step (1) includes: The basis functions are the relationship between the total photoelectric absorption cross section and the Compton scattering cross section of the photoelectric effect and energy. This decomposition is a two-effect decomposition. In medical diagnostics, biological research, and CT scan applications for security inspections, the interaction between X-rays and matter includes the photoelectric effect and Compton scattering: （2） in, This represents the total photoelectric absorption cross section of the photoelectric effect. The Compton scattering cross section, The total photon interaction cross section; The total photoelectric absorption cross section of the photoelectric effect is: （3） in, E is the effective atomic number, and E is the radiation energy. It is a constant; The Compton scattering cross section is: （4） in, It is a constant. Representing energy-related quantities: （5） （6） The linear decay coefficient of a substance is expanded as follows: （7） in, Represents Avogadro's constant. Indicates the effective atomic number, Represents the m-th power of the effective atomic number. Indicates atomic mass, It represents electron density.
4. The substance identification method according to claim 3, characterized in that, The decomposition of matter in step (1) includes solving for the decomposition coefficient. The attenuation of rays passing through matter can be expressed as a weighted average of the attenuation at different energies, as follows: （8） in, This represents the minimum energy of a ray. Indicates the maximum energy of the radiation; in, Line integral representing the decomposition coefficients: （9） in, Represents X-ray spectrum, Indicates the detector response, Represents a two-dimensional random transformation operator; The relationship between attenuated projection and the line integral of the decomposition coefficients is established using higher-order polynomials, and the formula is as follows: （10） in, Let represent the coefficients of the polynomial corresponding to the i-th basis function, where , This represents the maximum order of the polynomial. Indicates the first The logarithmic decay of each energy region, where J represents the number of energy regions. It is a cumulative multiplication operation.
5. The substance identification method according to claim 1, characterized in that, The formula for estimating the effective atomic number is: （14）。