An empirical correction method for material decomposition in energy-spectral CT
By employing an empirical decomposition method in energy-dispersive CT and combining the polynomial relationship between primary and secondary calibrators, the problem of insufficient decomposition accuracy was solved, achieving high-precision quantitative analysis of substances, which is applicable to biomedicine and non-destructive testing.
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
- 2024-05-31
- Publication Date
- 2026-05-26
AI Technical Summary
Existing energy-dispersive CT material decomposition algorithms have limited decomposition accuracy, are easily affected by the size of the calibration material and the hardening effect, and the decomposition results are easily affected by artifacts.
An empirical correction method for material decomposition using energy-dispersive CT is adopted. By selecting appropriate primary calibrators to establish polynomial relationships, material decomposition is performed using photon-counting energy-dispersive CT data, and empirical decomposition errors are evaluated and corrected using secondary calibrators, thereby achieving high-precision quantitative analysis of materials.
It improves the accuracy of substance decomposition, effectively corrects errors caused by calibration object size and hardening effect, and realizes high-precision measurement of substances of interest, applicable to biomedicine and non-destructive testing.
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Figure CN118711707B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of energy spectrum CT image processing, and specifically relates to an empirical correction method for energy spectrum CT material decomposition. Background Technology
[0002] Spectral CT has important applications in the quantitative identification of substances in biomedicine, non-destructive testing, and other fields. In non-destructive testing, it is used for quantitative measurement of explosive material concentrations and quantitative analysis of bone components in fossils. In biomedicine, it is used to differentiate the components of coronary atherosclerotic plaques based on the concentration of iodine contrast agents and to distinguish between different ventricles of cerebral hemorrhage. However, the independent application of spectral CT cannot achieve the purpose of substance decomposition. To obtain the ability to quantitatively analyze substances, substance decomposition algorithms are an important method for the identification and quantification of substances using spectral CT.
[0003] Common material decomposition methods are mainly divided into: projection domain decomposition, image domain decomposition, and one-step decomposition. Image domain decomposition is simple to operate, requiring only decomposition processing of the reconstructed image, but it is highly susceptible to artifact interference and has relatively poor decomposition accuracy. One-step decomposition has better decomposition accuracy, but its algorithm is highly complex, computationally intensive, and difficult to implement. Projection domain decomposition obtains the decomposed projection map by processing multi-energy-zone projection images, which can suppress hardening artifacts and is a hot research topic. However, it often requires accurate system response functions and spectral information, making modeling complex and placing high demands on the system. Furthermore, in practical applications, due to component aging, sputtering of anode material on the X-ray tube window, and other influences, the spectrum and detector response may change and must be measured periodically.
[0004] In experiments, researchers tend to favor simple and easy-to-use methods that can quantitatively analyze the scanned substances. Wong CK et al. described empirical decomposition methods as simple and easy to use, and widely adopted in practical applications. Among substance decomposition algorithms, empirical decomposition is a projection domain decomposition method based on experience and experimental data. William R. Brody et al. established a calibration process and used polynomial fitting to link the absorption characteristics and energy spectrum data of known substances with the substances to be scanned, thereby achieving substance identification. In practical applications, researchers are continuously improving and refining empirical decomposition methods. Inspired by the empirical cupping correction (ECC) method, Stenner et al. proposed the empirical dual energy calibration (EDEC) method. This method solves for the proportion of substance components by polynomial combination of multi-energy projection data in the projection domain and constraint of the combined polynomial image in the image domain. The proportion of substance components obtained through substance decomposition can be used to estimate the effective atomic number, thereby achieving substance identification. This method makes it possible to operate on the empirical decomposition method of the projection domain in the reconstructed image, further improving the convenience of the method.
[0005] Researchers Xiaomei Zhang, Duda MA, and others described common problems with empirical material decomposition algorithms. Empirical material decomposition models are susceptible to artifact interference, and the decomposition results and image quality require the selection of appropriate calibration materials and calibration phantoms of suitable sizes. Duda MA explained the impact of calibration phantoms of different sizes on decomposition accuracy. Furthermore, factors such as hardening artifacts in the scanned material also negatively affect decomposition accuracy. Summary of the Invention
[0006] To address the limitations of empirical decomposition algorithms and their susceptibility to the influence of calibration material size and hardening effects, this invention proposes an empirical correction method for energy dispersive spectroscopy (EDS) material decomposition, enabling quantitative analysis of substances using EDS. This method, based on an empirical decomposition algorithm, effectively improves the inaccuracy of decomposition values obtained by the algorithm, achieving quantitative measurement of substances of interest. The proposed EDS material decomposition empirical correction method consists of two parts: empirical material decomposition and decomposition correction. In the empirical material decomposition method, a suitable primary calibration material is selected, containing the material of the desired substance of interest. The number of material components is equal to the number of energy chambers in the EDS CT. A polynomial relationship is established between the EDS CT projection data of the primary calibration material and its material composition, and the material decomposition coefficients corresponding to the calibration material components are obtained. In the empirical decomposition correction, a series of samples of different concentrations are used to form a secondary calibration material. The sample material is the same as one of the substances of interest in the primary calibration material, and the maximum concentration does not exceed the concentration of the selected substance in the primary calibration material. Using the obtained decomposition coefficients of the corresponding substances, empirical decomposition of secondary calibration materials is performed. By referring to the actual concentration values of the secondary calibration materials, a relationship is established between the decomposition error and the decomposition value, enabling error estimation and correction of the empirical decomposition values. This invention, combined with photon counting spectroscopy CT, allows for complete matching of acquired X-ray energy data.
[0007] To achieve the above objectives, the present invention adopts the following technical solution:
[0008] A method for correcting material decomposition in energy-spectral CT, such as Figure 1 As shown, it includes the following steps:
[0009] Step (1) Empirical material decomposition of the substance scanned by energy-dispersive CT: Select a suitable primary calibration material, in which the material is the material of interest to be detected, and the number of material components is the same as the number of energy regions of the energy-dispersive CT used. Establish a polynomial relationship between the energy-dispersive CT projection data of the primary calibration material and the material composition of the primary calibration material using energy-dispersive CT, and obtain the material decomposition coefficients corresponding to the components of the primary calibration material. Use the material decomposition coefficients to perform empirical decomposition of the substance scanned by energy-dispersive CT to obtain the empirical decomposition value of the scanned substance;
[0010] Step (2) Correcting the empirical substance decomposition: A series of samples with different concentrations are used to form a secondary calibration compound. The sample material is the same as one substance of interest in the primary calibration compound, and the maximum concentration is not higher than the concentration of the selected substance in the primary calibration compound. Using the substance decomposition coefficient corresponding to this substance of interest in the primary calibration compound obtained in step (1), empirical substance decomposition is performed on the secondary calibration compound to obtain the empirical decomposition value of the secondary calibration compound. Referring to the actual decomposition value corresponding to the actual concentration value of the secondary calibration compound, the empirical decomposition error of the secondary calibration compound is obtained. A polynomial relationship between the empirical decomposition value and the empirical decomposition error of the secondary calibration compound is established using the least squares method. Then, using the polynomial relationship, the error of the empirical decomposition value of the scanned substance is obtained, and the empirical decomposition value of the substance scanned by the energy spectrum CT is corrected according to the error.
[0011] Further, step (1) includes:
[0012] The linear attenuation coefficient of any substance in energy-dispersive X-ray CT can be represented by a linear combination of the attenuation coefficients of multiple other substances:
[0013]
[0014] It is the position of any substance At point E, the linear attenuation coefficient in a photon beam with energy E. M represents the number of other substances set in the matrix. This represents the decay coefficient of the i-th substance at energy E. This indicates the pixel position of the i-th substance in energy-spectral CT. The decomposition value to be solved at this location. The multiple other substances are represented as the basic substances used for decomposition, or simply the base substances.
[0015] Furthermore, the physical process by which rays penetrate matter can be described as follows:
[0016]
[0017]
[0018] in I It is the intensity of the X-rays after the ray passes through the matter, while 𝐼0 is the initial intensity of the X-rays before the ray enters the matter. E min and 𝐸 max These are the minimum and maximum energies of the X-ray energy spectrum, respectively. Let represent the X-ray energy spectrum distribution function of CT at different energies E. This represents the detector efficiency of an X-ray detector relative to energy E. Let represent the two-dimensional Radon transform operator, and let represent the line integral of the ray passing through the path l. express The line integral;
[0019] In energy-dispersive spectroscopy (EDS) for material decomposition, the projection domain decomposition method uses the projection data of the base material to solve for the projected values of the material composition. Then, CT reconstruction was used to obtain the material decomposition values. .
[0020] In practice, we need to obtain the decomposition coefficients of the corresponding substances. This requires establishing the relationship between the multi-energy projection data of the primary calibration material and the projection data of the material's decomposition values through polynomial fitting. The primary calibration material typically consists of multiple base materials, the types of which are the same as the number of energy regions in the energy spectrum CT used. In the expression, we represent the estimated projection data of the primary calibration material's decomposition values as follows:
[0021]
[0022] In order to distinguish the estimated decomposition projection data of the calibrator from that of the analyte, This represents the projected decomposition values of the estimated calibration material. In the formula, , This represents the maximum order of the polynomial, and for each basis substance i, the decomposition coefficient vector. The total number of coefficients in is Each coefficient therein is used J represents the number of energy zones used in the spectral CT scan. Taking dual-energy CT as an example, the energy zones are set to two, which corresponds to the number of materials in the first-level calibration material being 2, i.e., J=2, i=1,2. The first-level calibration object Projected data of each energy region, among which Let be the intensity of the X-rays in the j-th energy region after passing through the first-order calibration material. This represents the initial X-ray intensity before the X-rays in the j-th energy region are incident;
[0023] To further obtain the decomposition coefficients of the corresponding substances, based on the projection data of the primary calibration material, formula (4) can be further transformed into:
[0024]
[0025] in This is the inverse transform of the Radon operator.
[0026] Next, we will calculate the decomposition coefficients of the corresponding substances. Since the material composition of the calibration material is known, we will calculate the estimated decomposition values of the first-order calibration material. The decomposition values corresponding to the actual material composition of the primary standard are minimized. This is achieved by minimizing the predicted values. The decomposition coefficients are determined by the difference between the actual value and the true value. The specific solution process uses the SVD decomposition method:
[0027]
[0028]
[0029] in, Let i be the decomposition value corresponding to the actual material composition of the i-th matrix material in the primary standard, and let the percentage content of each matrix material be used as prior knowledge. In this way, the decomposition coefficient of the corresponding matrix material i is obtained.
[0030] However, the decomposition coefficients obtained using primary calibration materials still introduce errors when decomposing the scanned substance. For the desired decomposition of a substance, using the empirical decomposition coefficients of a base substance of the same type to decompose the target object, the resulting empirical decomposition values and empirical decomposition errors can be described as follows:
[0031]
[0032] To better represent this, we decompose the target object using empirical decomposition coefficients of the same base material as the type of substance to be decomposed. The notation is then reformulated, where... This represents an empirical decomposition value obtained using a decomposition coefficient. This represents the error-free decomposition value of the target object. This represents empirical decomposition error.
[0033] For empirical polynomial decomposition, decomposition errors can arise from various sources, including artifacts, noise, and computational errors. The primary influence comes from the size of the calibration material. Empirical decomposition requires the hardening degree of the calibration material to be close to that of the scanned material, necessitating the selection of an appropriate calibration material size; otherwise, significant decomposition errors will occur. While it's difficult to describe the decomposition error precisely using formulas in the physical model, a relationship between the decomposition values and the decomposition error can be established using polynomial relationships, similar to empirical decomposition, by setting additional calibration materials.
[0034] Further, step (2) includes:
[0035] This invention evaluates and corrects empirical decomposition errors by setting up secondary calibration materials. During operation, the decomposition value obtained using the empirical decomposition coefficient of one of the base substances is corrected. First, the secondary calibration material needs to be empirically decomposed using this empirical decomposition coefficient. The secondary calibration material consists of a series of samples with different concentrations. The materials of the samples are the same as the base substance materials corresponding to the empirical decomposition coefficient used, and the maximum concentration of the samples is not higher than the concentration of the calibration material, to ensure that the decomposition value obtained through empirical decomposition does not exceed 1, i.e., the meaning represented by formula (7). The secondary calibration material is decomposed using the empirical decomposition coefficient, and a polynomial fitting relationship between the decomposition value and the true concentration value is established to obtain the correction coefficient for decomposition correction:
[0036]
[0037]
[0038] in It is a matrix representing the polynomial fitting matrix of the empirical decomposition values of the second-level calibration objects. This represents the m-th order fitting term of the empirical decomposition value of the s-th sample in the secondary calibration. The decomposition value represents the empirical decomposition coefficient of the s-th sample in the secondary standard compound obtained by applying it to a base substance in the primary standard compound. Decomposition error, is the m-th order fitting coefficient of the polynomial fitting coefficients.
[0039] By obtaining the correction coefficient Then, the empirical decomposition value can be substituted into formula (10) to estimate the error of the corresponding empirical decomposition value. The estimated empirical decomposition error is then subtracted to finally obtain a high-precision decomposition result.
[0040] In assessing the accuracy of the decomposition, the absolute value of the decomposition residuals is used. The absolute value of the percentage of decomposition residuals Conduct an assessment:
[0041]
[0042]
[0043] The advantages of this invention are as follows:
[0044] This method, based on empirical substance decomposition, estimates the error of empirical decomposition in the image domain and obtains high-precision decomposition results by designing secondary calibration materials. This invention effectively improves the accuracy of substance decomposition values, compensates for the shortcomings of empirical decomposition models, and enables high-precision measurement of substances using energy-dispersive spectroscopy (EDS). This invention can effectively correct decomposition errors caused by empirical calibration materials of different sizes, achieving quantitative measurement of contrast agent content in biomedicine. Furthermore, this invention has broad application prospects in biomedicine and non-destructive testing. Attached Figure Description
[0045] Figure 1 This is a flowchart of the method of the present invention.
[0046] Figure 2 The relationship between the decomposition error and decomposition value of the test analyte and the secondary calibration analyte is shown in the residual fitting curve of the secondary calibration analyte.
[0047] Figure 3 Reconstruct images and corresponding concentration maps of the test analytes, as well as images after decomposition.
[0048] (a) shows the reconstruction results for [34-50] keV, with the red circles indicating the selection method for the region of interest;
[0049] (b) is a graph showing the concentration of iohexol in the test sample;
[0050] (c) is a graph showing the concentration of iohexol obtained through empirical decomposition;
[0051] (d) is a graph of iohexol concentration obtained by empirical correction method.
[0052] Figure 4 A comparison diagram of the empirical decomposition and empirical correction results for the region of interest of the test object.
[0053] Figure 5 A comparison chart showing the results of the original empirically decomposed APE and those of the present invention under different sizes of empirical calibrators;
[0054] (a) represents the decomposition error of the original empirical decomposition method under four different calibration materials;
[0055] (b) represents the decomposition error of the present invention under four different calibration materials. Detailed Implementation
[0056] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.
[0057] The linear attenuation coefficient of any substance in energy-dispersive X-ray CT can be represented by a linear combination of the attenuation coefficients of multiple other substances. In this invention, we use dual-energy dual-substance decomposition:
[0058]
[0059] It is the position of any substance At this point, the linear attenuation coefficient in a photon beam with energy E. The number of base materials is set to be the same as the number of energy regions, which is equal to 2. This represents the decay coefficient of the i-th substance at energy E. This indicates the pixel position of the i-th substance in energy-spectral CT. The solution needs to be found at the given location. Furthermore, the physical process of rays penetrating matter can be described as follows:
[0060]
[0061]
[0062] in I It is the intensity of the X-rays after the ray passes through the matter, while 𝐼0 is the initial intensity of the X-rays before the ray enters the matter. E min and 𝐸 max These are the minimum and maximum energies of the X-ray energy spectrum, respectively. Let represent the X-ray energy spectrum distribution function of CT at different energies E. This represents the detector efficiency of an X-ray detector relative to energy E. Let represent the two-dimensional Radon transform operator, and let represent the line integral of the ray passing through the path l. express The line integral;
[0063] In energy-dispersive spectroscopy (EDS) for material decomposition, the projection domain decomposition method uses the projection data of the base material to solve for the projected values of the material composition. Then, CT reconstruction was used to obtain the material decomposition values. .
[0064] In practice, we need to obtain the decomposition coefficients of the corresponding substances. This requires establishing the relationship between the multi-energy projection data of the primary calibration material and the projection data of the material's decomposition values through polynomial fitting. The primary calibration material typically consists of multiple base materials, the types of which are the same as the number of energy regions in the energy spectrum CT used. In the expression, we represent the estimated projection data of the primary calibration material's decomposition values as follows:
[0065]
[0066] In order to distinguish the estimated decomposition projection data of the calibrator from that of the analyte, This represents the projected decomposition values of the estimated calibration material. In the formula, , This represents the maximum order of the polynomial, and for each basis substance i, the decomposition coefficient vector. The total number of coefficients in is Each coefficient therein is used express. Where j=1 and 2 represent the low-energy and high-energy projection data, respectively. j=1 and 2 represent the intensities of low-energy and high-energy X-rays after they pass through the matter, respectively. , j=1, 2 represent the initial X-ray intensities before low-energy and high-energy X-rays enter the matter, respectively;
[0067] To further obtain the decomposition coefficients of the corresponding substances, based on the projection data of the primary calibration material, formula (4) can be further transformed into:
[0068]
[0069] in This is the inverse transform of the Radon operator.
[0070] Next, we will calculate the decomposition coefficients of the corresponding substances. Since the material composition of the calibration material is known, we will calculate the estimated decomposition values of the first-order calibration material. The decomposition values corresponding to the actual material composition of the primary standard are minimized. This is achieved by minimizing the predicted values. The decomposition coefficients are determined by the difference between the actual value and the true value. The specific solution process uses the SVD decomposition method:
[0071]
[0072]
[0073] in, Let i be the decomposition value corresponding to the actual material composition of the i-th matrix material in the primary standard, and let the percentage content of each matrix material be used as prior knowledge. In this way, the decomposition coefficient of the corresponding matrix material i is obtained.
[0074] However, the decomposition coefficients obtained using primary calibration materials still introduce errors when decomposing the scanned substance. For the desired decomposition of a substance, using the empirical decomposition coefficients of a base substance of the same type to decompose the target object, the resulting empirical decomposition values and empirical decomposition errors can be described as follows:
[0075] To better represent this, we decompose the target object using empirical decomposition coefficients of the same base material as the type of substance to be decomposed. The notation is then reformulated, where... This represents an empirical decomposition value obtained using a decomposition coefficient. This represents the error-free decomposition value of the target object. This represents empirical decomposition error.
[0076] This invention evaluates and corrects empirical decomposition errors by setting up secondary calibration materials. During operation, the decomposition value obtained using the empirical decomposition coefficient of one of the base substances is corrected. First, the secondary calibration material needs to be empirically decomposed using this empirical decomposition coefficient. The secondary calibration material consists of a series of samples with different concentrations. The materials of the samples are the same as the base substance materials corresponding to the empirical decomposition coefficient used, and the maximum concentration of the samples is not higher than the concentration of the calibration material, to ensure that the decomposition value obtained through empirical decomposition does not exceed 1, i.e., the meaning represented by formula (7). The secondary calibration material is decomposed using the empirical decomposition coefficient, and a polynomial fitting relationship between the decomposition value and the true concentration value is established to obtain the correction coefficient for decomposition correction:
[0077]
[0078]
[0079] in It is a matrix representing the polynomial fitting matrix of the empirical decomposition values of the second-level calibration objects. This represents the m-th order fitting term of the empirical decomposition value of the s-th sample in the secondary calibration. The decomposition value represents the empirical decomposition coefficient of the s-th sample in the secondary standard compound obtained by applying it to a base substance in the primary standard compound. Decomposition error, represents the m-th order fitting coefficient of the polynomial. In practical applications, m is usually set to 2 or 3.
[0080] By obtaining the correction coefficient Then, the empirical decomposition value can be substituted into formula (10) to estimate the error of the corresponding empirical decomposition value. The estimated empirical decomposition error is then subtracted to finally obtain a high-precision decomposition result.
[0081] Application example:
[0082] The experimental section tested its application for quantitative measurement of contrast agents in biomedical experiments. A 150 mg / ml iohexol solution (15 mm diameter) and 15 mm diameter water were used as primary calibrators. For secondary calibrators, various concentrations of samples were prepared, with the sample material remaining the same as the calibrators: iohexol solution (Table 1), assembled using 10 mm diameter centrifuge tubes. The experimental equipment conditions are shown in Table 2.
[0083] Table 1 shows the concentrations of secondary calibration compounds and test substances.
[0084]
[0085] Table 2 shows the scanning conditions.
[0086]
[0087] This invention first plots the relationship between the empirical decomposition error and the empirical decomposition value of the secondary calibration material and the test material after empirical material decomposition, as shown in the figure. Figure 2 As shown.
[0088] This invention uses the actual concentration value of the test substance as a reference and compares the results of empirical decomposition and empirical correction methods, such as... Figure 3 , Figure 4 As shown.
[0089] To verify that this invention has good correction capabilities for empirical decomposition results under different calibration object sizes, we set up four sizes of empirical calibration objects. For example... Figure 4 As shown, the empirical correction results effectively reduced the decomposition error caused by calibration materials of different sizes.
[0090] Table 3 lists empirical calibration materials of different sizes.
[0091]
[0092] Comparison of the results of the original empirical decomposition of APE with those of the present invention under different sizes of empirical calibrators. Figure 5 As shown.
[0093] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.
Claims
1. An empirical correction method for material decomposition in energy-dispersive spectroscopy (EDS) CT, comprising the following steps: 1) Select a primary calibration material based on the material of the substance of interest. The number of material components in the primary calibration material is the same as the number of energy regions in the energy spectrum CT. The primary calibration material contains the substance of interest. Use energy spectrum CT to establish a first polynomial relationship between the energy spectrum CT projection data of the primary calibration material and the material components of the primary calibration material. Obtain the material decomposition coefficients corresponding to the material components of the primary calibration material by solving the first polynomial relationship. Then, perform empirical decomposition on the substance scanned by the energy spectrum CT based on the material decomposition coefficients to obtain the empirical decomposition values of the scanned substance. 2) Select a series of samples with different concentrations as secondary calibrators. The material of the samples is the same as that of the substance of interest in the primary calibrator, and the maximum concentration of the samples is not higher than the concentration of the substance of interest in the primary calibrator. Using the material decomposition coefficients corresponding to the substances of interest in the primary calibration material obtained in step 1), the secondary calibration material is empirically decomposed to obtain the empirical decomposition values of the secondary calibration material. Then, by referring to the actual decomposition value corresponding to the actual concentration value of the secondary standard, the empirical decomposition error of the secondary standard is obtained; Then, a second polynomial relationship is established between the empirical decomposition value and the empirical decomposition error of the secondary calibration material. The error of the empirical decomposition value of the substance scanned by the energy spectrum CT is obtained using the second polynomial relationship. The empirical decomposition value of the substance scanned by the energy spectrum CT is then corrected based on the error. Wherein, the second polynomial relation is Substituting the empirical decomposition values of the secondary calibrators into the second polynomial relationship yields the error of the empirical decomposition values of the substances scanned by the energy dispersive spectroscopy (EDS) CT. Then according to the formula Obtain the correction coefficient According to the correction factor The empirical decomposition values of the substances scanned by the energy-dispersive CT are corrected; wherein, the error , It is a matrix representing the polynomial fitting matrix of the empirical decomposition values of the second-level calibration objects. The m-th order fitting term represents the empirical decomposition value of the s-th sample in the secondary calibration. The decomposition value represents the empirical decomposition coefficient of the s-th sample in the secondary standard compound obtained by applying it to a base substance in the primary standard compound. Decomposition error, is the m-th order fitting coefficient of the polynomial fitting coefficients.
2. The method according to claim 1, characterized in that, The method for establishing the first polynomial relationship is as follows: The energy spectrum CT projection data of the first-order calibration material is used as the basis for... Transformed into the decomposition value of the first-level calibration material As the first polynomial relation; where... , The coefficient of decomposition of the i-th matrix substance in the first-order calibration compound represents the maximum order of the polynomial. include One coefficient, Decomposition coefficients One coefficient, J, represents the number of energy regions in the energy spectrum CT. This indicates that the primary calibrator is in the first... Projection data of each energy region This represents the intensity of X-rays from the j-th energy region after passing through the primary calibration material. This represents the initial X-ray intensity before the X-rays in the j-th energy region are incident; This is the inverse transform of the Radon operator.
3. The method according to claim 2, characterized in that, By minimizing The material decomposition coefficient of the primary calibration material is determined by the difference between the actual value and the actual value.
4. The method according to claim 3, characterized in that, The decomposition coefficients are obtained using the SVD decomposition method. .
5. The method according to claim 1, characterized in that, A second polynomial relationship between the empirical decomposition values and empirical decomposition errors of the second-level calibration material is established using the least squares method.