High-resolution dual-energy ct reconstruction method based on prior information

Abstract

The application discloses a high-resolution dual-energy CT reconstruction method based on prior information, comprising the following steps: step one, a high-resolution dual-energy CT scanning model; step two, an iterative dual-energy reconstruction algorithm based on BPF; step three, a CT iterative reconstruction algorithm based on prior information; step four, numerical experiment and result analysis; the high-resolution dual-energy CT reconstruction method based on prior information designs a hybrid type of dual-energy CT scanning system, studies the advantages of dual-energy CT material division and the advantages of high-resolution micro-CT, and proposes a CT iterative reconstruction algorithm based on prior information; the algorithm can perform high-resolution spectral reconstruction on the line pair card, reconstructs the spectral projection data first to obtain a low-resolution base image, optimally combines the base image as prior information with high-resolution projection data, and finally obtains a high-resolution base image, thereby avoiding the occurrence of the situation that a slight bone fracture is missed.

Description

Technical Field

[0001] This invention relates to the field of high-resolution dual-energy spectral CT reconstruction technology, specifically to a high-resolution dual-energy spectral CT reconstruction method based on prior information. Background Technology

[0002] CT, or computed tomography, uses precisely collimated X-ray beams, gamma rays, ultrasound, etc., along with highly sensitive detectors to scan a specific part of the human body in a series of cross-sections. It features fast scanning time and clear images and can be used to examine a variety of diseases. In medicine, dual-energy spectral CT is often used to diagnose skeletal diseases. However, current dual-energy spectral CT has relatively low spatial resolution, which can lead to partial volume effect and result in missed detection of minor fractures. Summary of the Invention

[0003] The purpose of this invention is to provide a high-resolution dual-energy spectral CT reconstruction method based on prior information to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a high-resolution dual-energy spectral CT reconstruction method based on prior information, comprising the following steps: Step 1, a high-resolution dual-energy spectral CT scanning model; Step 2, an iterative dual-energy spectral reconstruction algorithm based on BPF; Step 3, an iterative CT reconstruction algorithm based on prior information; Step 4, numerical experiments and result analysis.

[0005] In step one above, one set is designed as a high-resolution integrating detector, and the other set is designed as a photon counting detector. Under ideal conditions, assuming that the X-rays are formed by photons of a single energy E, and ignoring the effects of scattering and other factors, for monoenergetic X-rays, energy E is usually neglected. The projection data along the X-ray path L is then expressed as:

[0006] p(L)=-∫ L μ(x)dl

[0007] Where μ(x) represents the linear attenuation coefficient of the object under test, x represents its coordinate position, and l represents its thickness. Ignoring scattered photons, the multi-energy projection data along the X-ray path L is expressed as:

[0008]

[0009] Where μ(x, E) represents the linear attenuation coefficient of the object under test, E represents the photon energy, and S(E) is the normalized equivalent energy spectrum; in dual-energy spectral CT, the linear attenuation coefficient of the object under test is often decomposed into a linear combination of two basis functions, i.e.:

[0010]

[0011] in θ(E) and θ(E) are two energy-dependent basis functions, while f(x) and g(x) are position-dependent functions, independent of energy, representing the coefficients of the corresponding basis functions. There are generally two methods for selecting basis functions: one is physical effect decomposition, and the other is two-basis-material decomposition. In the physical effect decomposition method, the basis functions are:

[0012]

[0013] The basis functions represent the dependence of the photoelectric effect cross section on energy:

[0014]

[0015] The Compton cross section is expressed as a dependence on energy, where a = E / 510.975 keV; f(x) and g(x) represent the coefficient distributions of the two effect cross sections, respectively; in the bi-basic material decomposition method, the basis functions... θ(E) and θ(E) represent the mass decay coefficients of the two base materials, respectively, and f(x) and g(x) represent the density distribution images of the two base materials in the object under test, respectively; Substitute We can obtain:

[0016]

[0017] The problem of reconstructing the dual-energy spectrum is then transformed into knowing P k (L), k=1,2 The problem is to find f(x) and g(x); the high-resolution dual-energy spectral reconstruction model is transformed into a solution for two high-resolution matrix material images with different densities, given three sets of projection data: one set of high-resolution projection data and two sets of energy spectral projection data. and The problem stems from p(L)=-∫ L μ(x)dl and From a formal perspective, there are differences between energy-ignoring reconstruction and dual-energy spectral reconstruction for the same measured object. However, in general, they both reflect the structural information of different substances inside the same measured object, which can be approximated as μ(x)≈μ(x,E), thus establishing the relationship between energy-ignoring reconstruction and dual-energy spectral reconstruction.

[0018] In step two above, the specific steps of the IBPF algorithm are as follows:

[0019] 4) Assign an initial value to f (0) (x)=0,g (0) (x) = 0;

[0020] 5) Assume that after the nth iteration, the base material image f is obtained. (n) (x)=0,g (n)(x) = 0, calculate the reconstructed matrix material image along the energy spectrum projection path according to the following formula. The line integral for k = 1, 2 is denoted as and The formula is:

[0021]

[0022] 6) Estimate the projection path along the energy spectrum according to the following formula (1). Dual-energy projection data for k=1,2, where S k (E), k=1,2 represents the equivalent energy spectrum; according to the following formula (2), calculate the projection path along the energy spectrum. Weighting coefficients for k = 1, 2 and M (n) (L), Formula (1) is:

[0023]

[0024] Formula (2) is:

[0025]

[0026] 4) Calculate the path along the energy spectrum projection using the following formula. Weighted projected residuals for k=1,2 and The formula is:

[0027]

[0028] 5) Apply the BPF algorithm (denoted as BPF) to the weighted projection residuals respectively. Image reconstruction is performed using the BPF reconstruction operator to obtain the weighted projection residual image Δf1. (n) (x), and As shown in the following formula:

[0029]

[0030] f (n+1) (x)g (n+1) (x), the formula is as follows:

[0031] 6) Update the base material image to be reconstructed according to the following formula and

[0032]

[0033] 7) Determine if the convergence criterion is met. If it is met, stop the iteration; otherwise, go to step 2) and perform the next iteration. The reconstructed image does not depend on the geometric path of the rays, so the IBPF algorithm is suitable for both reconstructing high- and low-energy X-ray paths that are consistent and reconstructing high- and low-energy X-ray paths that are inconsistent.

[0034] In step three above, the steps of the CT iterative reconstruction algorithm based on prior information are as follows:

[0035] 1) Optimization Model Incorporating Prior Information: The high-resolution dual-energy spectral reconstruction model solves the image problem of two substrate materials with different densities using two sets of projection data of different types. Reconstruction algorithms differ for different types of projection data. For energy spectral projection data, we use the IBPF algorithm for dual-energy spectral reconstruction to obtain the base image, but the base image suffers from low spatial resolution. Prior information refers to the experience and data obtained before the experiment. For discretized CT reconstruction models, incorporating prior information during reconstruction is an important constraint, improving the accuracy and convergence rate of the reconstructed image. Therefore, we use the low-resolution base image as prior information and incorporate it into the model reconstructed from the high-resolution projection data, establishing an optimization model that integrates prior information. Thus, the objective function of the high-resolution dual-energy spectral reconstruction model is transformed into:

[0036]

[0037]

[0038] in, A high-resolution image of the low-density matrix material to be solved; This represents a high-resolution image of the high-density matrix material to be solved; A = {a i,j} represents the system matrix, a i,j Let f(x) represent the contribution of the j-th pixel to the i-th projection ray, where P is the high-resolution projection data obtained by the integrating detector; f(x) is a low-resolution image of the low-density matrix material reconstructed from the energy spectrum projection data, and serves as prior information.

[0039] 2) Gradient descent method: Let χ 2 express The objective function in the second half, then

[0040]

[0041] Therefore, the expression for the gradient descent algorithm is:

[0042]

[0043] Where Δ represents the current image objective function χ2 gradient, It is the gradient operator, where α represents the step size and d(i) is the increment factor. Indicates the current image objective function χ 2 The gradient direction;

[0044] 3) Iterative Reconstruction Algorithm Design: The CT iterative reconstruction algorithm based on prior information consists of three parts; the detailed solution steps are as follows:

[0045] 31) ART process:

[0046] 311) For image pixels x = (x1, x2, ..., x...) N ) T Assign initial value x (i) =(x1) (i) x2 (i) , ..., x N (i) ) T (i = 0, 1, ..., k-1), where N is the number of pixels, i is the number of iterations, and k is the total number of iterations;

[0047] 312) Input high-resolution projection data P = (P1, P2, ..., P2) detected by the model image or detector. M ) T Using the iterative formula, the relevant parameters in the ART algorithm are set, one iteration is completed, and x is obtained. (i+1) The iterative formula is:

[0048]

[0049] Where i is the ray number, M is the total number of rays, λ is the relaxation factor, and P i Let A be the projection value of the i-th ray. i Let i be the row vector of the i-th row of the system matrix A. For A i The transpose of ;

[0050] 314) Perform non-negative correction on the reconstructed image pixels, i.e.

[0051] 32) Gradient descent process:

[0052] 321) For image pixels Assign initial values,

[0053] 322) Calculate the increment factor using the following formula;

[0054] 322) Calculate χ 2gradient and gradient direction

[0055] 323) Perform a gradient descent using the iterative formula to obtain...

[0056] 324) Perform non-negative correction on the image pixels, i.e.

[0057] 325) The corrected image Used as initial values ​​for the next round of ART iteration;

[0058] In step four above, a two-based material decomposition model was used, and the result was compared with the base image reconstructed using the IBPF algorithm. To objectively evaluate the quality of the reconstructed image, we used peak signal-to-noise ratio (PSNR) and normalized root mean square error (NMSE) to evaluate the algorithm's performance. The formulas for calculating PSNR and NMSE are as follows:

[0059]

[0060] PSNR = 10 × log 10 (MAX 2 / MSE 2 )

[0061]

[0062] In the formula, f i,j Represents the pixel values ​​referenced from the image. This represents the pixel value of the image to be tested, M is the number of rows in the image, N is the number of columns in the image, and MAX represents the maximum pixel value in the reference image.

[0063] Preferably, in step three (1), μ(x) is the image reconstructed from the projection data P. θ(E) and θ(E) are two energy-dependent basis functions; for a high-resolution dual-spectral reconstruction model, we can... The problem is divided into two parts. The first part is solved using ART, and the second part is solved using gradient descent, so as to minimize the overall objective function.

[0064] Preferably, in step 3 (2), gradient descent is an iterative method suitable for solving least squares problems. It calculates the gradient of the objective function of the currently estimated image and then "pushes" the estimated image toward the minimum value of the objective function based on the gradient. It has superior performance in the fields of image denoising and image reconstruction.

[0065] Preferably, in step 3), the CT iterative reconstruction algorithm based on prior information consists of the following: first, reconstructing a low-resolution base image from the energy spectrum projection data using the IBPF algorithm; second, performing an ART reconstruction on the high-resolution projection data; and third, performing gradient descent. The increment factor and gradient direction in the gradient descent process use the low-resolution image of the low-density base material reconstructed by the IBPF algorithm and the results of the ART reconstruction. The initial value of the new round of ART iteration is generated by the gradient descent update. The two complement each other and are mutually conditional.

[0066] Preferably, in step three (313), the relaxation factor λ in the ART algorithm is used to control the convergence rate and improve the convergence condition, and its value range is generally from 0 to 2; λ<1 is an under-relaxation factor, which can improve the convergence condition; λ=1 is equivalent to not using a relaxation factor; λ>1 is an over-relaxation factor, which can speed up the convergence speed.

[0067] Preferably, in step three (325), after the ART process and gradient descent process, it is determined whether the reconstructed image meets the convergence condition, or the upper limit k of the number of iterations is manually determined, and finally a high-resolution image of the reconstructed substrate material with low density is output. In dual-energy spectroscopy CT reconstruction, high-resolution images of high-density substrate materials are crucial. The high-resolution projection data P obtained by the integrating detector is used to reconstruct the image μ(x) using ART, and the high-resolution image of the low-density matrix material is compared with that of the image. Using formula To obtain.

[0068] Compared with existing technologies, the beneficial effects of this invention are as follows: Addressing the issue of low resolution in dual-energy spectral CT imaging, this invention designs a hybrid dual-detector CT scanning system and proposes a CT iterative reconstruction algorithm based on prior information. This algorithm first reconstructs the energy spectral projection data to obtain a low-resolution base image, then uses the base image as prior information to optimize and combine it with high-resolution projection data to finally obtain a high-resolution base image, thereby avoiding the missed detection of minute fractures. Through theoretical analysis and numerical simulation experiments, the CT iterative reconstruction algorithm based on prior information is verified to perform energy spectral reconstruction on line-to-card pairs, ensuring the effectiveness and superiority of the high-resolution dual-energy spectral reconstruction model, and providing inspiration for subsequent chapters. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of the hybrid dual-detector CT scanning system of the present invention;

[0070] Figure 2 This is a flowchart of the CT iterative reconstruction algorithm based on prior information of the present invention;

[0071] Figure 3 A schematic diagram of the X-ray energy spectrum for the design and simulation of the test model of this invention;

[0072] Figure 4 This is a reconstruction result diagram of the test model of the present invention;

[0073] Figure 5 The test model for this invention is designed to reconstruct an image using high-resolution projection data via ART iterative reconstruction.

[0074] Figure 6 This is the combined single-energy diagram of the present invention;

[0075] Figure 7 This is a magnified view of the normalized grayscale variation curves of the middle row pixels of the two combined single-energy images of the present invention.

[0076] Figure 8 This is a flowchart of the method of the present invention. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Please see Figure 1-8 The present invention provides an embodiment of a high-resolution dual-energy spectral CT reconstruction method based on prior information, comprising the following steps: Step 1, a high-resolution dual-energy spectral CT scanning model; Step 2, an iterative dual-energy spectral reconstruction algorithm based on BPF; Step 3, an iterative CT reconstruction algorithm based on prior information; Step 4, numerical experiments and result analysis.

[0079] In step one above, one set is designed as a high-resolution integrating detector, and the other set is designed as a photon counting detector, such as... Figure 1 Under ideal conditions, assuming that X-rays are formed from photons of a single energy E, and ignoring the effects of scattering and other factors, for monoenergetic X-rays, the energy E is usually neglected. The projection data along the X-ray path L is then expressed as:

[0080] p(L)=-∫ L μ(x)dl

[0081] Where μ(x) represents the linear attenuation coefficient of the object under test, x represents its coordinate position, and l represents its thickness. Ignoring scattered photons, the multi-energy projection data along the X-ray path L is expressed as:

[0082]

[0083] Where μ(x, E) represents the linear attenuation coefficient of the object under test, E represents the photon energy, and S(E) is the normalized equivalent energy spectrum; in dual-energy spectral CT, the linear attenuation coefficient of the object under test is often decomposed into a linear combination of two basis functions, i.e.:

[0084]

[0085] in θ(E) and θ(E) are two energy-dependent basis functions, while f(x) and g(x) are position-dependent functions, independent of energy, representing the coefficients of the corresponding basis functions. There are generally two methods for selecting basis functions: one is physical effect decomposition, and the other is two-basis-material decomposition. In the physical effect decomposition method, the basis functions are:

[0086]

[0087] The basis functions represent the dependence of the photoelectric effect cross section on energy:

[0088]

[0089] The Compton cross section is expressed as a dependence on energy, where a = E / 510.975 keV; f(x) and g(x) represent the coefficient distributions of the two effect cross sections, respectively; in the bi-basic material decomposition method, the basis functions... θ(E) and θ(E) represent the mass decay coefficients of the two base materials, respectively, and f(x) and g(x) represent the density distribution images of the two base materials in the object under test, respectively; Substitute We can obtain:

[0090]

[0091] The problem of reconstructing the dual-energy spectrum is then transformed into knowing P k (L), k=1,2 The problem is to find f(x) and g(x); the high-resolution dual-energy spectral reconstruction model is transformed into a solution for two high-resolution matrix material images with different densities, given three sets of projection data: one set of high-resolution projection data and two sets of energy spectral projection data. and The problem stems from p(L)=-∫ L μ(x)dl and From a formal perspective, there are differences between energy-ignoring reconstruction and dual-energy spectral reconstruction for the same measured object. However, in general, they both reflect the structural information of different substances inside the same measured object, which can be approximated as μ(x)≈μ(x,E), thus establishing the relationship between energy-ignoring reconstruction and dual-energy spectral reconstruction.

[0092] In step two above, the specific steps of the IBPF algorithm are as follows:

[0093] 7) Assign an initial value to f (0) (x)=0,g (0) (x) = 0;

[0094] 8) Assume that after the nth iteration, the base material image f is obtained. (n) (x)=0,g (n) (x) = 0, calculate the reconstructed matrix material image along the energy spectrum projection path according to the following formula. The line integral for k = 1, 2 is denoted as and The formula is:

[0095]

[0096] 9) Estimate the projection path along the energy spectrum according to the following formula (1). Dual-energy projection data for k=1,2, where S k (E), k=1,2 represents the equivalent energy spectrum; according to the following formula (2), calculate the projection path along the energy spectrum. Weighting coefficients for k = 1, 2 and M (n) (L), Formula (1) is:

[0097]

[0098] Formula (2) is:

[0099]

[0100] 4) Calculate the path along the energy spectrum projection using the following formula. Weighted projected residuals for k=1,2

[0101] and The formula is:

[0102]

[0103] 5) Apply the BPF algorithm (denoted as BPF) to the weighted projection residuals respectively. Image reconstruction is performed using the BPF reconstruction operator to obtain the weighted projection residual image Δf1. (n) (x), and As shown in the following formula:

[0104]

[0105] f (n+1) (x)g (n+1)(x), the formula is as follows:

[0106] 6) Update the base material image to be reconstructed according to the following formula and

[0107]

[0108] 7) Determine if the convergence criterion is met. If it is met, stop the iteration; otherwise, go to step 2) and perform the next iteration. The reconstructed image does not depend on the geometric path of the rays, so the IBPF algorithm is suitable for both reconstructing high- and low-energy X-ray paths that are consistent and reconstructing high- and low-energy X-ray paths that are inconsistent.

[0109] In step three above, high-resolution images of low-density substrates are obtained based on prior information. The algorithm flowchart is as follows Figure 2 The steps of the CT iterative reconstruction algorithm based on prior information are as follows:

[0110] 1) Optimization Model Incorporating Prior Information: The high-resolution dual-energy spectral reconstruction model solves the image problem of two substrate materials with different densities using two sets of projection data of different types. Reconstruction algorithms differ for different types of projection data. For energy spectral projection data, we use the IBPF algorithm for dual-energy spectral reconstruction to obtain the base image, but the base image suffers from low spatial resolution. Prior information refers to the experience and data obtained before the experiment. For discretized CT reconstruction models, incorporating prior information during reconstruction is an important constraint, improving the accuracy and convergence rate of the reconstructed image. Therefore, we use the low-resolution base image as prior information and incorporate it into the model reconstructed from the high-resolution projection data, establishing an optimization model that integrates prior information. Thus, the objective function of the high-resolution dual-energy spectral reconstruction model is transformed into:

[0111]

[0112]

[0113] in, A high-resolution image of the low-density matrix material to be solved; This represents a high-resolution image of the high-density matrix material to be solved; A = {a i,j} represents the system matrix, a i,j Let P represent the contribution of the j-th pixel to the i-th projected ray; P is the high-resolution projection data obtained by the integrating detector; f(x) is the low-resolution image of the low-density matrix material reconstructed from the energy spectrum projection data, and serves as prior information; μ(x) is the image reconstructed from the projection data P. θ(E) and θ(E) are two energy-dependent basis functions; for a high-resolution dual-spectral reconstruction model, we can... The problem is divided into two parts. The first part is solved using ART, and the second part is solved using gradient descent, so as to minimize the overall objective function.

[0114] 2) Gradient Descent: Gradient descent is an iterative method suitable for solving least squares problems. It calculates the gradient of the objective function of the currently estimated image and then "pushes" the estimated image toward the minimum value of the objective function based on the gradient. It has superior performance in image denoising and image reconstruction. Let χ... 2 express The objective function in the second half, then

[0115]

[0116]

[0117] Therefore, the expression for the gradient descent algorithm is:

[0118]

[0119] Where △ represents the current image objective function χ 2 gradient, It is the gradient operator, where α represents the step size and d(i) is the increment factor. Indicates the current image objective function χ 2 The gradient direction;

[0120] 3) Iterative Reconstruction Algorithm Design: The CT iterative reconstruction algorithm based on prior information consists of three parts: First, a low-resolution base image is obtained by reconstructing the energy spectrum projection data using the IBPF algorithm; second, an ART reconstruction is performed on the high-resolution projection data; and third, gradient descent is performed. The increment factor and gradient direction in the gradient descent process utilize the low-resolution image of the low-density base material reconstructed by the IBPF algorithm and the results of the ART reconstruction. The initial value of the new round of ART iteration is generated by the gradient descent update. The two complement each other and are mutually conditional. The detailed solution steps are as follows:

[0121] 31) ART process:

[0122] 311) For image pixels x = (x1, x2, ..., x... N ) T Assign initial value x (i) =(x1) (i) x2 (i) , ..., x N (i) ) T(i = 0, 1, ..., k-1), where N is the number of pixels, i is the number of iterations, and k is the total number of iterations;

[0123] 312) Input high-resolution projection data P = (P1, P2, ..., P2) detected by the model image or detector. M ) T Using the iterative formula, the relevant parameters in the ART algorithm are set, one iteration is completed, and x is obtained. (i+1) The iterative formula is:

[0124]

[0125] Where i is the ray number, M is the total number of rays, λ is the relaxation factor, and P i Let A be the projection value of the i-th ray. i Let i be the row vector of the i-th row of the system matrix A. For A i The transpose of ;

[0126] 315) Perform non-negative correction on the reconstructed image pixels, i.e. In the ART algorithm, the relaxation factor λ is used to control the convergence rate and improve the convergence condition. Its value range is generally from 0 to 2. λ < 1 is an under-relaxation factor, which can improve the convergence condition; λ = 1 is equivalent to not using a relaxation factor; λ > 1 is an over-relaxation factor, which can speed up the convergence speed.

[0127] 32) Gradient descent process:

[0128] 321) For image pixels Assign initial values,

[0129] 323) Calculate the increment factor using the following formula;

[0130]

[0131] 322) Calculate χ 2 gradient and gradient direction

[0132] 323) Perform a gradient descent using the iterative formula to obtain...

[0133] 324) Perform non-negative correction on the image pixels, i.e.

[0134] 325) The corrected image Used as initial values ​​for the next round of ART iteration;

[0135] After the ART and gradient descent processes, the reconstructed image is judged to meet the convergence condition, or an upper limit k for the number of iterations is manually determined. Finally, a high-resolution image of the low-density substrate material is output. In dual-energy spectroscopy CT reconstruction, high-resolution images of high-density substrate materials are crucial. The high-resolution projection data P obtained by the integrating detector is used to reconstruct the image μ(x) using ART, and the high-resolution image of the low-density matrix material is compared with that of the image. Using formula Seek;

[0136] In step four above, a two-based material decomposition model was used, and the result was compared with the base image reconstructed using the IBPF algorithm. To objectively evaluate the quality of the reconstructed image, we used peak signal-to-noise ratio (PSNR) and normalized root mean square error (NMSE) to evaluate the algorithm's performance. The formulas for calculating PSNR and NMSE are as follows:

[0137]

[0138] PSNR = 10 × log 10 (MAX 2 / MSE 2 )

[0139]

[0140] In the formula, f i,j Represents the pixel values ​​referenced from the image. This represents the pixel value of the image to be tested, where M is the number of rows in the image, N is the number of columns in the image, and MAX represents the maximum pixel value in the image to be referenced.

[0141] To address the issue of missed detection of minute fractures in medical diagnosis, we designed the test model as a pair of line cards and small circles containing water and bone materials, with a size of 256×256. Figure 3 As shown in Figure (a), and Figure 3 (a) in the diagram represents the test model. Figure 3 (b) shows the simulated X-ray energy spectrum; the two sets of line pairs and four sets of small circles represent bone material, each line pair is 0.6 mm wide and 0.6 mm apart; the other areas represent water material; the X-ray energy spectra used in the simulation experiment are 80 kV and 120 kV, such as... Figure 3 As shown in Figure (b), the energy spectrum data was obtained using the open-source simulation software Spectrum GUI; the mass decay coefficient of the model was obtained from the National Institute of Standards and Technology (NIST) website.

[0142] In the simulation experiment, the CT scan parameters were set as follows: the distance from the X-ray source focal point to the turntable center (SOD) was 200 mm, the distance from the X-ray source focal point to the detector center (SDD) was 250 mm, and the projection angle was 360°; the element length of the photon counting detector was 0.776 mm, and the number of elements was 128; the element length of the high-resolution integrating detector was 0.194 mm, and the number of elements was 512; the imaging field of view radius was 38.969685 mm.

[0143] In the simulation experiment, the parameters of CT reconstruction were finally determined after a large number of repeated experiments and were set as follows: the base image of energy spectrum reconstruction is the result of three iterations; the image of water-based material with low density is used as prior information. In the CT iteration process based on the prior information, the relaxation factor λ1 is 0.9, the step size of gradient descent α is 0.1, and the total number of iterations k1 is 10; the relaxation factor λ2 of high-resolution ART reconstruction is 1.3, and the number of iterations k2 is 30.

[0144] The reconstruction results of the test model are as follows Figure 4 As shown, and Figure 4 (a) is the water-based image reconstructed by the IBPF algorithm. Figure 4 (b) is a water-based image reconstructed by CT iterative reconstruction based on prior information. Figure 4 Image (c) is the bone matrix image reconstructed by the IBPF algorithm. Figure 4 (d) shows the bone base image reconstructed by CT iterative reconstruction based on prior information. The first column is the result of the three-step energy spectrum reconstruction iteration of the IBPF algorithm, and the second column is the CT iterative reconstruction result based on prior information. The result of ART iterative reconstruction of high-resolution projection data is shown below. Figure 5 As shown, and Figure 5 (a) in the diagram represents the test model. Figure 5 (b) in the image is an image reconstructed by ART iterative reconstruction of high-resolution projection data; the combined monoenergetic image of the three-step energy spectrum reconstruction iteration of the IBPF algorithm and the combined monoenergetic image of CT iterative reconstruction based on prior information are shown below. Figure 6 As shown, and Figure 6 In the diagram, (a) represents the combined monoenergetic image of the IBPF algorithm. Figure 6 (b) in the figure represents a combined monoenergetic image of the CT iterative reconstruction algorithm based on prior information;

[0145] We calculated the PSNR and NMSE indices for the two combined single-energy images, as shown in the table of reconstruction results for the combined single-energy images. To more clearly demonstrate the reconstruction effect of the line pair card portion, we locally magnified the normalized grayscale variation curve of the pixels in the middle row (row 128) of the combined single-energy image, as shown in the table. Figure 7 As shown; the reconstruction results of the combined single-energy images are shown in the table below:

[0146]

[0147] from Figure 4 and Figure 5 As can be seen, the high-resolution dual-energy spectroscopy reconstruction model overcomes the shortcomings of both the dual-energy spectroscopy reconstruction model and the microscopic reconstruction model, combining the high-resolution advantage of the microscopic reconstruction model with the material discrimination advantage of the dual-energy spectroscopy reconstruction model to obtain a high-resolution image with material discrimination. Figure 6 and Figure 7 The results show that the combined monoenergetic images from the CT iterative reconstruction algorithm based on prior information can more accurately distinguish different materials in the online card matching part. From the reconstruction effect table of the combined monoenergetic images, it can be seen that compared to the combined monoenergetic images from the IBPF algorithm, the combined monoenergetic images from the CT iterative reconstruction algorithm based on prior information have a higher PSNR and a lower NMSE, resulting in better image reconstruction performance. Figures 4 to 7 The indicators in the table of reconstruction results of combined single-energy images show that the combined single-energy images of the CT iterative reconstruction algorithm based on prior information are closer to the test model; thus, this experiment verifies the correctness and effectiveness of the high-resolution dual-energy spectrum reconstruction model for line-to-line card spectrum reconstruction.

[0148] Based on the above, the advantages of this invention are that, addressing the problem of low resolution in dual-energy spectral CT imaging, this invention designs a hybrid dual-detector CT scanning system and proposes a CT iterative reconstruction algorithm based on prior information. This algorithm first reconstructs the energy spectral projection data to obtain a low-resolution base image, then uses the base image as prior information to optimize and combine it with high-resolution projection data to finally obtain a high-resolution base image. Through theoretical analysis and numerical simulation experiments, the CT iterative reconstruction algorithm based on prior information is verified to perform energy spectral reconstruction on line-to-card pairs, ensuring the effectiveness and superiority of the high-resolution dual-energy spectral reconstruction model, and providing inspiration for subsequent chapters.

[0149] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A high-resolution dual-energy spectral CT reconstruction method based on prior information, comprising the following steps: Step 1: High-resolution dual-energy spectral CT scanning model; Step 2: Iterative dual-energy spectral reconstruction algorithm based on BPF; Step 3: CT iterative reconstruction algorithm based on prior information; Step 4: Numerical experiments and result analysis; Its features are: In step one above, in a vertically positioned dual-source, dual-detector CT scanning system, one set is designed as a high-resolution integrating detector, and the other set is designed as a photon counting detector. This yields a high-resolution dual-energy spectral CT scanning model, resulting in one set of high-resolution projection data and two sets of energy spectral projection data. The dual-energy data obtained from the photon counting detector is reconstructed based on the model below. In dual-energy spectroscopy CT, the linear attenuation coefficient of the object under test is often decomposed into a linear combination of two basis functions, namely: in θ(E) and θ(E) are two energy-dependent basis functions, while f(x) and g(x) are position-dependent functions, independent of energy, representing the coefficients of the corresponding basis functions. The basis functions are selected according to the method of bi-basic material decomposition. In the bi-basic material decomposition method, the basis functions... θ(E) and θ(E) represent the mass decay coefficients of the two base materials, respectively, and f(x) and g(x) represent the density distribution images of the two base materials in the object under test, respectively. The corresponding energy spectrum projection data are expressed as follows: The dual-energy spectrum reconstruction problem is then transformed into: given p k (L), k=1,2 The problem is to find f(x) and g(x). Therefore, the high-resolution dual-energy spectral reconstruction model is transformed into solving for two high-resolution matrix material images with different densities, based on three sets of known projection data: one set of high-resolution projection data and two sets of energy spectral projection data. and The problem stems from p(L)=-∫ L μ(x)dl and From a formal perspective, there are differences between energy-ignoring reconstruction and dual-energy spectral reconstruction for the same measured object. However, in general, they both reflect the structural information of different substances inside the same measured object, which can be approximated as μ(x)≈μ(x,E), thus establishing the relationship between energy-ignoring reconstruction and dual-energy spectral reconstruction. In step two above, in order to perform high-resolution dual-energy spectral CT reconstruction based on prior information, the following IBPF algorithm was designed, with the specific steps as follows: 1) Assign an initial value to f (0) (x)=0,g (0) (x) = 0; 2) Assume that after the nth iteration, the base material image f is obtained. (n) (x)=0,g (n) (x)=0, calculate the reconstructed matrix material image along the energy spectrum projection path L∈l according to the following formula. k The line integral of k = 1, 2 is denoted as and The formula is: 3) Estimate the path L ∈ l along the energy spectrum projection path according to the following formula (1). k Dual-energy projection data for k=1,2, where S k (E), k=1,2 represents the equivalent energy spectrum; according to the following formula (2), calculate the projection path L∈l along the energy spectrum. k Weighting coefficients for k = 1, 2 and M (n) (L), Formula (1) is: Formula (2) is: 4) Calculate the path L∈l along the energy spectrum projection path according to the following formula. k Weighted projected residuals for k=1,2 and The formula is: 5) Apply the BPF algorithm to the weighted projected residuals respectively, and denote... Using the BPF reconstruction operator, image reconstruction is performed to obtain the weighted projection residual image. and As shown in the following formula: 6) Update the base material image to be reconstructed f according to the following formula. (n+1) (x) and g (n+1) (x), the formula is as follows: 7) Determine if the convergence criterion is met. If it is met, stop the iteration; otherwise, go to step 2) and perform the next iteration. The reconstructed image does not depend on the geometric path of the rays, so the IBPF algorithm is suitable for both reconstructing high- and low-energy X-ray paths that are consistent and reconstructing high- and low-energy X-ray paths that are inconsistent. In step three above, the steps of the CT iterative reconstruction algorithm based on prior information are as follows: 1) Optimization Model Incorporating Prior Information: The high-resolution dual-energy spectral reconstruction model solves the image problem of two substrate materials with different densities using two sets of projection data of different types. Reconstruction algorithms differ for different types of projection data. For energy spectral projection data, we use the IBPF algorithm for dual-energy spectral reconstruction to obtain the base image, but the base image suffers from low spatial resolution. Prior information refers to the experience and data obtained before the experiment. For discretized CT reconstruction models, incorporating prior information during reconstruction is an important constraint, improving the accuracy and convergence rate of the reconstructed image. Therefore, we use the low-resolution base image as prior information and incorporate it into the model reconstructed from the high-resolution projection data, establishing an optimization model that integrates prior information. Thus, the objective function of the high-resolution dual-energy spectral reconstruction model is transformed into: in, A high-resolution image of the low-density matrix material to be solved; This represents a high-resolution image of the high-density matrix material to be solved; A = {a i,j } represents the system matrix, a i,j Let f(x) represent the contribution of the j-th pixel to the i-th projection ray, where P is the high-resolution projection data obtained by the integrating detector; f(x) is a low-resolution image of the low-density matrix material reconstructed from the energy spectrum projection data, and serves as prior information. 2) Gradient descent method: Let χ 2 express The objective function in the second half, then Therefore, the expression for the gradient descent algorithm is: Where △ represents the current image objective function χ 2 gradient, It is the gradient operator, where α represents the step size and d(i) is the increment factor. Indicates the current image objective function χ 2 The gradient direction; 3) Iterative Reconstruction Algorithm Design: The CT iterative reconstruction algorithm based on prior information consists of three parts; the detailed solution steps are as follows: 31) ART process: 311) For image pixels x = (x1, x2, ..., x... N ) T Assign initial values Where N is the number of pixels, i is the number of iterations, and k is the total number of iterations; 312) Input high-resolution projection data P = (P1, P2, ..., P2) detected by the model image or detector. M ) T Using the iterative formula, the relevant parameters in the ART algorithm are set, one iteration is completed, and x is obtained. (i+1) The iterative formula is: Where i is the ray number, M is the total number of rays, λ is the relaxation factor, and P i Let A be the projection value of the i-th ray. i Let i be the row vector of the i-th row of the system matrix A. For A i The transpose of ; 313) Perform non-negative correction on the reconstructed image pixels, i.e. 32) Gradient descent process: 321) For image pixels Assign initial values, 321) Calculate the increment factor using the following formula; 322) Calculate χ 2 gradient and gradient direction 323) Perform a gradient descent using the iterative formula to obtain... 324) Perform non-negative correction on the image pixels, i.e. 325) The corrected image Used as initial values ​​for the next round of ART iteration; In step four above, a two-based material decomposition model was used, and the result was compared with the base image reconstructed using the IBPF algorithm. To objectively evaluate the quality of the reconstructed image, we used peak signal-to-noise ratio (PSNR) and normalized root mean square error (NMSE) to evaluate the algorithm's performance. The formulas for calculating PSNR and NMSE are as follows: PSNR=10×log 10 (MAX 2 / MSE 2 ) In the formula, f i,j Represents the pixel values ​​referenced from the image. This represents the pixel value of the image to be tested, M is the number of rows in the image, N is the number of columns in the image, and MAX represents the maximum pixel value in the reference image.

2. The high-resolution dual-energy spectral CT reconstruction method based on prior information according to claim 1, characterized in that: In step 3(1), μ(x) is the image reconstructed from the projection data P. θ(E) and θ(E) are two energy-dependent basis functions; for a high-resolution dual-spectral reconstruction model, we can... The problem is divided into two parts. The first part is solved using ART, and the second part is solved using gradient descent, so as to minimize the overall objective function.

3. The high-resolution dual-energy spectral CT reconstruction method based on prior information according to claim 1, characterized in that: In step 3(2), gradient descent is an iterative method suitable for solving least squares problems. It calculates the gradient of the objective function of the currently estimated image and then "pushes" the estimated image toward the minimum value of the objective function based on the gradient. It has superior performance in the fields of image denoising and image reconstruction.

4. The high-resolution dual-energy spectral CT reconstruction method based on prior information according to claim 1, characterized in that: In step 3), the CT iterative reconstruction algorithm based on prior information consists of the following: first, reconstructing a low-resolution base image from the energy spectrum projection data using the IBPF algorithm; second, performing an ART reconstruction on the high-resolution projection data; and third, performing gradient descent. The increment factor and gradient direction in the gradient descent process use the low-resolution image of the low-density base material reconstructed by the IBPF algorithm and the results of the ART reconstruction. The initial value of the new round of ART iteration is generated by the gradient descent update. The two complement each other and are mutually conditional.

5. The high-resolution dual-energy spectral CT reconstruction method based on prior information according to claim 1, characterized in that: In step 313), the relaxation factor λ in the ART algorithm is used to control the convergence rate and improve the convergence condition. The value range is generally from 0 to 2. λ<1 is an under-relaxation factor, which can improve the convergence condition. λ=1 is equivalent to not using a relaxation factor. λ>1 is an over-relaxation factor, which can speed up the convergence speed.

6. The high-resolution dual-energy spectral CT reconstruction method based on prior information according to claim 1, characterized in that: In step 325), after the ART process and gradient descent process, it is determined whether the reconstructed image meets the convergence condition, or the upper limit k of the number of iterations is manually determined, and finally the high-resolution image of the reconstructed low-density substrate is output. In dual-energy spectroscopy CT reconstruction, high-resolution images of high-density substrate materials are crucial. The high-resolution projection data P obtained by the integrating detector is used to reconstruct the image μ(x) using ART, and the high-resolution image of the low-density matrix material is compared with that of the image. Using formula To obtain.

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