Image reconstruction method for brain hemorrhage magnetic induction tomography based on improved nr algorithm

Abstract

The application discloses a brain hemorrhage magnetic induction tomography image reconstruction method based on an improved NR algorithm, and comprises the following steps: obtaining coil detection phase data and a sensitivity matrix by using an established brain hemorrhage MIT finite element model; introducing a regularization penalty term based on a target function of a traditional NR algorithm and solving an iterative formula of the algorithm, determining optimization parameters in the algorithm by a v method, and taking a conductivity distribution calculated by using a linear back projection algorithm as an initial value of iteration of the improved NR algorithm; introducing a projection operator P Ensuring that the algorithm converges on a convex set each time; determining an optimal threshold value or a maximum number of iterations, and outputting a final conductivity distribution. Compared with a traditional magnetic induction tomography image reconstruction algorithm, the application has better image reconstruction quality, can effectively reduce image reconstruction artifacts, and can detect brain hemorrhage.

Description

Technical Field

[0001] This invention belongs to the field of magnetic induction tomography technology, specifically relating to a method for reconstructing brain hemorrhage images based on an improved NR algorithm. Background Technology

[0002] Intracranial diseases pose a significant threat to human health. Stroke, also known as cerebrovascular accident, is a common and prevalent neurological disease, the second leading cause of death and a major cause of disability worldwide. Intracerebral hemorrhage (ICH), primarily caused by the rupture or leakage of blood vessels in the brain, is a life-threatening condition that kills approximately 1.4 to 1.65 million people globally each year. Currently, commonly used medical imaging techniques for ICH include computed tomography (CT) and magnetic resonance imaging (MRI). However, these methods have limitations. Prolonged exposure to radiation and strong magnetic fields can be harmful, and both are expensive, making them difficult to obtain in less developed areas. Furthermore, the equipment is bulky and difficult to transport, and the testing process is lengthy. Neither method can provide real-time and continuous monitoring for patients.

[0003] Magnetic Induction Tomography (MIT) is a technique that uses electromagnetic detection principles to image the passive electromagnetic properties (i.e., conductivity, permeability, and dielectric constant) of an object. Image reconstruction algorithms are crucial at MIT and are essential for improving image quality. Currently, MIT image reconstruction algorithms can be divided into one-step imaging algorithms and iterative algorithms. One-step imaging algorithms mainly include the LBP algorithm and the Tikhonov regularization algorithm. These algorithms have fast imaging speeds but lower reconstruction accuracy. Iterative algorithms include the Landweber algorithm, the Newton-Raphson (NR) algorithm, and the Conjugate Gradient Least Squares (CGLS) algorithm. These algorithms have higher image reconstruction accuracy but require more iterations and are time-consuming. In addition, classical image reconstruction algorithms have low accuracy, large errors, and significant artifacts, which directly affect the determination of the location and amount of brain hemorrhage. Summary of the Invention

[0004] To address the issues of low accuracy, large errors, and significant artifacts in traditional image reconstruction methods for cerebral hemorrhage using magnetic induction tomography (MIT), this invention provides a method for reconstructing cerebral hemorrhage images based on an improved NR algorithm, implemented through the following technical solution:

[0005] A method for reconstructing brain hemorrhage images based on an improved NR algorithm includes the following steps:

[0006] S1: Using the established MIT finite element model of cerebral hemorrhage, the coil detection phase data is obtained through cyclic excitation and cyclic detection. and sensitivity matrix S;

[0007] S2: Introduce a regularization penalty term ||Δσ k -Δσ k-1 By constraining the objective function of the NR algorithm, the image reconstruction problem of MIT (Middle Brain Hemorrhage) is transformed into the following objective function optimization problem:

[0008]

[0009] In the formula, the first term is the difference between the calculated and detected phase difference, the second term is the difference between the change in conductivity distribution at the current moment and the change in conductivity distribution at the previous moment, and β k These are the weighting coefficients of the second term, and their optimal values ​​are determined using the v method.

[0010] S3: The conductivity distribution calculated by the linear back projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm, and the number of iterations k = 0;

[0011] S4: Solve the objective function in S2 using the idea of ​​NR iteration, obtain the iterative formula of the improved NR algorithm, and introduce the projection operator P to constrain the algorithm;

[0012] S5: Determine the optimal threshold ε or the maximum number of iterations N. Update the conductivity distribution based on S3 and S4. If the iteration termination condition is met, output the current conductivity distribution value Δσ. k+1 Visualize it, and if the iteration count k = k + 1 is not satisfied, return to S3;

[0013] Preferably, in S2, β k Determined using the v method, the calculation formula is as follows:

[0014]

[0015] In the formula, k is the number of iterations, and v is selected based on empirical methods;

[0016] Preferably, the conductivity distribution calculated using the linear back-projection algorithm in step S3 is used as the initial value Δσ0 for the iteration of the improved NR algorithm:

[0017]

[0018] In the formula, is the detected value of the coil, and S is the sensitivity matrix.

[0019] Preferably, the specific steps of S4 are as follows:

[0020] S4.1: Expand the objective function (1) and find its descent gradient and Hessian matrix, where a regularization matrix αI is added to the Hessian matrix to reduce its ill-conditioned nature:

[0021]

[0022] H k =(F′(Δσ)) T F′(Δσ)+αI (5)

[0024] In the formula, F′(Δσ) is the sensitivity matrix, I is the identity matrix, and α is selected based on human experience.

[0025] S4.2: Substitute equations (4) and (5) into the formula of the NR iterative algorithm. Let F′(Δσ) be represented by S:

[0026]

[0027] S4.3: Introduce the projection operator P to constrain the algorithm:

[0028]

[0029] In the formula, P is the projection operator on a non-negative convex set, which ensures that the solution of each iteration is non-negative and bounded, and converges to a convex set. f(Δσ) is the conductivity distribution function obtained in each iteration.

[0030] The beneficial effects of this invention are:

[0031] This invention proposes a method for reconstructing MRI images of cerebral hemorrhage based on an improved NR algorithm. A regularization penalty term is introduced into the objective function to improve the algorithm's iterative efficiency and reconstruction accuracy. A linear back-projection algorithm is used to improve the initial value of the NR algorithm's iterations, increasing the convergence speed. A projection operator P is introduced to ensure that the algorithm converges to a convex set in each iteration. This invention reduces artifacts in reconstructed images of cerebral hemorrhage, improves the accuracy of image reconstruction, and makes the reconstructed images closer to the actual cerebral hemorrhage situation, thus providing a new and effective method for detecting MIT (Mixed Detection) of cerebral hemorrhage. Attached Figure Description

[0032] Figure 1 This is a flowchart of the present invention.

[0033] Figure 2 This is the finite element simulation model established by this invention.

[0034] Figure 3This is a schematic diagram of the bleeding volumes of 24ml, 14ml, and 2ml set in the finite element model of this invention.

[0035] Figure 4 These are the electromagnetic characteristic parameters of each component in the finite element model of this invention at a frequency of 1MHz.

[0036] Figure 5 This is a comparison chart of the reconstruction results of the present invention with those of the Tikhonov algorithm, Landweber algorithm, CGLS algorithm, and NR algorithm under a 24ml hemorrhage condition.

[0037] Figure 6 This is a comparison chart of the reconstruction results of the present invention with those of the Tikhonov algorithm, Landweber algorithm, CGLS algorithm, and NR algorithm under a 14ml hemorrhage condition.

[0038] Figure 7 This is a comparison chart of the reconstruction results of the present invention with those of the Tikhonov algorithm, Landweber algorithm, CGLS algorithm, and NR algorithm under a 2ml bleeding condition. Detailed Implementation

[0039] In order to provide a clear and complete description of the technical solution and technical effects of the present invention, the following embodiments are provided for detailed explanation;

[0040] Example 1

[0041] To achieve magnetic induction tomography image reconstruction in cases of severe cerebral hemorrhage, such as Figure 2 As shown, the established MIT finite element model of cerebral hemorrhage includes an air domain, a coil array, and layers such as the scalp, skull, cerebrospinal fluid, and brain parenchyma. Figure 3 As shown, to simulate a real cerebral hemorrhage, a spherical hemorrhage with a volume of 24 ml was added to the model. The simulation was set with an excitation frequency of 1 MHz and an excitation current of 1 A. During the simulation, electromagnetic property parameters (specifically, conductivity and dielectric constant values) of different brain tissues in the model at 1 MHz were assigned. The electromagnetic property parameters of each tissue are as follows: Figure 4 As shown (data sourced from a public database), this three-dimensional cranial model can better simulate actual cerebral hemorrhage.

[0042] according to Figure 1 The process shown describes how, after setting up the simulation model, image reconstruction is performed according to this invention. The specific steps of the method are as follows:

[0043] S1: Using the established MIT finite element model of cerebral hemorrhage, the coil detection phase data is obtained through cyclic excitation and cyclic detection. and sensitivity matrix S;

[0044] S2: Objective function based on the traditional NR algorithm, introducing a regularization penalty term ||Δσ k -Δσ k-1 By constraining the objective function, the image reconstruction problem of MIT (Middle East Reconstruction of Brain Hemorrhage) is transformed into the following objective function optimization problem:

[0045]

[0046] In the formula, the first term is the difference between the calculated and detected phase difference, the second term is the difference between the change in conductivity distribution at the current moment and the change in conductivity distribution at the previous moment, and β k These are the weighting coefficients of the second term, and their optimal values ​​are determined using the v method.

[0047] S3: The conductivity distribution calculated by the linear back projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm, and the number of iterations k = 0;

[0048] S4: Solve the objective function in S2 using the idea of ​​NR iteration, obtain the iterative formula of the improved NR algorithm, and introduce the projection operator P to constrain the algorithm;

[0049] S5: Determine the optimal threshold ε or the maximum number of iterations N. Update the conductivity distribution based on S3 and S4. If the iteration termination condition is met, output the current conductivity distribution value Δσ. k+1 Visualize it, and if the iteration count k = k + 1 is not satisfied, return to S3.

[0050] In S2, β k Determined using the v method, the calculation formula is as follows:

[0051]

[0052] In the formula, k is the number of iterations, and v is chosen as 8 based on experience.

[0053] In step S3, the conductivity distribution calculated using the linear back-projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm.

[0054]

[0055] In the formula, It is a 56×1 dimensional coil detection value, and S is a 56×1575 dimensional sensitivity matrix.

[0056] S4 specifically includes the following steps:

[0057] S4.1: Expand the objective function and find its descent gradient and Hessian matrix, where a regularization matrix αI is added to the Hessian matrix to reduce its ill-conditioned nature.

[0058]

[0059] H k =(F′(Δσ)) T F′(Δσ)+αI (5)

[0061] In the formula, F′(Δσ) is the sensitivity matrix, I is the identity matrix, and α is selected as 0.7 based on human experience.

[0062] S4.2: Substitute equations (4) and (5) into the formula of the NR iterative algorithm. Let F′(Δσ) be represented by S:

[0063]

[0064] S4.3: Introduce the projection operator P to constrain the algorithm:

[0065]

[0066] In the formula, P is the projection operator on a non-negative convex set, which ensures that the solution of each iteration is non-negative and bounded, and converges to a convex set. f(Δσ) is the conductivity distribution function obtained in each iteration.

[0067] This example uses four different image reconstruction algorithms to verify the performance of the proposed reconstruction method: the Tikhonov algorithm, the Landweber algorithm, the CGLS algorithm, and the NR algorithm. Figure 5 The image shows a comparison of the reconstruction results of the present invention and four algorithms under a 24ml bleeding condition.

[0068] Example 2

[0069] To achieve magnetic induction tomography image reconstruction in cases of moderate cerebral hemorrhage, such as Figure 2 As shown, the established MIT finite element model of cerebral hemorrhage includes an air domain, a coil array, and layers such as the scalp, skull, cerebrospinal fluid, and brain parenchyma. Figure 3 As shown, to simulate a real cerebral hemorrhage, a spherical hemorrhage with a volume of 14 ml was added to the model. The simulation was set with an excitation frequency of 1 MHz and an excitation current of 1 A. During the simulation, electromagnetic property parameters (specifically, conductivity and dielectric constant values) of different brain tissues in the model at 1 MHz were assigned. The electromagnetic property parameters of each tissue are as follows: Figure 4 As shown (data sourced from a public database), this three-dimensional cranial model can better simulate actual cerebral hemorrhage.

[0070] according to Figure 1The process shown describes how, after setting up the simulation model, image reconstruction is performed according to this invention. The specific steps of the method are as follows:

[0071] S1: Using the established MIT finite element model of cerebral hemorrhage, the coil detection phase data is obtained through cyclic excitation and cyclic detection. and sensitivity matrix S;

[0072] S2: Objective function based on the traditional NR algorithm, introducing a regularization penalty term ||Δσ k -Δσ k-1 By constraining the objective function, the image reconstruction problem of MIT (Middle East Reconstruction of Brain Hemorrhage) is transformed into the following objective function optimization problem:

[0073]

[0074] In the formula, the first term is the difference between the calculated and detected phase difference, the second term is the difference between the change in conductivity distribution at the current moment and the change in conductivity distribution at the previous moment, and β k These are the weighting coefficients of the second term, and their optimal values ​​are determined using the v method.

[0075] S3: The conductivity distribution calculated by the linear back projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm, and the number of iterations k = 0;

[0076] S4: Solve the objective function in S3 using the idea of ​​NR iteration, obtain the iterative formula of the improved NR algorithm, and introduce the projection operator P to constrain the algorithm.

[0077] S5: Determine the optimal threshold ε or the maximum number of iterations N. Update the conductivity distribution based on S3 and S4. If the iteration termination condition is met, output the current conductivity distribution value Δσ. k+1 Visualize it, and if the iteration count k = k + 1 is not satisfied, return to S3.

[0078] In S2, β k Determined using the v method, the calculation formula is as follows:

[0079]

[0080] In the formula, k is the number of iterations, and v is chosen as 8 based on experience.

[0081] In step S3, the conductivity distribution calculated using the linear back-projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm.

[0082]

[0083] In the formula, It is a 56×1 dimensional coil detection value, and S is a 56×1575 dimensional sensitivity matrix.

[0084] S4 specifically includes the following steps:

[0085] S4.1: Expand the objective function (1) and find its descent gradient and Hessian matrix, where a regularization matrix αI is added to the Hessian matrix to reduce its ill-conditioned nature:

[0086]

[0087] H k =(F′(Δσ)) T F′(Δσ)+αI (5)

[0089] In the formula, F′(Δσ) is the sensitivity matrix, I is the identity matrix, and α is selected as 0.75 based on human experience.

[0090] S4.2: Substitute equations (4) and (5) into the formula of the NR iterative algorithm. Let F′(Δσ) be represented by S:

[0091]

[0092] S4.3: Introduce the projection operator P to constrain the algorithm:

[0093]

[0094] In the formula, P is the projection operator on a non-negative convex set, which ensures that the solution of each iteration is non-negative and bounded, and converges to a convex set. f(Δσ) is the conductivity distribution function obtained in each iteration.

[0095] This example uses four different image reconstruction algorithms to verify the performance of the proposed reconstruction method: the Tikhonov algorithm, the Landweber algorithm, the CGLS algorithm, and the NR algorithm. Figure 6 The image shows a comparison of the reconstruction results of the present invention and four algorithms under a 14ml bleeding condition.

[0096] Example 3

[0097] To achieve magnetic induction tomography image reconstruction in cases of microbleeds in the brain, such as Figure 2 As shown, the established MIT finite element model of cerebral hemorrhage includes an air domain, a coil array, and layers such as the scalp, skull, cerebrospinal fluid, and brain parenchyma. Figure 3As shown, to simulate a real cerebral hemorrhage, a 2ml spherical hemorrhage was added to the model. The simulation was set with an excitation frequency of 1MHz and an excitation current of 1A. During the simulation, electromagnetic property parameters (specifically, conductivity and dielectric constant values) of different brain tissues in the model at 1MHz were assigned. The electromagnetic property parameters of each tissue are shown below. Figure 4 As shown (data sourced from a public database), this three-dimensional cranial model can better simulate actual cerebral hemorrhage.

[0098] according to Figure 1 The process shown describes how, after setting up the simulation model, image reconstruction is performed according to this invention. The specific steps of the method are as follows:

[0099] S1: Using the established MIT finite element model of cerebral hemorrhage, the coil detection phase data is obtained through cyclic excitation and cyclic detection. and sensitivity matrix S;

[0100] S2: Objective function based on the traditional NR algorithm, introducing a regularization penalty term ||Δσ k -Δσ k-1 By constraining the objective function, the image reconstruction problem of MIT (Middle East Reconstruction of Brain Hemorrhage) is transformed into the following objective function optimization problem:

[0101]

[0102] In the formula, the first term is the difference between the calculated and detected phase difference, the second term is the difference between the change in conductivity distribution at the current moment and the change in conductivity distribution at the previous moment, and β k These are the weighting coefficients of the second term, and their optimal values ​​are determined using the v method.

[0103] S3: The conductivity distribution calculated by the linear back projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm, and the number of iterations k = 0;

[0104] S4: Solve the objective function in S2 using the idea of ​​NR iteration, obtain the iterative formula of the improved NR algorithm, and introduce the projection operator P to constrain the algorithm;

[0105] S5: Determine the optimal threshold ε or the maximum number of iterations N. Update the conductivity distribution based on S3 and S4. If the iteration termination condition is met, output the current conductivity distribution value Δσ. k+1 Visualize it, and if the iteration count k = k + 1 is not satisfied, return to S3.

[0106] In S2, β k Determined using the v method, the calculation formula is as follows:

[0107]

[0108] In the formula, k is the number of iterations, and v is chosen as 8 based on experience.

[0109] In step S3, the conductivity distribution calculated using the linear back-projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm.

[0110]

[0111] In the formula, It is a 56×1 dimensional coil detection value, and S is a 56×1575 dimensional sensitivity matrix.

[0112] S4 specifically includes the following steps:

[0113] S4.1: Expand the objective function (1) and find its descent gradient and Hessian matrix, where a regularization matrix αI is added to the Hessian matrix to reduce its ill-conditioned nature:

[0114]

[0115] H k =(F′(Δσ)) T F′(Δσ)+αI (5)

[0117] In the formula, F′(Δσ) is the sensitivity matrix, I is the identity matrix, and α is selected as 0.8 based on human experience.

[0118] S4.2: Substitute equations (4) and (5) into the formula of the NR iterative algorithm. Let F′(Δσ) be represented by S:

[0119]

[0120] S4.3: Introduce the projection operator P to constrain the algorithm:

[0121]

[0122] In the formula, P is the projection operator on a non-negative convex set, which ensures that the solution of each iteration is non-negative and bounded, and converges to a convex set. f(Δσ) is the conductivity distribution function obtained in each iteration.

[0123] This example uses four different image reconstruction algorithms to verify the performance of the proposed reconstruction method: the Tikhonov algorithm, the Landweber algorithm, the CGLS algorithm, and the NR algorithm. Figure 5 The image shows a comparison of the reconstruction results of the present invention and four algorithms under a 2ml bleeding condition.

[0124] Further comparative verification is provided:

[0125] To verify the improvement effects of Examples 1-3, this invention uses image reconstruction error and correlation coefficient to evaluate the improvement effects:

[0126]

[0127]

[0128] In the formula, Δσ true For the true conductivity distribution, Δσ rec To reconstruct the conductivity distribution, and Δσ true and Δσ rec The average value was calculated; the reconstruction error and correlation coefficient of the images reconstructed by the present invention and the four image reconstruction algorithms were calculated for bleeding volumes of 24ml, 14ml, and 2ml in Examples 1-3, respectively, and summarized in Tables 1 and 2:

[0129] Table 1. Correlation coefficients of image reconstruction at different hemorrhage volumes.

[0130]

[0131] Table 2. Reconstruction errors of images at different hemorrhage volumes.

[0132]

[0133]

[0134] from Figures 5-7 As can be seen from Tables 1 and 2:

[0135] All five imaging algorithms reconstructed the location of brain hemorrhage under different hemorrhage conditions. The hemorrhage range reconstructed by this invention basically matches the actual range and is closer to the true size of the brain hemorrhage. At the same time, the artifacts around the brain hemorrhage in the reconstructed image are less than those of the four traditional algorithms, and the boundary between the brain hemorrhage and the background is clearer, making the judgment of the amount of hemorrhage more accurate. The correlation coefficient of the reconstructed image is larger than that of the other four image reconstruction algorithms, and the reconstruction error is smaller than that of the other four image reconstruction algorithms, indicating that the image quality reconstructed by this invention is better.

[0136] Unlike existing technologies, this invention provides a method for reconstructing brain hemorrhage images using magnetic induction tomography (MRI) based on an improved NR algorithm. A regularization penalty term is introduced into the objective function to improve the algorithm's iterative efficiency and reconstruction accuracy. A linear back-projection algorithm is used to improve the initial value of the NR algorithm's iterations, increasing convergence speed. A projection operator is introduced to ensure that the algorithm converges to a convex set in each iteration. This invention reduces artifacts in reconstructed brain hemorrhage images, improves image reconstruction accuracy, and produces reconstructed images that more closely resemble the actual brain hemorrhage, capable of reconstructing brain hemorrhages with a volume of 2 ml. Therefore, it provides a new and effective method for detecting the minimum mitochondrial volume (MIT) of brain hemorrhage.

[0137] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for reconstructing brain hemorrhage images using magnetic induction tomography based on an improved NR algorithm, characterized in that, Includes the following steps: S1: Using the established MIT finite element model of cerebral hemorrhage, the coil detection phase data is obtained through cyclic excitation and cyclic detection. and sensitivity matrix S; S2: Introduce a regularization penalty term ||Δσ k -Δσ k-1 By constraining the objective function of the NR algorithm, the image reconstruction problem of MIT (Middle Brain Hemorrhage) is transformed into the following objective function optimization problem: In the formula, the first term is the difference between the calculated and detected phase difference, the second term is the difference between the change in conductivity distribution at the current moment and the change in conductivity distribution at the previous moment, and β k These are the weighting coefficients of the second term, and their optimal values ​​are determined using the v method. S3: The conductivity distribution calculated by the linear back projection algorithm is used as the initial value Δσ0 for the iteration of the improved NR algorithm, and the number of iterations k = 0; S4: Solve the objective function in S2 using the idea of ​​NR iteration, obtain the iterative formula of the improved NR algorithm, and introduce the projection operator P to constrain the algorithm; S5: Determine the optimal threshold ε or the maximum number of iterations N. Update the conductivity distribution based on S3 and S4. If the iteration termination condition is met, output the current conductivity distribution value Δσ. k+1 Visualize it, and if the iteration count k = k + 1 is not satisfied, return to S3.

2. The method for reconstructing brain hemorrhage images based on the improved NR algorithm according to claim 1, characterized in that, β in S2 k Determined using the v method, the calculation formula is as follows: In the formula, k is the number of iterations, and v is selected based on empirical methods.

3. The method for reconstructing brain hemorrhage images based on the improved NR algorithm according to claim 1, characterized in that, The conductivity distribution calculated using the linear back-projection algorithm in S3 is used as the initial value Δσ0 for the iteration of the improved NR algorithm. In the formula, is the detected value of the coil, and S is the sensitivity matrix.

4. The method for reconstructing brain hemorrhage images based on the improved NR algorithm according to claim 1, characterized in that, The specific steps of S4 are as follows: S4.1: Expand the objective function (1) and find its descent gradient and Hessian matrix, where a regularization matrix αI is added to the Hessian matrix to reduce its ill-conditioned nature: H k =(F′(Δσ)) T F′(Δσ)+αI (5) In the formula, F′(Δσ) is the sensitivity matrix, I is the identity matrix, and α is selected based on human experience; S4.2: Substitute equations (4) and (5) into the formula of the NR iterative algorithm. Let F′(Δσ) be represented by S: S4.3: Introduce the projection operator P to constrain the algorithm: In the formula, P is the projection operator on a non-negative convex set, which ensures that the solution of each iteration is non-negative and bounded, and converges to a convex set. f(Δσ) is the conductivity distribution function obtained in each iteration.

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