Regularization parameter estimation method for lung three-dimensional electrical impedance tomography

Abstract

The invention discloses a regularization parameter estimation method for lung three-dimensional electrical impedance tomography, and belongs to the technical field of lung imaging reconstruction, and the method comprises the steps: obtaining voltage data measured by a lung boundary electrode, and constructing a target function comprising lung conductivity distribution and noise statistical characteristics; converting a regularization parameter estimation problem into a maximum marginal likelihood estimation problem based on an objective function; based on the maximum marginal likelihood estimation problem, adopting a stochastic approximation near-end gradient algorithm to carry out iterative optimization on the regularization parameter until convergence, and obtaining an optimal regularization parameter adaptive to the current ventilation state of the lung; and based on the optimal regularization parameter, obtaining the maximum posteriori estimation fusing the data fidelity term and the lung total variation prior, and reconstructing a lung conductivity distribution image. According to the method, details and boundary information of the lung structure can be better reserved, the edge of the generated image is sharper, the contrast ratio is higher, and the accuracy of lung image generation is improved.

Description

Technical Field

[0001] This invention belongs to the field of lung imaging reconstruction technology, and in particular relates to a regularized parameter estimation method for three-dimensional electrical impedance tomography of the lungs. Background Technology

[0002] Electrical impedance tomography (EIT) is a radiation-free, low-cost, bedside, real-time functional imaging technique. Due to its millisecond-level temporal resolution and millimeter-level spatial resolution, EIT is particularly suitable for lung imaging.

[0003] In lung imaging, EIT can provide detailed information about lung ventilation and perfusion. However, image reconstruction in EIT is essentially a large-scale three-dimensional ill-conditioned inverse problem: boundary measurements are extremely insensitive to changes in internal conductivity, with condition numbers as high as 10. 16 -10 18 Measurement noise, model error, and numerical discretization error are all amplified exponentially. To suppress pathological behavior, the academic community generally adopts regularization strategies, among which the total variation (TV) prior has become the mainstream choice for three-dimensional high-resolution EIT because it can preserve sharp interfaces and suppress smooth artifacts, which is especially important for lung imaging.

[0004] However, the degree of TV regularization is determined by the hyperparameter. control: If the value is too small, the noise is amplified, resulting in a false high conductivity anomaly; If the value is too large, the boundary is over-penalized, the conductivity jump becomes blurred, and it becomes difficult to achieve a clinically acceptable error (≤1mm interface positioning deviation). Currently, The selection of the model still relies on "L-curve artificial visual measurement" or "simulation template prior measurement," requiring dozens of repeated reconstructions, taking several hours, and cannot be updated online in response to dynamic changes in intraoperative noise, electrode contact impedance, or physiological state. Such dynamic changes are particularly common in lung imaging because breathing and heartbeat affect the conductivity distribution in the lungs.

[0005] Therefore, lung EIT urgently needs a regularization intensity setting method that does not require manual prior knowledge, can be measured in a single measurement, and automatically matches the current lung ventilation / perfusion status to ensure the accuracy of the reconstructed image. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a regularized parameter estimation method for three-dimensional electrical impedance tomography of the lungs, comprising the following steps:

[0007] Obtain voltage data measured by lung boundary electrodes and construct an objective function that includes lung conductivity distribution and noise statistics.

[0008] Based on the objective function, the regularization parameter estimation problem is transformed into the maximum marginal likelihood estimation problem, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs.

[0009] Based on the maximum marginal likelihood estimation problem, the regularization parameter is iteratively optimized using the stochastic approximation proximal gradient algorithm until convergence, thus obtaining the optimal regularization parameter that adapts to the current ventilation state of the lungs.

[0010] Based on the optimal regularization parameter, the maximum a posteriori estimate of the fusion data fidelity term and the lung total variation prior is obtained, and the lung conductivity distribution image is reconstructed.

[0011] Optionally, the process of acquiring voltage data measured by lung boundary electrodes and constructing an objective function that includes lung conductivity distribution and noise statistical characteristics includes:

[0012] The safe injection current and corresponding boundary voltage data measured by the lung boundary electrode are obtained. Combined with the complete electrode model and additive Gaussian noise, the observation equation including the lung conductivity distribution and noise statistical characteristics is obtained.

[0013] Based on the observation equation, a convex objective function is constructed with the lung finite element mesh conductivity as the unknown quantity, taking into account both data fidelity and total variational regularity.

[0014] Optionally, based on the objective function, the regularization parameter estimation problem is transformed into a maximum marginal likelihood estimation problem. The process of maximizing the marginal likelihood and matching it with the actual observed voltage in the lungs includes:

[0015] Based on the objective function, the posterior distribution of lung conductivity with regularization parameter as the only hyperparameter is obtained;

[0016] Based on the posterior distribution of lung conductivity, the marginal likelihood function of the observed voltage at the lung boundary is obtained;

[0017] Based on the marginal likelihood function, a problem statement is obtained to estimate the regularization parameter by maximizing the marginal likelihood, so that the estimation result matches the actual observed voltage in the lung.

[0018] Optionally, based on the maximum marginal likelihood estimation problem, the regularization parameter is iteratively optimized using a stochastic approximation proximal gradient algorithm until convergence, to obtain the optimal regularization parameter that adapts to the current ventilation state of the lungs. The process includes:

[0019] Based on the maximum marginal likelihood estimation problem, a solution strategy is obtained that uses a stochastic approximation near-end gradient algorithm to iteratively optimize the regularization parameter.

[0020] According to the solution strategy, the iterative steps of sampling from the posterior distribution of the lungs using the Moreau-Yosida unadjusted Langevin algorithm and combining it with Fisher's identity are used to obtain the unbiased estimate of the marginal likelihood gradient.

[0021] Based on the iterative steps, a convergence condition is obtained that stops when the parameter change is less than a threshold or when the maximum number of iterations is reached, thereby obtaining the optimal regularization parameter that is adapted to the current ventilation state of the lungs.

[0022] Optionally, the process of obtaining the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior based on the optimal regularization parameter, and reconstructing the lung conductivity distribution image, includes:

[0023] Based on the aforementioned optimal regularization parameter, the data fidelity term and the lung total variation prior are weighted and fused into a maximum a posteriori estimation problem.

[0024] Based on the maximum a posteriori estimation problem, the TV functional is transformed into a series of unconstrained problem-based obstacle representations using the logarithmic obstacle function.

[0025] The obstacle representation is solved using a line search Gauss-Newton algorithm.

[0026] The process is iterated until the internal convergence criterion is met, and a lung conductivity distribution image that retains the sharp boundaries of the lung lobes is reconstructed.

[0027] Optionally, the internal convergence criterion of the line search Gauss-Newton algorithm is that if the gradient norm is less than a set threshold, the solution of the current subproblem is terminated, and the conductivity distribution image with sharp lung lobe boundaries is output.

[0028] The present invention also provides a regularized parameter estimation system for three-dimensional electrical impedance tomography of the lungs, for implementing the method, the system comprising:

[0029] The data acquisition module is used to acquire voltage data measured by the lung boundary electrodes and construct an objective function that includes the lung conductivity distribution and noise statistical characteristics.

[0030] The parameter transformation module is used to transform the regularized parameter estimation problem into a maximum marginal likelihood estimation problem based on the objective function, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs.

[0031] The parameter optimization module is used to iteratively optimize the regularization parameters based on the maximum marginal likelihood estimation problem using a stochastic approximation proximal gradient algorithm until convergence, thereby obtaining the optimal regularization parameters that are adapted to the current ventilation state of the lungs.

[0032] The image reconstruction module is used to obtain the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior based on the optimal regularization parameter, and reconstruct the lung conductivity distribution image.

[0033] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0034] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0035] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

[0036] Compared with the prior art, the present invention has the following advantages and technical effects:

[0037] This invention addresses the practical problems in 3D electrical impedance tomography (EIT) of the lungs, such as the difficulty in automatically selecting regularization parameters, the reliance on manual adjustment in existing methods, and sensitivity to noise levels and mesh refinement. It proposes a regularization parameter estimation method for EIT of the lungs. This method achieves efficient solution through the Stochastic Proximal Gradient Algorithm (SAPG) and the Proximal MCMC Sampler (MYULA), eliminating the reliance on prior information and manual trial-and-error in traditional methods, and realizing fully automatic unsupervised estimation of regularization parameters. In the field of lung imaging, this method can better preserve the details and boundary information of lung structures, generating images with sharper edges and higher contrast. Even with changes in noise levels or mesh refinement, it maintains stable reconstruction results, improving the accuracy of lung image generation. Attached Figure Description

[0038] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0039] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention. Detailed Implementation

[0040] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0041] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0042] Example 1

[0043] In lung imaging, pulmonary electrical impedance tomography (EIT) is highly sensitive to pathological problems due to variations in lung tissue properties. This necessitates precise adjustment of the regularization parameter to obtain accurate lung images. Problems with the regularization parameter can lead to inaccurate representation of certain changes in lung tissue, such as those caused by pulmonary edema or pulmonary embolism. For example, the regularization parameter... A change of just 5% can cause the boundary position error of the reconstructed image to exceed one voxel, thus reducing the accuracy of lung images.

[0044] Secondly, EIT technology requires manual parameter adjustment based on real-time data, which is insufficient for existing TV prior knowledge. The error is usually determined by "L-curve + visual inspection" or by discrete error estimation based on simulation templates. It requires 20–40 repetitions of reconstruction and takes 2–3 hours. This is because different operators may have different adjustment habits and preferences, which may lead to huge errors in lung imaging.

[0045] Furthermore, in lung imaging, due to the complexity of lung structure and the high-dimensionality of data, traditional Bayesian methods may not be able to accurately estimate lung ventilation distribution.

[0046] Furthermore, in lung imaging, the irregularity of lung structure and the complexity of ventilation distribution place high demands on the optimization of sampling strategies. Traditional sampling methods may not meet the requirements of high-resolution imaging, especially in the peripheral regions of the lungs, which may lead to blurred and inaccurate images.

[0047] Furthermore, during lung imaging, EIT data may contain a significant amount of noise due to factors such as respiratory movements and electrocardiographic interference. This noise may be amplified during 3D reconstruction, leading to a deterioration in image quality. Maintaining image clarity and accuracy in Gaussian noise or more complex noise environments is a major challenge.

[0048] To address the aforementioned problems in existing technologies, this embodiment proposes a regularized parameter estimation method for three-dimensional electrical impedance tomography (EIT) of the lungs. This method is entirely driven by observational data, requires no manual intervention or prior measurements, and uses a stochastic proximal gradient-Markov chain hybrid algorithm to achieve efficient solutions for high-dimensional, non-smooth, and nonlinear inverse problems, thereby constructing accurate lung images.

[0049] like Figure 1 As shown, the method specifically includes the following steps:

[0050] Obtain voltage data measured by lung boundary electrodes and construct an objective function that includes lung conductivity distribution and noise statistics.

[0051] Based on the objective function, the regularization parameter estimation problem is transformed into the maximum marginal likelihood estimation problem, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs.

[0052] Based on the maximum marginal likelihood estimation problem, the regularization parameter is iteratively optimized using the stochastic approximation proximal gradient algorithm until convergence, thus obtaining the optimal regularization parameter that adapts to the current ventilation state of the lungs.

[0053] Based on the optimal regularization parameter, the maximum a posteriori estimate of the fusion data fidelity term and the lung total variation prior is obtained, and the lung conductivity distribution image is reconstructed.

[0054] The feasible process of acquiring voltage data measured by lung boundary electrodes and constructing an objective function that includes lung conductivity distribution and noise statistics includes:

[0055] The safe injection current and corresponding boundary voltage data measured by the lung boundary electrode are obtained. Combined with the complete electrode model and additive Gaussian noise, the observation equation including the lung conductivity distribution and noise statistical characteristics is obtained. Based on the observation equation, a convex objective function is constructed with the lung finite element mesh conductivity as the unknown quantity, taking into account both data fidelity and total variational regularity.

[0056] As a feasible implementation method, the process of problem modeling and objective function construction includes:

[0057] First, a complete electrode model (CEM) is used to describe the physical process of EIT, and the model is discretized using the finite element method. In the observation model, the measurement noise is assumed to be additive Gaussian noise, thus constructing a convex data fidelity term. To improve the quality of the reconstructed image, total variation (TV) regularization is chosen as the prior model, and a smoothing TV function and a barrier function are introduced to handle the non-negativity constraint of conductivity, ensuring that the entire objective function has good convexity. Specifically:

[0058] In the field of lung imaging, electrical impedance tomography (EIT) technology is increasingly widely used, and its physical processes can be described by a complete electrode model (CEM):

[0059]

[0060] in, For the boundary target domain The conductivity distribution is particularly important in lung imaging because changes in lung conductivity are closely related to the ventilation status of lung tissue. For domain The electric potential in Electrode The number of. Additionally, and These are current and potential, respectively, and these data are crucial for reconstructing the conductivity distribution of the lungs. Let be the contact impedance corresponding to the electrode, and to ensure the uniqueness of the solution, it must also satisfy:

[0061]

[0062] The first condition is given by the conservation of charge, and the second condition is the choice of the ground potential energy level.

[0063] Next, the model is discretized using the finite element method, and the potential in equations (1)-(4) is... and conductivity Approximated as:

[0064]

[0065] in, and These are the basis functions for electrical potential and conductivity, respectively. In lung imaging, selecting appropriate basis functions is crucial for accurately reconstructing the conductivity distribution of the lungs. The basis functions in this embodiment... It is a second-order piecewise polynomial, with basis functions It is a piecewise linear function. It is related to electric potential Correlation coefficient It is related to conductivity The correlation coefficients. The finite-dimensional representation of conductivity is... This method allows for a more accurate simulation of the electrical conductivity distribution in the lungs, thereby improving the accuracy and reliability of lung imaging.

[0066] In the observation model, the measurement noise is assumed to be additive Gaussian noise. In lung imaging, this noise model helps this embodiment to more accurately simulate and correct for uncertainties in the measurement process. Based on this choice, the observation model for EIT in this embodiment is written as follows:

[0067]

[0068] Among them, data vector It consists of measuring electrode potential. It is a mapping obtained from the FE approximation of CEM. It is the covariance matrix and average Gaussian noise distribution. Thus, the data fidelity term:

[0069]

[0070] It is convex. This fidelity factor ensures the consistency between the reconstructed lung conductivity distribution in this embodiment and the actual measured data.

[0071] To improve the quality of the reconstructed image, total variation (TV) regularization is chosen as the prior model, which can be written as:

[0072]

[0073] Where the function Defined as:

[0074]

[0075] In the formula, , , for , , Discrete differential operator corresponding to coordinate direction, index For elements in a finite element mesh, is the regularization parameter. In lung imaging, TV regularization helps preserve the sharp boundaries of lung structures while suppressing noise.

[0076] The prior model includes positive constraints. To avoid negative conductivity: when When the component is positive, Otherwise, it is zero.

[0077] Furthermore, since the TV prior is convex, the objective function satisfies convexity. When choosing the likelihood model and prior model as described above, the posterior can be expressed as:

[0078]

[0079] This posterior distribution guides the reconstruction of the lung conductivity distribution, ensuring that the reconstruction results are consistent with both the measurement data and physical and biological plausibility. In this way, this embodiment enables more accurate lung imaging.

[0080] Implementable transformation of the regularized parameter estimation problem into a maximum marginal likelihood estimation problem based on the objective function, and the process of maximizing the marginal likelihood and matching it with the actual observed voltage in the lungs, includes:

[0081] Based on the objective function, the posterior distribution of lung conductivity with the regularization parameter as the only hyperparameter is obtained; based on the posterior distribution of lung conductivity, the marginal likelihood function of the lung boundary observation voltage is obtained; based on the marginal likelihood function, a problem statement is obtained to estimate the regularization parameter by maximizing the marginal likelihood, so that the estimation result matches the actual lung observation voltage.

[0082] The feasible process, based on the maximum marginal likelihood estimation problem, involves iteratively optimizing the regularization parameters using a stochastic approximation proximal gradient algorithm until convergence, to obtain the optimal regularization parameters that best suit the current ventilation state of the lungs. This process includes:

[0083] Based on the maximum marginal likelihood estimation problem, a solution strategy is obtained that uses a stochastic approximation proximal gradient algorithm to iteratively optimize the regularization parameter. According to the solution strategy, an iterative step is taken to sample from the posterior distribution of the lungs using the Moreau-Yosida unadjusted Langevin algorithm and combine it with Fisher's identity to obtain an unbiased estimate of the marginal likelihood gradient. According to the iterative step, a convergence condition is obtained that stops when the parameter change is less than a threshold or when the maximum number of iterations is reached, thereby obtaining the optimal regularization parameter that is adapted to the current ventilation state of the lungs.

[0084] As a feasible implementation method, the regularization parameter estimation process includes:

[0085] Within the Bayesian framework, the regularization parameter estimation problem is transformed into a maximum marginal likelihood estimation problem. Specifically, the goal is to find the regularization parameter that maximizes the marginal likelihood of the observed data. Since marginal likelihood involves high-dimensional integrals and cannot be directly calculated, the Stochastic Approximation Proximal Gradient (SAPG) algorithm is used to optimize the problem, approximating the optimal parameter through an iterative approach.

[0086] To compute the gradient of the marginal likelihood, the gradient is expressed as the expectation of the posterior distribution using Fisher's identity. This expectation is estimated by sampling the posterior distribution. For this purpose, the efficient near-end MCMC sampler MYULA, specifically designed for handling high-dimensional log-concave distributions with non-smooth terms, is employed to obtain samples from the posterior distribution.

[0087] After obtaining the gradient estimate, the regularization parameter is optimized using the Stochastic Approximation Proximal Gradient (SAPG) algorithm. This algorithm approximates the gradient using the Erkoff Chain Monte Carlo (MCMC) method and updates the parameter in each iteration. Under appropriate step size and sample size, the SAPG algorithm converges to the maximum marginal likelihood, thus obtaining the optimal regularization parameter.

[0088] The specific process includes:

[0089] Assuming conductivity and regularization parameters The prior distribution is:

[0090] (12)

[0091] in, It is a conditional prior distribution. yes The prior distribution of .

[0092] Within the Empirical Bayesian framework, regularization parameters It is estimated by maximizing the marginal likelihood. Marginal likelihood Represented as:

[0093] (13)

[0094] in, It is observation data. It is the likelihood function. It is a conditional prior distribution.

[0095] The objective of maximum marginal likelihood estimation is to maximize the marginal likelihood function.

[0096] (14)

[0097] This method is particularly useful in lung imaging because it allows for automatic adjustment of regularization parameters to accommodate the complexity of lung conductivity distribution and the characteristics of measurement noise. In this way, this embodiment can improve the accuracy and reliability of lung imaging.

[0098] Due to direct calculation This is not feasible. This embodiment uses the MCMC method to approximate it, and the specific steps are as follows:

[0099] (1) Define the objective function:

[0100] (15)

[0101] in, These are observational data from the lung imaging process. It is the regularization parameter.

[0102] (2) Using the MCMC method to generate samples This embodiment uses the Moreau-Yosida unadjusted Langevin algorithm (MYULA). The iterative formula for MYULA is as follows:

[0103] (16)

[0104] in, It's the step length. It is a random variable that follows a standard normal distribution. This step helps to simulate the uncertainty in the distribution of lung conductivity.

[0105] Then, the marginal likelihood can be approximated by the following formula:

[0106] (17)

[0107] This approximation method allows this embodiment to estimate the regularization parameter without directly calculating complex integrals.

[0108] (3) In order to optimize This embodiment uses the Stochastic Proximal Gradient Algorithm (SAPG). The core idea of ​​SAPG is to replace the expected value with the MCMC estimator to obtain the gradient estimate.

[0109] (18)

[0110] The specific steps are as follows:

[0111] ① Initialization and sample size ;

[0112] ②For each step :

[0113] From the posterior distribution Samples generated in ;

[0114] Calculate gradient estimation: ;

[0115] Update the learning rate (using a decreasing strategy): ;

[0116] in, It is the initial learning rate. It is a positive number, usually taken as wait.

[0117] renew : ;

[0118] ③ Convergence judgment:

[0119] when The iteration stops when the change is less than a certain threshold or when the maximum number of iterations is reached.

[0120] Using this method, the regularization parameters in this embodiment can be automatically adjusted. This is to accommodate the complexity of conductivity distribution and the characteristics of measurement noise during lung imaging. This helps improve the accuracy and reliability of lung imaging.

[0121] The feasible process of reconstructing the lung conductivity distribution image by obtaining the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior based on the optimal regularization parameter includes:

[0122] Based on the optimal regularization parameter, the data fidelity term and the total variational prior of the lungs are weighted and fused into a maximum a posteriori estimation problem. According to the maximum a posteriori estimation problem, the TV functional is transformed into a series of unconstrained problem barrier representations using the logarithmic barrier function. The barrier representations are solved using the line search Gauss-Newton algorithm. The iteration is performed until the internal convergence criterion is met, and a lung conductivity distribution image that retains the sharp boundaries of the lung lobes is reconstructed.

[0123] Furthermore, the internal convergence criterion of the line search Gauss-Newton algorithm is that if the gradient norm is less than a set threshold, the solution to the current subproblem is terminated, and the conductivity distribution image that preserves the sharp boundaries of the lung lobes is output.

[0124] As a feasible implementation method, the image reconstruction process includes:

[0125] Once the optimal regularization parameters are obtained, they are substituted into the maximum a posteriori estimation problem to reconstruct the conductivity distribution by minimizing the weighted sum of the data fidelity term and the TV regularization term. To solve this optimization problem, the constraint function method is used to transform the constrained problem into an unconstrained one, and a line search Gauss-Newton algorithm is used to solve it, thus obtaining the final conductivity image. Specifically:

[0126] Once the optimal regularization parameter is obtained, it is substituted into the maximum a posteriori estimation problem (11) to reconstruct the conductivity distribution by minimizing the weighted sum of the data fidelity term and the TV regularization term. This embodiment considers using the Gauss-Newton method to solve this problem. This method requires the differentiability of the objective function; to obtain differentiability, a smooth approximation is usually used, such as... , where constant With this approximation, the TV functional (10) becomes:

[0127] (19)

[0128] In the formula, , , for , , Discrete differential operator corresponding to coordinate direction, index For elements in a finite element mesh, This is the regularization parameter.

[0129] In lung imaging, this smoothing process helps preserve edge information in the image while avoiding non-physiological conductivity distributions.

[0130] Prior parameters They are usually chosen to be mutually equal: for all , Using (19), the MAP estimate is obtained as follows:

[0131] (20)

[0132] To address the constrained optimization problem (20), this embodiment uses a barrier function to reformulate the problem as a series of unconstrained problems. The barrier problem is written as:

[0133] (twenty one)

[0134] (twenty two)

[0135] When the selected parameter sequence is hour,

[0136] (twenty three)

[0137] The solution converges to the solution of the constraint problem (20). The optimization problem (21) is solved using the line search Gauss-Newton algorithm. The stopping criterion for the internal iteration (fixed k) is selected as follows:

[0138] (twenty four)

[0139] in, In this embodiment, the stopping threshold is used as the reference. .

[0140] Using this method, this embodiment can effectively reconstruct the electrical conductivity distribution of the lungs, improving the accuracy and reliability of lung imaging.

[0141] Iterative Generalized Tikhonov Regularization (Iterative GTR) is a method for solving the nonlinear inverse problem in electrical impedance tomography (EIT). In EIT, the goal is to reconstruct the distribution of conductivity in the body by applying a current to the surface and measuring the voltage. The Iterative GTR method optimizes the estimate of the conductivity distribution through an iterative process, using regularization techniques to address ill-posed problems caused by data noise and measurement errors. Regularization helps prevent overfitting of the solution and provides more stable image reconstruction results.

[0142] The Graz Consensus Reconstruction Algorithm for EIT (GREIT) is a specific EIT image reconstruction algorithm that uses a dual-grid scheme: a coarse two-dimensional grid for conductivity reconstruction and a fine three-dimensional grid for precise forward computation. This approach can improve reconstruction accuracy but may increase computation time and resource consumption.

[0143] In comparison, the method proposed in this embodiment performs better in terms of image reconstruction quality. It outperforms the Iterative GTR method in noise suppression, generating smoother and cleaner images. It also surpasses the GREIT method in stability and consistency, which may exhibit some discontinuities and artifacts. The method proposed in this embodiment can generate more accurate, clearer, and more reliable images, which is of great significance for subsequent image analysis and clinical applications.

[0144] In summary, the Iterative GTR method is a general iterative regularization method, while GREIT is a specific EIT reconstruction algorithm. The method proposed in this embodiment improves both image quality and reconstruction stability, providing superior image reconstruction results.

[0145] This embodiment proposes a method for automatically selecting regularization parameters in three-dimensional electrical impedance tomography (EIT) of the lungs, combining the Stochastic Proximal Gradient Algorithm (SAPG) and the Proximal MCMC Sampler (MYULA) for solution. Numerical experiments verify that this method achieves significant beneficial effects in the following aspects:

[0146] 1. Fully automatic unsupervised parameter estimation: Traditional regularization parameters require manual trial and error or rely on prior information. This method can automatically estimate parameters using only observed data, without manual intervention or reference to real values, which significantly improves the practicality and automation level of the algorithm.

[0147] 2. Image sharpness: The images generated by this method appear sharper with sharper edges. This indicates that the method can better preserve the details and structural information of the image during image reconstruction.

[0148] 3. Contrast: Images generated by this method have higher contrast, with more pronounced differences between different regions. This helps to more accurately identify and distinguish different features and structures in the image.

[0149] In summary, the automatic selection method for regularization parameters proposed in this embodiment achieves high-precision, highly automated, boundary-preserving, and robust reconstruction results in EIT imaging, providing strong support for the promotion of EIT in practical applications such as medicine and geophysics.

[0150] Example 2

[0151] Based on the same general inventive concept, this invention also provides a regularized parameter estimation system for three-dimensional electrical impedance tomography (EIT) of the lungs. The system provided by this invention is described below, and the system described below can be referred to in conjunction with the method described above. The system includes:

[0152] The data acquisition module is used to acquire voltage data measured by the lung boundary electrodes and construct an objective function that includes the lung conductivity distribution and noise statistical characteristics.

[0153] The parameter transformation module is used to transform the regularized parameter estimation problem into a maximum marginal likelihood estimation problem based on the objective function, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs.

[0154] The parameter optimization module is used to iteratively optimize the regularization parameters based on the maximum marginal likelihood estimation problem using a stochastic approximation proximal gradient algorithm until convergence, thereby obtaining the optimal regularization parameters that are adapted to the current ventilation state of the lungs.

[0155] The image reconstruction module is used to obtain the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior based on the optimal regularization parameter, and reconstruct the lung conductivity distribution image.

[0156] Example 3

[0157] This embodiment also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in Embodiment 1.

[0158] Example 4

[0159] This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0160] Example 5

[0161] This embodiment also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0162] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A regularized parameter estimation method for three-dimensional electrical impedance tomography of the lungs, characterized in that, Includes the following steps: Obtain voltage data measured by lung boundary electrodes and construct an objective function that includes lung conductivity distribution and noise statistics. Based on the objective function, the regularization parameter estimation problem is transformed into the maximum marginal likelihood estimation problem, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs. Based on the maximum marginal likelihood estimation problem, the regularization parameter is iteratively optimized using the stochastic approximation proximal gradient algorithm until convergence, thus obtaining the optimal regularization parameter that adapts to the current ventilation state of the lungs. Based on the optimal regularization parameter, the maximum a posteriori estimate of the fusion data fidelity term and the lung total variation prior is obtained, and the lung conductivity distribution image is reconstructed.

2. The method according to claim 1, characterized in that, The process of acquiring voltage data measured by lung boundary electrodes and constructing an objective function that includes lung conductivity distribution and noise statistics includes: The safe injection current and corresponding boundary voltage data measured by the lung boundary electrode are obtained. Combined with the complete electrode model and additive Gaussian noise, the observation equation including the lung conductivity distribution and noise statistical characteristics is obtained. Based on the observation equation, a convex objective function is constructed with the lung finite element mesh conductivity as the unknown quantity, taking into account both data fidelity and total variational regularity.

3. The method according to claim 1, characterized in that, Based on the objective function, the regularization parameter estimation problem is transformed into a maximum marginal likelihood estimation problem. The process of maximizing the marginal likelihood and matching it with the actual observed voltage in the lungs includes: Based on the objective function, the posterior distribution of lung conductivity with regularization parameter as the only hyperparameter is obtained; Based on the posterior distribution of lung conductivity, the marginal likelihood function of the observed voltage at the lung boundary is obtained; Based on the marginal likelihood function, a problem statement is obtained to estimate the regularization parameter by maximizing the marginal likelihood, so that the estimation result matches the actual observed voltage in the lung.

4. The method according to claim 1, characterized in that, Based on the maximum marginal likelihood estimation problem, the regularization parameter is iteratively optimized using a stochastic approximation proximal gradient algorithm until convergence. The process of obtaining the optimal regularization parameter that adapts to the current ventilation state of the lungs includes: Based on the maximum marginal likelihood estimation problem, a solution strategy is obtained that uses a stochastic approximation near-end gradient algorithm to iteratively optimize the regularization parameter. According to the solution strategy, the iterative steps of sampling from the posterior distribution of the lungs using the Moreau-Yosida unadjusted Langevin algorithm and combining it with Fisher's identity are used to obtain the unbiased estimate of the marginal likelihood gradient. Based on the iterative steps, a convergence condition is obtained that stops when the parameter change is less than a threshold or when the maximum number of iterations is reached, thereby obtaining the optimal regularization parameter that is adapted to the current ventilation state of the lungs.

5. The method according to claim 1, characterized in that, Based on the optimal regularization parameter, the process of obtaining the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior, and reconstructing the lung conductivity distribution image, includes: Based on the aforementioned optimal regularization parameter, the data fidelity term and the lung total variation prior are weighted and fused into a maximum a posteriori estimation problem. Based on the maximum a posteriori estimation problem, the TV functional is transformed into a series of unconstrained problem-based obstacle representations using the logarithmic obstacle function. The obstacle representation is solved using a line search Gauss-Newton algorithm. The process is iterated until the internal convergence criterion is met, and a lung conductivity distribution image that retains the sharp boundaries of the lung lobes is reconstructed.

6. The method according to claim 5, characterized in that, The internal convergence criterion of the line search Gauss-Newton algorithm is that if the gradient norm is less than a set threshold, the solution to the current subproblem is terminated, and the conductivity distribution image that preserves the sharp boundaries of the lung lobe is output.

7. A regularized parameter estimation system for three-dimensional electrical impedance tomography of the lungs, characterized in that, The system for implementing the method according to any one of claims 1-6 comprises: The data acquisition module is used to acquire voltage data measured by the lung boundary electrodes and construct an objective function that includes the lung conductivity distribution and noise statistical characteristics. The parameter transformation module is used to transform the regularized parameter estimation problem into a maximum marginal likelihood estimation problem based on the objective function, so as to maximize the marginal likelihood and match it with the actual observed voltage in the lungs. The parameter optimization module is used to iteratively optimize the regularization parameters based on the maximum marginal likelihood estimation problem using a stochastic approximation proximal gradient algorithm until convergence, thereby obtaining the optimal regularization parameters that are adapted to the current ventilation state of the lungs. The image reconstruction module is used to obtain the maximum a posteriori estimate of the fused data fidelity term and the lung total variation prior based on the optimal regularization parameter, and reconstruct the lung conductivity distribution image.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.

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