Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography

Moving morphable component (MMC) topology optimization with different void structure scaling factors

The explicit topology optimization method based on moving morphable component (MMC) has attracted more and more attention, and components are the basic building blocks of the implementation of MMC method. In the present work, a MMC topology optimization method based on component with void structure is followed with interest. On the basis of analyzing the characteristics of components used by MMC method, the topology description function for component with void structure is presented, where a quantitative scaling factor is introduced without increasing the number of design variables. Taking the minimum flexibility as the optimization objective, an example of short beam is analyzed with different void structure scaling factors. The results show that different scaling factors have a greater impact on the final topology optimization structure, and an ideal topology structure can be obtained with an appropriate scaling factor. Finally, some problems in the optimization process are analyzed and indicate that appropriate mesh density should be chose for component with void structure in order to achieve good optimization results.

MMV-Net: A Multiple Measurement Vector Network for Multifrequency Electrical Impedance Tomography

Multifrequency electrical impedance tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods suffer from low spatial resolution, unconstrained frequency correlation, and high computational cost. Deep learning has been extensively applied in solving the EIT inverse problem in biomedical and industrial process imaging. However, most existing learning-based approaches deal with the single-frequency setup, which is inefficient and ineffective when extended to the multifrequency setup. This article presents a multiple measurement vector (MMV) model-based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net considers the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers for the MMV problem (MMV-ADMM). The nonlinear shrinkage operator associated with the weighted l2,1 regularization term of MMV-ADMM is generalized in MMV-Net with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to better capture intrafrequency and interfrequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. The results show superior image quality, convergence performance, noise robustness, and computational efficiency against the conventional MMV-ADMM and the state-of-the-art deep learning methods.

Research Trends and Hotspots of Medical Electrical Impedance Tomography Algorithms: A Bibliometric Analysis From 1987 to 2021

Electrical impedance tomography (EIT) is a gradually maturing medical imaging technique that relies on computational algorithms for reconstructing and visualizing internal conductivity distributions within the human body. To provide a comprehensive and objective understanding of the current state and trends in the EIT algorithm research, we conducted bibliometric analysis on a 25-year EIT algorithm research dataset sourced from Web of Science Core Collections. We visualized publication characteristics, collaboration patterns, keywords, and co-cited references. The results indicate a steady increase in annual publications over recent decades. The United States, United Kingdom, China, and South Korea contributed 60% of the articles collaboratively. Keyword analysis unveiled three distinct stages in the evolution of EIT algorithm research: the establishment of fundamental algorithm frameworks, optimization for improved imaging performance, and the development of algorithms for clinical applications. Additionally, there has been a shift in research focus from traditional theories to the incorporation of new methods, such as artificial intelligence. Co-cited references suggest that integrating EIT with other established imaging techniques may emerge as a new trend in EIT algorithm research. In summary, EIT algorithms have been a consistent research focus, with current efforts centered on optimizing algorithms to enhance imaging performance. The emerging research trend involves utilizing more diverse and intersecting algorithms.

Effective Electrical Impedance Tomography Based on Enhanced Encoder-Decoder Using Atrous Spatial Pyramid Pooling Module

Electrical impedance tomography (EIT) is a noninvasive and radiation-free imaging method. As a "soft-field" imaging technique, in EIT, the target signal in the center of the measured field is frequently swamped by the target signal at the edge, which restricts its further application. To alleviate this problem, this study presents an enhanced encoder-decoder (EED) method with an atrous spatial pyramid pooling (ASPP) module. The proposed method enhances the ability to detect central weak targets by constructing an ASPP module that integrates multiscale information in the encoder. The multilevel semantic features are fused in the decoder to improve the boundary reconstruction accuracy of the center target. The average absolute error of the imaging results by the EED method reduced by 82.0%, 83.6%, and 36.5% in simulation experiments and 83.0%, 83.2%, and 36.1% in physical experiments compared with the errors of the damped least-squares algorithm, Kalman filtering method, and U-Net-based imaging method, respectively. The average structural similarity improved by 37.3%, 42.9%, and 3.6%, and 39.2%, 45.2%, and 3.8% in the simulation and physical experiments, respectively. The proposed method provides a practical and reliable means of extending the application of EIT by solving the problem of weak central target reconstruction under the effect of strong edge targets in EIT.

Fast Iterative Shrinkage-Thresholding Algorithm with Continuation for Brain Injury Monitoring Imaging Based on Electrical Impedance Tomography

Electrical impedance tomography (EIT) is low-cost and noninvasive and has the potential for real-time imaging and bedside monitoring of brain injury. However, brain injury monitoring by EIT imaging suffers from image noise (IN) and resolution problems, causing blurred reconstructions. To address these problems, a least absolute shrinkage and selection operator model is built, and a fast iterative shrinkage-thresholding algorithm with continuation (FISTA-C) is proposed. Results of numerical simulations and head phantom experiments indicate that FISTA-C reduces IN by 63.2%, 47.2%, and 29.9% and 54.4%, 44.7%, and 22.7%, respectively, when compared with the damped least-squares algorithm, the split Bergman, and the FISTA algorithms. When the signal-to-noise ratio of the measurements is 80-50 dB, FISTA-C can reduce IN by 83.3%, 72.3%, and 68.7% on average when compared with the three algorithms, respectively. Both simulation and phantom experiments suggest that FISTA-C produces the best image resolution and can identify the two closest targets. Moreover, FISTA-C is more practical for clinical application because it does not require excessive parameter adjustments. This technology can provide better reconstruction performance and significantly outperforms the traditional algorithms in terms of IN and resolution and is expected to offer a general algorithm for brain injury monitoring imaging via EIT.

Advances of deep learning in electrical impedance tomography image reconstruction

Electrical impedance tomography (EIT) has been widely used in biomedical research because of its advantages of real-time imaging and nature of being non-invasive and radiation-free. Additionally, it can reconstruct the distribution or changes in electrical properties in the sensing area. Recently, with the significant advancements in the use of deep learning in intelligent medical imaging, EIT image reconstruction based on deep learning has received considerable attention. This study introduces the basic principles of EIT and summarizes the application progress of deep learning in EIT image reconstruction with regards to three aspects: a single network reconstruction, deep learning combined with traditional algorithm reconstruction, and multiple network hybrid reconstruction. In future, optimizing the datasets may be the main challenge in applying deep learning for EIT image reconstruction. Adopting a better network structure, focusing on the joint reconstruction of EIT and traditional algorithms, and using multimodal deep learning-based EIT may be the solution to existing problems. In general, deep learning offers a fresh approach for improving the performance of EIT image reconstruction and could be the foundation for building an intelligent integrated EIT diagnostic system in the future.

Adaptively Regularized Bases-Expansion Subspace Optimization Methods for Electrical Impedance Tomography

OBJECTIVE

In this work, to deal with the difficulties in choosing regularization weighting parameters and low spatial resolution problems in difference electrical impedance tomography (EIT), we propose two adaptively regularized bases-expansion subspace optimization methods (AR-BE-SOMs).

METHODS

Firstly, an adaptive L1-norm based total variation (TV) regularization is introduced under the framework of BE-SOM. Secondly, besides the additive regularization, an adaptive weighted L2-norm multiplicative regularization is further proposed. The regularized objective functions are optimized by conjugate gradient method, where the unknowns in both methods are update alternatively between induced contrast current (ICC) and conductivity domain.

CONCLUSION

Both numerical and experimental tests are conducted to validate the proposed methods, where AR-BE-SOMs show better edge-preserving, anti-noise performance, lower relative errors, and higher structure similarity indexes than BE-SOM.

SIGNIFICANCE

Unlike the common regularization techniques in EIT, the proposed regularization factors can be obtained adaptively during the optimization process. More importantly, ARBE-SOMs perform well in reconstructions of some challenging geometry with sharp corners such as the heart and lung phantoms, deformation phantoms, triangles and even rectangles. It is expected that the proposed AR-BE-SOMs will find their applications for high-quality lung health monitoring and other clinical applications.

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

An efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis functions

AbstractObjective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.

METHODS

A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem.

RESULTS

Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.

CONCLUSION

The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.

SIGNIFICANCE

Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Shape-Driven EIT Reconstruction Using Fourier Representations

Shape-driven approaches have been proposed as an effective strategy for the electrical impedance tomography (EIT) reconstruction problem in recent years. In order to augment the shape-driven approaches, we propose a new method that transforms the shape to be reconstructed as basic primitives directly modeled by using Fourier representations. To allow automatic topological changes between the basic primitives and surrounding objects simultaneously, Boolean operations are employed. The Boolean operations with direct representation of primitives can be utilized for dimensionality and ill-posedness reduction, enabling feasible shape and topology optimization with shape-driven approaches. As a proof of principle, we leverage the proposed method for two dimensional shape reconstruction in EIT with various conductivity distributions. We demonstrate that our method is able to improve EIT reconstructions by enabling accurate shape and topology optimization.

Shape-Driven Difference Electrical Impedance Tomography

This work proposes a novel shape-driven reconstruction approach for difference electrical impedance tomography (EIT). In the proposed approach, the reconstruction problem is formulated as a shape reconstruction problem and solved via an explicit and geometrical methodology, where the geometry of the embedded inclusions is represented by a shape and topology description function (STDF). To incorporate more geometry and prior information directly into the reconstruction and to provide better flexibility in the solution process, the concept of a moving morphable component (MMC) is applied here implying that MMC is treated as the basic building block of the embedded inclusions. Simulations, phantom studies, and in vivo pig data are used to test the proposed approach for the most popular biomedical application of EIT - lung imaging - and the performance is compared with the conventional linear approach. In addition, the modality's robustness is studied in cases where (i) modeling errors are caused by inhomogeneity in the background conductivity, and (ii) uncertainties in the contact impedances and reference state are present. The results of this work indicate that the proposed approach is tolerant to modeling errors and is fairly robust to typical EIT uncertainties, producing greatly improved image quality compared to the conventional linear approach.