Higher order total variation regularization for EIT reconstruction

High-resolution conductivity reconstruction by electrical impedance tomography using structure-aware hybrid-fusion learning

BACKGROUND

Electrical impedance tomography (EIT) has gained considerable attention in the medical field for the diagnosis of lung-related diseases, owing to its non-invasive and real-time characteristics. However, due to the ill-posedness and underdetermined nature of the inverse problem in EIT, suboptimal reconstruction performance and reduced robustness against the measurement noise and modeling errors are common issues.

OBJECTIVES

This study aims to mine the deep feature information from measurement voltages, acquired from the EIT sensor, to reconstruct the high-resolution conductivity distribution and enhance the robustness against the measurement noise and modeling errors using the deep learning method.

METHODS

A novel data-driven method named the structure-aware hybrid-fusion learning (SA-HFL) is proposed. SA-HFL is composed of three main components: a segmentation branch, a conductivity reconstruction branch, and a feature fusion module. These branches work in tandem to extract different feature information from the measurement voltage, which is then fused to reconstruct the conductivity distribution. The unique aspect of this network is its ability to utilize different features extracted from various branches to accomplish reconstruction objectives. To supervise the training of the network, we generated regular-shaped and lung-shaped EIT datasets through numerical calculations.

RESULTS

The simulations and three experiments demonstrate that the proposed SA-HFL exhibits superior performance in qualitative and quantitative analyses, compared with five cutting-edge deep learning networks and the optical image-guided group sparsity (IGGS) method. The evaluation metrics, relative error (RE), mean structural similarity index (MSSIM), and peak signal-to-noise ratio (PSNR), are improved by implementing the SA-HFL method. For the regular-shaped dataset, the values are 0.119 (RE), 0.9882 (MSSIM), and 31.03 (PSNR). For the lung-shaped dataset, the values are 0.257 (RE), 0.9151 (MSSIM), and 18.67 (PSNR). Furthermore, the proposed network can be executed with appropriate parameters and efficient floating-point operations per second (FLOPs), concerning network complexity and inference speed.

CONCLUSIONS

The reconstruction results indicate that fusing feature information from different branches enhances the accuracy of conductivity reconstruction in the EIT inverse problem. Moreover, the study shows that fusing different modalities of information to reconstruct the EIT conductivity distribution may be a future development direction.

Majorization–Minimization Total Variation Solution Methods for Electrical Impedance Tomography

Inverse problems arise in many areas of science and engineering, such as geophysics, biology, and medical imaging. One of the main imaging modalities that have seen a huge increase in recent years is the noninvasive, nonionizing, and radiation-free imaging technique of electrical impedance tomography (EIT). Other advantages of such a technique are the low cost and ubiquitousness. An imaging technique is used to recover the internal conductivity of a body using measurements from electrodes from the body’s surface. The standard procedure is to obtain measurements by placing electrodes in the body and measuring conductivity inside the object. A current with low frequency is applied on the electrodes below a threshold, rendering the technique harmless for the body, especially when applied to living organisms. As with many inverse problems, EIT suffers from ill-posedness, i.e., the reconstruction of internal conductivity is a severely ill-posed inverse problem and typically yields a poor-quality solution. Moreover, the desired solution has step changes in the electrical properties that are typically challenging to be reconstructed by traditional smoothing regularization methods. To counter this difficulty, one solves a regularized problem that is better conditioned than the original problem by imposing constraints on the regularization term. The main contribution of this work is to develop a general ℓp regularized method with total variation to solve the nonlinear EIT problem through a iteratively reweighted majorization–minimization strategy combined with the Gauss–Newton approach. The main idea is to majorize the linearized EIT problem at each iteration and minimize through a quadratic tangent majorant. Simulated numerical examples from complete electrode model illustrate the effectiveness of our approach.

Impedance-Optical Dual-Modal Cell Culture Imaging With Learning-Based Information Fusion

While Electrical Impedance Tomography (EIT) has found many biomedicine applications, better image quality is needed to provide quantitative analysis for tissue engineering and regenerative medicine. This paper reports an impedance-optical dual-modal imaging framework that primarily targets at high-quality 3D cell culture imaging and can be extended to other tissue engineering applications. The framework comprises three components, i.e., an impedance-optical dual-modal sensor, the guidance image processing algorithm, and a deep learning model named multi-scale feature cross fusion network (MSFCF-Net) for information fusion. The MSFCF-Net has two inputs, i.e., the EIT measurement and a binary mask image generated by the guidance image processing algorithm, whose input is an RGB microscopic image. The network then effectively fuses the information from the two different imaging modalities and generates the final conductivity image. We assess the performance of the proposed dual-modal framework by numerical simulation and MCF-7 cell imaging experiments. The results show that the proposed method could improve the image quality notably, indicating that impedance-optical joint imaging has the potential to reveal the structural and functional information of tissue-level targets simultaneously.

Application of Particle Swarm Optimization with Simulated Annealing in MIT Regularization Image Reconstruction

Background and Objectives: Due to the soft-field effect of the electromagnetic field and the limit of detection, image reconstruction of magnetic induction tomography has to recover more complex electrical characteristics from very few signals. These cause a problem which have underdetermination, nonlinearity, and ill-posed characteristics, and therefore lead to many difficulties in finding its solution. Although many regularization image reconstruction methods exist, they are not suitable for MIT applications due to regularization parameter selection. The purpose of this paper is to study the principle of particle swarm optimization with simulated annealing, and to propose a regularization method for reconstruction, which will provide a new way to solve the MIT image problems. Methods and Models: Firstly, the regularization principle of image reconstruction of MIT will be analyzed. Then the hybrid regularization algorithm, including Tikhonov and NOSER regularization, will be developed, using the dimension of the Hessian matrix as a penalty term respecting the prior knowledge. PSO-SA algorithm will be applied to obtain an optimal solution for regularization parameters. Finally, six typical numerical models and approximately symmetrical cerebral hemorrhage models by COMSOL will be carried out, and the voltage signals obtained from the simulation will be used to verify the proposed reconstruction method. Results: Through the simulation results, the proposed imaging method has the average CC values of 0.9932, 0.8286 and the average RE values of 0.4982, 0.8320 for simple and complex models, respectively. Moreover, when the SNR changes from 55dB to 35dB, the CC value of the cerebral hemorrhage model reduced by 0.1034. The results demonstrate the effectiveness and high theoretical feasibility of the proposed method in MIT image reconstruction. Conclusions: This study indicates the potential application of PSO-SA algorithm in regularization imaging problem. Compared with traditional regularization imaging methods, the proposed method has the advantages of better accuracy, robustness and noise resistance, showing the certain application value in other similar ill-ness imaging problems.

Thoracic electrical impedance tomography in Chinese hospitals: a review of clinical research and daily applications

Chinese scientists and researchers have a long history with electrical impedance tomography (EIT), which can be dated back to the 1980s. No commercial EIT devices for chest imaging were available until the year 2014 when the first device received its approval from the China Food and Drug Administration. Ever since then, clinical research and daily applications have taken place in Chinese hospitals. Up to this date (2019.11) 47 hospitals have been equipped with 50 EIT devices. Twenty-three SCI publications are recorded and a further 21 clinical trials are registered. Thoracic EIT is mainly used in patients before or after surgery, or in intensive care units (ICU). Application fields include the development of strategies for protective lung ventilation (e.g. tidal volume and positive end-expiratory pressure (PEEP) titration, recruitment, choice of ventilation mode and weaning from ventilator), regional lung perfusion monitoring, perioperative monitoring, and potential feedback for rehabilitation. The main challenges for promoting clinical use of EIT are the financial cost and the education of personnel. In this review, the past, present and future of EIT in China are introduced and discussed.