Inverse problems are essential to imaging applications. In this letter, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.

Electrical impedance tomography (EIT) is developed to investigate the internal conductivity changes of an object through a series of boundary electrodes, and has become increasingly attractive in a broad spectrum of applications. However, the design of optimal tomography image reconstruction algorithms has not achieved the adequate level of progress and matureness. In this paper, we propose an efficient and high-resolution EIT image reconstruction method in the framework of sparse Bayesian learning. Significant performance improvement is achieved by imposing structure-aware priors on the learning process to incorporate the prior knowledge that practical conductivity distribution maps exhibit clustered sparsity and intra-cluster continuity. The proposed method not only achieves high-resolution estimation and preserves the shape information even in low signal-to-noise ratio scenarios but also avoids the time-consuming parameter tuning process. The effectiveness of the proposed algorithm is validated through comparisons with state-of-the-art techniques using extensive numerical simulation and phantom experiment results.

In this work, we consider the reconstruction of three-dimensional (3D) conductivity distribution using electrical impedance tomography (EIT) technique. A high-resolution and efficient algorithm is developed to solve the EIT inverse problem. The presented algorithm is extended upon a recently proposed novel EIT reconstruction approach based on structure-aware sparse Bayesian learning (SA-SBL). The correlation between proximal layers in the 3D geometry are incorporated into the structure prior to improve the reconstruction accuracy. In addition, an efficient approach based on approximate message passing is developed to accelerate the large-scale 3D learning process. To validate the algorithm, numerical experiments using real recorded data are conducted. The visual and quantitative-metric comparisons show that the proposed method outperforms the existing methods in terms of reconstruction accuracy and computational complexity in all test cases. The SA-SBL based reconstruction approach can preserve the 3D structure of medical volume, reduce the systematic artifacts, and improve the computational efficiency.

This paper presents the design and evaluation of a configurable, fast multi-frequency Electrical Impedance Tomography (mfEIT) system for real-time 2D and 3D imaging, particularly for biomedical imaging. The system integrates 32 electrode interfaces and the current frequency ranges from 10 kHz to 1 MHz. The system incorporates the following novel features. First, a fully adjustable multi-frequency current source with current monitoring function is designed. Second, a flexible switching scheme is developed for arbitrary sensing configuration and a semi-parallel data acquisition architecture is implemented for high-frame-rate data acquisition. Furthermore, multi-frequency digital quadrature demodulation is accomplished in a high-capacity Field Programmable Gate Array. At last, a 3D imaging software, visual tomography, is developed for real-time 2D and 3D image reconstruction, data analysis, and visualization. The mfEIT system is systematically tested and evaluated from the aspects of signal to noise ratio (SNR), frame rate, and 2D and 3D multi-frequency phantom imaging. The highest SNR is 82.82 dB on a 16-electrode sensor. The frame rate is up to 546 fps at serial mode and 1014 fps at semi-parallel mode. The evaluation results indicate that the presented mfEIT system is a powerful tool for real-time 2D and 3D imaging.

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 $l_{2,1}$ 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.