Inverse problems are essential to imaging applications. In this paper, 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.

Magnetic induction tomography (MIT) is a non-intrusive and non-invasive method that can image the cross-sectional conductivity distribution inside the object without contact. Target applications are conductive fluid testing in biomedical or industrial processes. The gradiometer coil is used as the front-end sensor of the proposed MIT system. As demonstrated through theoretical analysis and numerical simulation, the phase sensitivity to the conductivity of the gradiometer is greatly enhanced by eliminating the primary voltage with differential coils. The sensitivity is tunable by the residual voltage. The experimental test illustrates that 2 • /(Sm −1) sensitivity can be achieved at 10 MHz. The eight-channel MIT system MIT hardware is based on a dual-channel data acquisition board PCI-5122 at 100-MS/S sample rate per channel and a waveform generator PCI-5412 as the 10-MHz excitation source. One frame of data contains 64 phase measurements, and each is calculated with the built-in fast Fourier transform (FFT) function on LabVIEW. With full-period sampling and averaging, the sensor array can achieve less than 5-m • phase noise. The system yields good long-term stability with a phase drift less than 20 m • over 4 h. We use a FEM model to solve the forward problem and then reconstruct the 2D images by a one-step Laplacian regularization algorithm. The experimental phantom tests show that the system is capable of imaging the conductivity distribution and also indicate that the images' quality becomes better by tuning an appropriate regularization coefficient. INDEX TERMS Conductive fluid, gradiometer coil, inverse problem, Laplacian regularization, magnetic induction tomography.

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A prototype of an electrocardiogram (ECG) signal acquisition system with multiple unipolar capacitively coupled electrodes is designed and experimentally tested. Capacitively coupled electrodes made of a standard printed circuit board (PCB) are used as the sensing electrodes. Different from the conventional measurement schematics, where one single lead ECG signal is acquired from a pair of sensing electrodes, the sensing electrodes in our approaches operate in a unipolar mode, i.e., the biopotential signals picked up by each sensing electrodes are amplified and sampled separately. Four unipolar electrodes are mounted on the backrest of a regular chair and therefore four channel of signals containing ECG information are sampled and processed. It is found that the qualities of ECG signal contained in the four channel are different from each other. In order to pick up the ECG signal, an index for quality evaluation, as well as for aggregation of multiple signals, is proposed based on phase space reconstruction. Experimental tests are carried out while subjects sitting on the chair and clothed. The results indicate that the ECG signals can be reliably obtained in such a unipolar way.

Imaging the bio-impedance distribution of the brain can provide initial diagnosis of acute stroke. This paper presents a compact and non-radiative tomographic modality, i.e. multifrequency electromagnetic tomography (mfEMT), for the initial diagnosis of acute stroke. The mfEMT system consists of 12 channels of gradiometer coils with adjustable sensitivity and excitation frequency. To solve the image reconstruction problem of mfEMT, we propose an enhanced Frequency-Constrained Sparse Bayesian Learning (FC-SBL) to simultaneously reconstruct the conductivity distribution at all frequencies. Based on the Multiple Measurement Vector (MMV) model in the Sparse Bayesian Learning (SBL) framework, FC-SBL can recover the underlying distribution pattern of conductivity among multiple images by exploiting the frequency constraint information. Both simulations and experiments were conducted to evaluate the performance of FC-SBL. Results showed that the proposed FC-SBL method is robust to noisy data for image reconstruction problems of mfEMT compared to the single measurement vector model, which is promising to detect acute stroke in the brain region with enhanced spatial resolution and in a calibration-free manner.

Multi-frequency 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 paper 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 non-linear 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 intra-and inter-frequency 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.

Multi-frequency 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 address the multi-frequency setup. In this paper, we present a Multiple Measurement Vector (MMV) model based learning algorithm named MMV-Net to solve the mfEIT image reconstruction problem. MMV-Net takes into account the correlations between mfEIT images and unfolds the update steps of the Alternating Direction Method of Multipliers (ADMM) for the MMV problem. The non-linear shrinkage operator associated with the weighted l2,1 regularization term is generalized with a cascade of a Spatial Self-Attention module and a Convolutional Long Short-Term Memory (ConvLSTM) module to capture intra-and inter-frequency dependencies. The proposed MMV-Net was validated on our Edinburgh mfEIT Dataset and a series of comprehensive experiments. All reconstructed results show superior image quality, convergence performance and noise robustness against the state of the art.

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