Unrolling Reweighted Total Variation-Based Split Bregman Iterative Framework for Electrical Impedance Tomography Image Reconstruction

Abstract

Electrical impedance tomography (EIT) is one of the typical ill-posed inverse problems, where serious ill-posedness and the linear approximation of the forward operator lead to obvious distortions and artifacts in the degraded reconstructions, further limiting its practical application. The learning-based strategies with image enhancement have been introduced into EIT reconstruction and also achieved improvements. Nevertheless, this idea ignores the priori knowledge of physical information, while not fully exploiting data consistency, resulting in poor generalization and interpretability. In this work, a reweighted Split Bregman (SB) iterative algorithm is proposed regularized by total variation firstly, referred to as RwTVSB. Moreover, the RwTVSB iteration is unrolled into a neural network-based learning framework, dubbed as RwTVSB-Net. The reweighted matrix is introduced to the SB iteration, which could overcome the loss of information of the forward operator due to the linear approximation and also enhance the constraints of the physical priori. Specifically, (1) a network based on residual connection and SE-attention is designed to update the reweighted matrix. (2) Further, a U-shaped architecture with deformable large kernel convolution, dilated convolution, and cross-attention is embedded into this unrolling framework to learn the soft threshold operator. This not only maintains consistency with the RwTVSB iterative algorithm but also uses multi-scale features to fusion information at multiple levels. Both simulated and real-world measured data are employed to validate the effectiveness and advantages of the proposed RwTVSB-Net. The visual reconstructions and quantitative metrics show that RwTVSB-Net outperforms other state-of-the-art methods. In addition, the robustness of the method is tested and validated on multiple imaging tasks.