TranIU-Net: Indicative Electrical Tomography Imaging Based on Implicit Unrolling Transformer

Deep unrolling networks have rapidly gained popularity in image reconstruction by integrating data-driven networks with iterative model-driven reconstruction algorithms. Technically, existing unrolling networks could easily break down and produce sub-optimal results due to inadequate iterations and limited receptive fields. Another challenge is that mainstream algorithms are established in isolation from the physical system and confined to digital realm. This paper proposes a novel implicit unrolling Transformer architecture, dubbed TranIU-Net, that extracts local contents and non-local dependencies to assist iterative learning, and forms indicative imaging mechanism to guide system design. Concretely, TranIU-Net unrolls the proximal gradient algorithm into a trainable network with structural interpretability. Using only constant memory cost, the implicit mapping is analytically built to guarantee the convergence through the fixed-point at unlimited depth. To consider intrinsic correlation and sparsity in reconstructed images, an embedded Transformer module is developed to capture multi-scale information with hybrid receptive fields and assign self-aware granularity with learnt significance estimator, making it an efficient backbone for implicit unrolling network. Additionally, with adaptive and flexible architecture, TranIU-Net explores a new imaging mechanism by indicating structure design and measurement condition, bridging the gap between algorithm and imaging system to facilitate reconstruction quality. Extensive numerical simulations and practical experiments of electrical tomography reconstruction demonstrate that the proposed TranIU-Net outperforms state-of-the-art alternatives in different scenarios from both quantitative and qualitative perspectives.