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FISTA-Net Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging

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Document pages: 11 pages

Abstract: Inverse problems are essential to imaging applications. In this paper, wepropose a model-based deep learning network, named FISTA-Net, by combining themerits of interpretability and generality of the model-based Fast IterativeShrinkage Thresholding Algorithm (FISTA) and strong regularization andtuning-free advantages of the data-driven neural network. By unfolding theFISTA into a deep network, the architecture of FISTA-Net consists of multiplegradient descent, proximal mapping, and momentum modules in cascade. Differentfrom FISTA, the gradient matrix in FISTA-Net can be updated during iterationand a proximal operator network is developed for nonlinear thresholding whichcan be learned through end-to-end training. Key parameters of FISTA-Netincluding the gradient step size, thresholding value and momentum scalar aretuning-free and learned from training data rather than hand-crafted. We furtherimpose positive and monotonous constraints on these parameters to ensure theyconverge properly. The experimental results, evaluated both visually andquantitatively, show that the FISTA-Net can optimize parameters for differentimaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray ComputationalTomography (X-ray CT). It outperforms the state-of-the-art model-based and deeplearning methods and exhibits good generalization ability over othercompetitive learning-based approaches under different noise levels.

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