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

Jinxi Xiang, Yonggui Dong, Yunjie Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1329 - 1339
JournalIEEE Transactions on Medical Imaging
Issue number5
Early online date25 Jan 2021
Publication statusPublished - May 2021


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