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

TL;DR

FISTA-Net is a deep learning model that unfolds the FISTA algorithm into a trainable network, improving inverse imaging tasks by combining interpretability, adaptability, and superior performance across multiple imaging modalities.

Contribution

This paper introduces FISTA-Net, a novel deep network that integrates FISTA's interpretability with learnable parameters, enabling adaptive and efficient inverse problem solutions in imaging.

Findings

Outperforms state-of-the-art methods in EMT and X-ray CT tasks.

Learns parameters from data, eliminating manual tuning.

Demonstrates strong generalization across noise levels.

Abstract

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.