ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing

TL;DR

ISTA-Net is a deep network inspired by optimization algorithms that efficiently reconstructs natural images in compressive sensing, combining interpretability with high accuracy and speed.

Contribution

The paper introduces ISTA-Net, a novel deep network that unrolls the ISTA optimization algorithm for CS, with end-to-end learnable parameters, and proposes an enhanced residual version, ISTA-Net+.

Findings

Outperforms state-of-the-art CS methods in accuracy.

Maintains fast computational speed.

Effective in residual domain for better reconstruction.

Abstract

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $\ell_1$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed {ISTA-Net}$^+$, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.