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{this http URL}.

本研究致力于发展一种快速而准确的压缩感知（CS）自然图像重建算法，通过结合传统基于优化和最近基于网络的 CS 方法的优点，提出了一种新颖的结构化深度网络 ISTA-Net，并通过端到端学习来训练其所有参数，我们的实验表明，IST-Net 在保持快速计算速度的同时，可以优于现有基于优化和基于网络的 CS 方法。