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

arXiv: https://arxiv.org/abs/1706.07929 · HTML: https://mlsanity.com/paper/1706.07929/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [CSI Feedback with Model-Driven Deep Learning of Massive MIMO Systems](https://mlsanity.com/paper/2112.06405/) (2021)
- [Deep Radon Prior: A Fully Unsupervised Framework for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2401.00135/) (2023)
- [PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems](https://mlsanity.com/paper/2305.11056/) (2023)

## Abstract (arXiv)

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 ℓ1 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: textslhttp://jianzhang.tech/projects/ISTA-Net.