# ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing

arXiv: https://arxiv.org/abs/2103.11554 · HTML: https://mlsanity.com/paper/2103.11554/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [Simultaneous Fidelity and Regularization Learning for Image Restoration](https://mlsanity.com/paper/1804.04522/) (2018)
- [Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization](https://mlsanity.com/paper/1404.7566/) (2014)

## Built on by (most cited first, 30 of 39)

- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [HerosNet: Hyperspectral Explicable Reconstruction and Optimal Sampling Deep Network for Snapshot Compressive Imaging](https://mlsanity.com/paper/2112.06238/) (2021)
- [Real-world Image Dehazing with Coherence-based Pseudo Labeling and Cooperative Unfolding Network](https://mlsanity.com/paper/2406.07966/) (2024)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [DRPCA-Net: Make Robust PCA Great Again for Infrared Small Target Detection](https://mlsanity.com/paper/2507.09541/) (2025)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [LR-CSNet: Low-Rank Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2212.09088/) (2022)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [DISTA-Net: Dynamic Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2505.19148/) (2025)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Lightweight Deep Unfolding Networks with Enhanced Robustness for Infrared Small Target Detection](https://mlsanity.com/paper/2509.08205/) (2025)
- [GA-HQS: MRI reconstruction via a generically accelerated unfolding approach](https://mlsanity.com/paper/2304.02883/) (2023)
- [SeqCSIST: Sequential Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2507.09556/) (2025)
- [Model-Guided Multi-Contrast Deep Unfolding Network for MRI Super-resolution Reconstruction](https://mlsanity.com/paper/2209.07030/) (2022)
- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)
- [RadioDUN: A Physics-Inspired Deep Unfolding Network for Radio Map Estimation](https://mlsanity.com/paper/2506.08418/) (2025)
- [ICRICS: Iterative Compensation Recovery for Image Compressive Sensing](https://mlsanity.com/paper/2207.09594/) (2022)
- [Uformer-ICS: A U-Shaped Transformer for Image Compressive Sensing Service](https://mlsanity.com/paper/2209.01763/) (2022)
- [On Generalization Bounds for Deep Compound Gaussian Neural Networks](https://mlsanity.com/paper/2402.13106/) (2024)
- [DSCSNet: A Dynamic Sparse Compression Sensing Network for Closely-Spaced Infrared Small Target Unmixing](https://mlsanity.com/paper/2603.21192/) (2026)
- [CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization](https://mlsanity.com/paper/2605.05136/) (2026)
- [A Lightweight Recurrent Learning Network for Sustainable Compressed Sensing](https://mlsanity.com/paper/2304.11674/) (2023)

## Abstract (arXiv)

While deep neural networks have achieved impressive success in image compressive sensing (CS), most of them lack flexibility when dealing with multi-ratio tasks and multi-scene images in practical applications. To tackle these challenges, we propose a novel end-to-end flexible ISTA-unfolding deep network, dubbed ISTA-Net++, with superior performance and strong flexibility. Specifically, by developing a dynamic unfolding strategy, our model enjoys the adaptability of handling CS problems with different ratios, i.e., multi-ratio tasks, through a single model. A cross-block strategy is further utilized to reduce blocking artifacts and enhance the CS recovery quality. Furthermore, we adopt a balanced dataset for training, which brings more robustness when reconstructing images of multiple scenes. Extensive experiments on four datasets show that ISTA-Net++ achieves state-of-the-art results in terms of both quantitative metrics and visual quality. Considering its flexibility, effectiveness and practicability, our model is expected to serve as a suitable baseline in future CS research. The source code is available on https://github.com/jianzhangcs/ISTA-Netpp.