# Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing

arXiv: https://arxiv.org/abs/2606.03666 · HTML: https://mlsanity.com/paper/2606.03666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [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)
- [DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing](https://mlsanity.com/paper/1702.05743/) (2017)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Multi-Channel Deep Networks for Block-Based Image Compressive Sensing](https://mlsanity.com/paper/1908.11221/) (2019)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [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)
- [FSOINet: Feature-Space Optimization-Inspired Network for Image Compressive Sensing](https://mlsanity.com/paper/2204.05503/) (2022)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [Deep Unfolding Network for Image Compressed Sensing by Content-adaptive Gradient Updating and Deformation-invariant Non-local Modeling](https://mlsanity.com/paper/2310.10033/) (2023)
- [An efficient deep convolutional laplacian pyramid architecture for CS reconstruction at low sampling ratios](https://mlsanity.com/paper/1804.04970/) (2018)
- [Adaptive Measurement Network for CS Image Reconstruction](https://mlsanity.com/paper/1710.01244/) (2017)

## Abstract (arXiv)

Recent deep unfolding networks (DUNs) have advanced Compressive Sensing (CS) by effectively integrating iterative optimization with deep learning architectures. However, most CS approaches predominantly confine their inference to a single solution space, neglecting the inherent ill-posedness of CS problems that intrinsically permits multiple plausible candidate hypotheses. In this paper, a novel Multi-Hypothesis Collaborative Deep Unfolding CS Network (MHC-DUN) is proposed, which explicitly models and leverages multiple hypotheses by jointly optimizing across diverse solution spaces. Specifically, following the Proximal Gradient Descent algorithm, MHC-DUN jointly performs gradient descent and proximal mapping within this multi-hypothesis paradigm. i) For gradient descent, a well-designed AlphaNet is introduced to dynamically predict spatially varying step sizes for all hypotheses, enabling collaborative gradient updates across multiple solutions. ii) For proximal operator, a sophisticated multi-hypothesis collaborative proximal mapping module is designed, which leverages both intra-hypothesis and inter-hypothesis correlation priors to jointly refine multiple solutions. To enable end-to-end training, a novel composite loss function is designed, which balances measurement fidelity, hypothesis diversity, and reconstruction accuracy, encouraging exploration of complementary solutions while maintaining reconstruction fidelity. Experimental results reveal that the proposed CS method outperforms existing CS networks.