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

2026-06-02

AI Summary

This work addresses the inherent ill-posedness of image compressive sensing, which admits multiple plausible solutions, yet existing deep unfolding methods typically recover only a single solution. To overcome this limitation, we propose the Multi-Hypothesis Collaborative Deep Unfolding Network (MHC-DUN), which explicitly models the multi-hypothesis solution space within a deep unfolding framework for the first time. Our approach employs AlphaNet to dynamically predict spatially adaptive step sizes and introduces a cross-hypothesis collaborative proximal mapping module to enable information exchange among hypotheses. Furthermore, we design a composite loss function that jointly optimizes measurement fidelity, reconstruction accuracy, and hypothesis diversity. Experimental results demonstrate that the proposed method significantly outperforms existing deep unfolding networks in both reconstruction quality and solution diversity.

Abstract

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.

Problem

• Compressive Sensing
• Ill-posedness
• Multi-hypothesis
• Image Reconstruction
• Deep Unfolding

Innovation

• Multi-Hypothesis
• Deep Unfolding Network
• Compressive Sensing
• Collaborative Optimization
• Proximal Mapping