Title: Moving Past Single-Point Inference: A Multi-Hypothesis Collaborative Deep Unfolding Framework for Image Compressive Sensing

Abstract:

Deep Unfolding Networks (DUNs) have recently propelled the field of Compressive Sensing (CS) forward by seamlessly merging iterative optimization techniques with deep learning structures. Nevertheless, the majority of current CS methodologies restrict their inference to a solitary solution space, thereby overlooking the fundamental ill-posed nature of CS problems, which naturally allows for various plausible candidate hypotheses. To address this limitation, we introduce a novel Multi-Hypothesis Collaborative Deep Unfolding CS Network (MHC-DUN). This framework explicitly captures and utilizes multiple hypotheses by jointly optimizing across a variety of solution spaces.

Grounded in the Proximal Gradient Descent algorithm, MHC-DUN executes both gradient descent and proximal mapping within this multi-hypothesis context. Specifically:

i) In the gradient descent phase, we introduce AlphaNet, a specially crafted network that dynamically forecasts spatially varying step sizes for every hypothesis. This mechanism facilitates collaborative gradient updates across the multiple solutions.

ii) For the proximal operator, we design an advanced multi-hypothesis collaborative proximal mapping module. This component exploits both intra-hypothesis and inter-hypothesis correlation priors to simultaneously refine the multiple solutions.

To facilitate end-to-end training, we formulate a new composite loss function. This function strikes a balance among measurement fidelity, hypothesis diversity, and reconstruction accuracy. It encourages the discovery of complementary solutions while ensuring high reconstruction fidelity. Our experimental findings demonstrate that the proposed CS method surpasses existing CS networks.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC