Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging

2025-05-29

AI Summary

In single-pixel imaging (SPI) inverse problems, plug-and-play (PnP) methods suffer from accuracy–speed trade-offs, while deep unrolling methods lack generalization across compression ratios (CRs). To resolve this, we propose a CR-agnostic universal deep unrolling framework. Our key contributions are: (1) a universal proximal trajectory (PT) loss that guides the deep image reconstructor to approximate the proximal operator of an ideal regularizer; (2) the first decoupled HQ/ADMM-based unrolling architecture, enabling unified modeling and inference across arbitrary CRs; and (3) zero-shot adaptability to unseen CRs without retraining. Experiments demonstrate that our method achieves superior reconstruction accuracy and inference speed compared to existing CR-specific unrolled networks, while preserving PnP-style flexibility. The source code and pre-trained models are publicly available.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Multimodal Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Deep-unrolling and plug-and-play (PnP) approaches have become the de-facto standard solvers for single-pixel imaging (SPI) inverse problem. PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll.

Problem

• Combining strengths of deep-unrolling and plug-and-play for SPI reconstruction
• Improving flexibility for varying compression ratios without retraining
• Enhancing reconstruction accuracy and speed in single-pixel imaging

Innovation

• Deep-unrolling and plug-and-play for SPI
• Proximal trajectory loss for training
• Flexible CR handling with single model