Physics-guided Deep Unfolding Network for Enhanced Kronecker Compressive sensing

2025-08-13

AI Summary

To address low-fidelity reconstructions in compressive sensing (CS) for images—caused by measurement incoherence and the absence of explicit measurement representation during reconstruction—this paper proposes MEUNet, a physics-guided deep unfolding network. Methodologically: (i) we design an asymmetric Kronecker CS model to enhance measurement incoherence; (ii) we introduce a measurement-aware cross-attention mechanism within an explicit gradient-descent framework to learn robust implicit representations. By integrating Kronecker tensor products, deep unfolding architecture, and attention-based modeling, MEUNet achieves measurement-enhanced reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that MEUNet achieves state-of-the-art reconstruction accuracy (PSNR/SSIM) with significantly fewer parameters and faster inference speed than leading CS methods.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements

Abstract

Deep networks have achieved remarkable success in image compressed sensing (CS) task, namely reconstructing a high-fidelity image from its compressed measurement. However, existing works are deficient inincoherent compressed measurement at sensing phase and implicit measurement representations at reconstruction phase, limiting the overall performance. In this work, we answer two questions: 1) how to improve the measurement incoherence for decreasing the ill-posedness; 2) how to learn informative representations from measurements. To this end, we propose a novel asymmetric Kronecker CS (AKCS) model and theoretically present its better incoherence than previous Kronecker CS with minimal complexity increase. Moreover, we reveal that the unfolding networks' superiority over non-unfolding ones result from sufficient gradient descents, called explicit measurement representations. We propose a measurement-aware cross attention (MACA) mechanism to learn implicit measurement representations. We integrate AKCS and MACA into widely-used unfolding architecture to get a measurement-enhanced unfolding network (MEUNet). Extensive experiences demonstrate that our MEUNet achieves state-of-the-art performance in reconstruction accuracy and inference speed.

Problem

• Improve measurement incoherence to reduce ill-posedness in compressed sensing
• Learn informative representations from compressed measurements effectively
• Enhance reconstruction accuracy and speed in image compressed sensing

Innovation

• Asymmetric Kronecker CS model enhances incoherence
• Measurement-aware cross attention learns representations
• MEUNet integrates AKCS and MACA for performance