Physics-guided Deep Unfolding Network for Enhanced Kronecker Compressive sensing

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.