Breaking Measurement Barriers: From Compressed Sensing to Deep Reconstruction

Abstract

Deep learning methods have achieved remarkable success in image compressed sensing (CS) task, namely reconstructing a high-fidelity image from its compressed measurement. However, existing methods are deficient in incoherent compressed measurement at sensing phase and implicit measurement representations at reconstruction phase, limiting the overall performance. In this work, we answer two questions: (i) how to improve the measurement incoherence for decreasing the ill-posedness; (ii) 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 increase of complexity. Moreover, apart from the explicit measurement representations in gradient descent projection in unfolding networks, we further propose a measurement-aware cross attention (MACA) mechanism to learn implicit measurement representations. We integrate AKCS and MACA into a widely-used unfolding architecture to get a measurement-enhanced unfolding network (MEUNet). Extensive experiments demonstrate that the proposed MEUNet achieves state-of-the-art (SOTA) performance in reconstruction accuracy with high efficiency.