PIU-CR: Physics-Informed Deep Unfolding Network with SAR-Optical Image Fusion for Cloud Removal

Multi-modal cloud removal exploits complementary optical and synthetic aperture radar (SAR) images to restore cloud-degraded remote sensing images. Most existing methods rely on black-box, data-driven architectures with limited interpretability of cross-modal interactions. Although some attempts introduce physical priors into networks, their oversimplified formulations fail to faithfully characterize the underlying physical imaging process and the networks remain loosely coupled with optimization variables. To address these issues, we propose a physics-informed deep unfolding network for cloud removal via optical-SAR image fusion, termed as PIU-CR. We first formulate cloud removal as a physics-informed optimization problem. Specifically, we fundamentally ground the optimization in the physical imaging mechanism of cloud degradation by embedding the atmospheric scattering model into data fidelity term. Then, the regularization terms establish an explicit cross-modal interaction mechanism, overcoming the single-modal information scarcity and the obscure, uninterpretable interactions in black-box models. They are dedicated to SAR-guided structure and spectral regularization, jointly introducing cross-modal structural feature alignment and coordinated spectral consistency constraints. The resulting optimization problem is then unfolded into a multi-stage neural network with dedicated structure and spectral branches. Each stage corresponds to explict optimization iteration step, enabling interpretable and effective reconstruction process. Experiments demonstrate that the proposed method outperforms state-of-the-art methods.