Thick Cloud Removal in Multitemporal Remote Sensing Images via Sobel-Consistency and Subspace-Based Spatiospectral Low-Rank Tensor Regularization

Thick cloud removal is a critical preprocessing step for multitemporal remote sensing images (MTRSIs), as it directly determines the reliability of downstream analysis and applications. In MTRSIs, the same geographic region is observed at different times, and the underlying edge structures often remain physically consistent across temporal observations. Leveraging this intrinsic property, we introduce a Sobel-consistent term that explicitly enforces temporal consistency of edge-related features, thereby improving the reconstruction of fine structures and textures in cloud-obscured regions. Building on this insight, we propose a novel thick cloud removal model that integrates Sobel-based edge consistency with subspace-based spatiospectral low-rank tensor regularization. In this model, intrinsic images derived from subspace representation are organized into a fourth-order tensor, and low-rank constraints are applied to jointly capture the spatial, spectral, and temporal correlations inherent in MTRSIs. To efficiently solve the resulting optimization problem, we introduce an algorithm based on proximal alternating minimization. Experiments on both simulated and real-world MTRSI datasets demonstrate that the proposed method achieves superior reconstruction accuracy and visual fidelity, validating the physical interpretability and effectiveness of the approach.