Robust multi-subspace tensor dictionary learning for multi-temporal image reconstruction

Abstract Multi-temporal image reconstruction under cloud corruption is a profoundly ill-posed inverse problem. The existing low-rank regularization methods mainly rely on a single-subspace assumption, which inadequately captures the intrinsic structure of the multi-temporal image that inherently lies in a union of multiple tensor subspaces. To break this fundamental limitation, we propose a multi-subspace tensor dictionary learning model. The model learns a self-representation tensor dictionary to uncover the underlying multi-subspace structure of the image data. Moreover, a data-adaptive tensor nuclear norm is introduced to characterize the distinct low-rank properties of both the dictionary and the coefficient tensor. Compared to the single-subspace model, the proposed model provides a more promising regularization paradigm to exploit the complex tensor structures. An efficient proximal alternating minimization algorithm is developed to solve the resulting nonconvex optimization problem, with theoretical guarantees establishing convergence to a critical point. Experimental evaluations on multiple multi-temporal image datasets validate the advantages of the proposed method, demonstrating its efficacy and robustness as a regularization strategy for ill-posed multi-temporal inverse problems.