Enhanced Low-Rank and Sparse Tucker Decomposition For Image Completion

Recent advancements in low-rank tensor measures have addressed tensor completion challenges, particularly in image completion (IC) tasks. However, the most current low rankness is often based on the unfolding matrix's rank summation. Moreover, it ignores the local similarity or adapts over-smoothed regularization to the image data, which could be unreliable in high-level corruption recovery. This paper proposes a novel Tucker-based model to consider global and local information in imaging. Specifically, the weighted factor matrix rank and core tensor sparsity are used to encode the global low rankness, while graph regularization is employed to characterize the local similarity. This paper proposes a linearized alternating direction method (LADM) with easy subproblems for solving the IC task. Extensive experiments demonstrate the accuracy of our proposal, even under extreme cases, such as 99% missing scenario.