Tensor Completion via Nonlocal Tensor Wheel Decomposition for Hyperspectral Image Recovery

Tensor completion aims to recover original data from its degraded observations and has shown promise in processing incomplete hyperspectral images (HSIs). Many previous studies have indicated that global correlation and nonlocal self-similarity (NSS) are two important priors for tensor completion. Recently, tensor wheel (TW) decomposition has demonstrated excellent performance in the tensor completion problem. However, it overlooks NSS. To address this limitation, a novel nonlocal TW (NL-TW) decomposition-based method is presented for tensor completion, which leverages both the aforementioned priors. The method consists of two main steps. In the first step, we introduce TW decomposition to the entire degraded tensor to generate an initial completion result. In the second step, similar patches in the initial completion result are first stacked into NSS groups, and TW decomposition is then applied to each grouped tensor to obtain the final completion result. In addition, the NL-TW decomposition-based tensor completion method is solved by a proximal alternating minimization (PAM)-based optimization algorithm, which has a theoretical convergence guarantee. Extensive experiments on three real datasets with different sampling rates (SRs) demonstrate the effectiveness of the proposed NL-TW method compared with other methods.