Nonlocal Patch-Based Fully Connected Tensor Network Decomposition for Multispectral Image Inpainting

Multispectral image (MSI) inpainting plays an important role in real applications. Recently, fully connected tensor network (FCTN) decomposition has been shown the remarkable ability to fully characterize global correlation. Considering global correlation and nonlocal self-similarity (NSS) of MSIs, this letter introduces FCTN decomposition to the whole MSI and its NSS groups and proposes a novel nonlocal patch-based FCTN (NL-FCTN) decomposition for MSI inpainting. More specially, the NL-FCTN decomposition-based method, which increases tensor order by stacking similar small-sized patches to NSS groups, cleverly leverages the remarkable ability of FCTN decomposition to deal with higher-order tensors. Besides, we propose an efficient proximal alternating minimization (PAM)-based algorithm to solve the proposed NL-FCTN decomposition-based model with a theoretical convergence guarantee. Extensive experiments on MSIs demonstrate that the proposed method achieves the state-of-the-art inpainting performance among all compared methods.