Patched-tube unitary transform for robust tensor completion

The aim of the robust tensor completion problem for third-order tensors is to recover a low-rank tensor from incomplete and/or corrupted observations. In this paper, we develop a patched-tubes unitary transform method for robust tensor completion. The proposed method is to extract similar patched-tubes to form a third-order sub-tensor, and then a transformed tensor singular value decomposition is employed to recover such low-rank incomplete and/or corrupted sub-tensor. Here the unitary transform matrix for transformed tensor singular value decomposition is constructed by using left singular vectors of the unfolding matrix arising from such sub-tensor. Moreover, we establish the perturbation results of the transformed tensor singular value decomposition for patched-tubes tensor completion. Extensive numerical experiments on hyperspectral, video and face data sets are presented to demonstrate the superior performance of the proposed patched-tubes unitary transform method over testing state-of-the-art robust tensor completion methods.