Non-local Patch-based Low-rank Tensor Ring Completion for Visual Data.

Tensor completion is the problem of estimating the missing entries of a partially observed tensor with a certain low-rank structure. It improves on matrix completion for image and video data by capturing additional structural information intrinsic to such data. % With more inherent information involving in tensor structure than matrix, tensor completion has shown better performance compared with matrix completion especially in image and video data. Traditional completion algorithms treat the entire visual data as a tensor, which may not always work well especially when camera or object motion exists. In this paper, we develop a novel non-local patch-based tensor ring completion algorithm. In the proposed approach, similar patches are extracted for each reference patch along both the spatial and temporal domains of the visual data. The collected patches are then formed into a high-order tensor and a tensor ring completion algorithm is proposed to recover the completed tensor. A novel interval sampling-based block matching (ISBM) strategy and a hybrid completion strategy are also proposed to improve efficiency and accuracy. Further, we develop an online patch-based completion algorithm to deal with streaming video data. An efficient online tensor ring completion algorithm is proposed to reduce the time cost. Extensive experimental results demonstrate the superior performance of the proposed algorithms compared with state-of-the-art methods.