Visual data completion via local sensitive low rank tensor learning

The problems of estimating missing values in visual data appear ubiquitously in computer vision applications including image inpainting, video inpainting, hyperspectral data recovery, and magnetic resonance imaging (MRI) data recovery. Recently, it is shown that tensor completion, which generalizes matrix completion to multiway data of higher order, could accurately estimate the overall data structure and achieves state-of-the-art performance for video completion. However, current tensor-based approaches implicitly assume that the partially observed video is globally low rank, which is too stringent for practical applications where the input video could include multiple heterogeneous episodes and the global correlation between frames is not high. To tackle this problem, we propose a novel local sensitive formulation of tensor learning where we assume instead that the video is inter-correlated in a local manner, leading to a representation of the observed tensor as a weighted sum of low-rank tensors. Computationally, we also design efficient scheme for solving the resulting learning problem based on the alternating direction method of multipliers (ADMM). Our experiments show improvements in prediction accuracy over classical approaches for visual data completion tasks.