Self representation based methods for tensor completion problem

Tensor, the higher-order data array, naturally arises in many fields, such as information sciences, seismic data reconstruction, physics, video inpainting and so on. In this paper, we intend to provide a new model to recover a tensor, based on self-representation, for the all-mode unfoldings of the desired tensor, regardless of the tensor rank. The suggested idea generalizes self-representation to tensor and recovers an incomplete tensor by reconstructing one fiber by others in such a way that they all belong to the same subspace. We design least-square and low-rank self-representation algorithms based on the Linearized Alternating Direction Method utilizing this concept. We show that the proposed algorithms converge to the rank-minimization of the incomplete tensor.