Low-Rank Tensor Ring Model for Completing Missing Visual Data

Low rank tensor factorization can be viewed as a higher order generalization of low-rank matrix factorization, both of which have been used for image and video representation and reconstruction from compressive measurements. In this paper, we present an algorithm for recovering low-rank tensors from massively under-sampled or missing data. We use low-rank tensor ring (TR) factorization to model images and videos. We observed that TR factorization models are robust to random missing entries but they fail in the cases when large blocks or slices of data are missing. We developed the following two types of algorithms to fill large missing blocks: An algorithm that incrementally updates the tensor rank and implicitly enforces correlations among different modes of the tensor. A framework to incorporate information about similarities between different modes of the tensor to enforce explicit similarity constraints between the missing and known parts of the tensors. We present simulation experiments on YaleB dataset to demonstrate the performance of our methods.