Tensor Completion with Shift-invariant Cosine Bases

Abstract

In this study, we discuss a technique of tensor completion using multi-way delay-embedding, which is an emerging framework for the tensor completion problem. This consists of simple three steps: (1) multi-way delay-embedding transform (MDT) of the input incomplete tensor, (2) completing the transformed high-order tensor, (3) inverse MDT of the completed high-order tensor. In spite of the simplicity, it can be used as a powerful tool for recovering the missing elements and slices of tensors. In this paper, we propose an improvement method for MDT based tensor completion by exploiting a common phenomenon that the most real signals are commonly having Fourier bases as shift-invariant features in its auto-correlation matrix. By considering the cosine bases in high-order tensor, several factor matrices in the low-rank tensor decomposition problem can be automatically decided. The experimental results show the advantages of the proposed method.