Tensor Versus Matrix Completion: A Comparison With Application to Spectral Data

Tensor completion recently emerged as a generalization of matrix completion for higher order arrays. This problem formulation allows one to exploit the structure of data that intrinsically have multiple dimensions. In this work, we recall a convex formulation for minimum (multilinear) ranks completion of arrays of arbitrary order. Successively we focus on completion of partially observed spectral images; the latter can be naturally represented as third order tensors and typically exhibit intraband correlations. We compare different convex formulations and assess them through case studies.