Low tubal rank tensor recovery using the Bürer-Monteiro factorisation approach. Application to optical coherence tomography

Abstract

In this paper, we study the low-tubal-rank tensor completion problem, i.e., the problem of recovering a third-order tensor by observing a subset of its entries, when these entries are selected uniformly at random. We propose a mathematical analysis of an extension of the Bürer-Monteiro factorisation approach to this problem. We then illustrate the use of the Bürer-Monteiro approach on a challenging OCT reconstruction problem on both synthetic and real world data, using an alternating minimisation algorithm.