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

Mohamed Ibrahim Assoweh , Stéphane Chrétien , Brahim Tamadazte

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 chalenging OCT reconstruction problem on both synthetic and real world data, using an alternating minimisation algorithm.

Mots clés: Tensor completion; t-SVD; Low rank estimation; Bürer-Monteiro approach

Domaines: Statistiques [math.ST]

Mohamed Ibrahim Assoweh, Stéphane Chrétien, Brahim Tamadazte. Low tubal rank tensor recovery using the Bürer-Monteiro factorisation approach. Application to optical coherence tomography. Journal of Computational and Applied Mathematics, 2022. ⟨hal-03716332⟩