Stable low-rank matrix recovery via null space properties

• Published in: Information and inference Vol. 5; no. 4; pp. 405 - 441
• Main Authors: Kabanava, Maryia, Kueng, Richard, Rauhut, Holger, Terstiege, Ulrich
• Format: Journal Article
• Language: English
• Published: Oxford University Press 01.12.2016
• Subjects: low-rank matrix recovery; positive semidefinite least squares problem; phase retrieval; convex optimization; complex projective designs; nuclear norm minimization; random measurements; quantum state tomography

The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modelled probabilistically. We derive sufficient conditions on the minimal amount...