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The task of reconstructing a low rank matrix from incomplete linearmeasurements arises in areas such as machine learning, quantum state tomographyand in the phase retrieval problem. In this note, we study the particular setupthat the measurements are taken with respect to rank one matrices constructedfrom the elements of a random tight frame. We consider a convex optimizationapproach and show both robustness of the reconstruction with respect to noiseon the measurements as well as stability with respect to passing toapproximately low rank matrices. This is achieved by establishing a version ofthe null space property of the corresponding measurement map.

Low-rank matrix recovery via rank one tight frame measurements