On the robustness of noise-blind low-rank recovery from rank-one measurements

We prove new results about the robustness of well-known convex noise-blind optimization formulations for reconstruction low-rank matrices from an underdetermined system random linear measurements. Specifically, our address Hermitian rank-one measurements as used in a version phase retrieval problem; that is, each measurement can be represented inner product unknown matrix and outer given realization standard complex Gaussian vector. obtain by establishing with high probability operator consisting independent realizations such exhibits so-called Schatten-1 quotient property, which corresponds to lower bound inradius their image nuclear norm (Schatten-1) unit ball. complement analysis numerical experiments comparing solutions noise-aware formulations. These confirm methods exhibit comparable