Rank-One Measurements of Low-Rank PSD Matrices Have Small Feasible Sets
T. Mitchell Roddenberry,
Santiago Segarra,
Anastasios Kyrillidis
Abstract:We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one projections of an approximately low-rank PSD matrix, we characterize the radius of the set of PSD matrices that satisfy the measurements. This result yields a sampling rate to guarantee singleton solution sets when the true matrix is exactly low-rank, such that the choice of the ob… Show more
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