Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements

• Published in: IEEE transactions on information theory Vol. 57; no. 4; pp. 2342 - 2359
• Main Authors: Candès, Emmanuel J, Plan, Y
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Applied sciences; Compressed sensing; Convex optimization; Dantzig selector; Error correction & detection; Exact sciences and technology; Information processing; Information theory; Information, signal and communications theory; Linear matrix inequalities; Matrix; matrix completion; Measurement uncertainty; Minimization; Noise; Noise measurement; norm of random matrices; oracle inequalities and semidefinite programming; Sparse matrices; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Singularity; Isometry; oracle inequalities and semidefinite programming; matrix completion; Transmission protocol; Theoretical study; norm of random matrices; Dantzig selector; Constrained optimization; Linear combination; Convex optimization; Minimax method; Routing protocols; Oracle

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm minimization stably recovers a low-rank matrix from a constant number...