Low-rank matrix completion in a general non-orthogonal basis

This paper considers theoretical analysis of recovering a low rank matrix given few expansion coefficients with respect to any basis. The current approach generalizes the existing for low-rank completion problem sampling under entry sensing or symmetric orthonormal is based on dual certificates using basis approach. We introduce condition called correlation condition. can be computed in time O ( n 3 ) and holds many cases deterministic If underlying obeys coherence parameter ? , additional mild assumptions, our main result shows that true recovered very high probability from r log 2 ? uniformly random coefficients.