High-Dimensional Matched Subspace Detection When Data are Missing

We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, wellstudied problem when the signal is completely observed. Highdimensional testing problems in which it may be prohibitive or impossible to obtain a complete observation motivate this work. The signal is represented as a vector in Rn , but we only observe m n of its elements. We show that reliable detection is possible, under mild incoherence conditions, as long as m is slightly greater than the dimension of the subspace in question.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Laura Balzano, Benjamin Recht, Robert Nowak
• Keywords: Complete Observation, CORR 2010, Education, Incomplete Signal, Subspace Detection