  We consider the problem of deciding whether a highly incomplete signal lies
within a given subspace. This problem, Matched Subspace Detection, is a
classical, well-studied problem when the signal is completely observed. High-
dimensional 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 R^n, 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.
