High-Dimensional Matched Subspace Detection When Data are Missing

Abstract

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.

References in corpus (1)

• Quantum state tomography via compressed sensing

Cited by in corpus (6)

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• Local Convergence of an Algorithm for Subspace Identification from Partial Data
• Tensor Matched Kronecker-Structured Subspace Detection for Missing Information