High-Dimensional Matched Subspace Detection When Data are Missing

Laura Balzano; Bejamin Recht; Robert Nowak

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arXiv · 1002.0852

High-Dimensional Matched Subspace Detection When Data are Missing

Laura Balzano·Bejamin Recht·Robert Nowak

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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.

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Laura Balzano, Bejamin Recht, Robert Nowak. 2011-01-21. High-Dimensional Matched Subspace Detection When Data are Missing. https://arxiv.org/abs/1002.0852

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