Compressive binary search

Mark A. Davenport; Ery Arias-Castro

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arXiv · 1202.0937

Compressive binary search

Mark A. Davenport·Ery Arias-Castro

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Abstract

In this paper we consider the problem of locating a nonzero entry in a high-dimensional vector from possibly adaptive linear measurements. We consider a recursive bisection method which we dub the compressive binary search and show that it improves on what any nonadaptive method can achieve. We also establish a non-asymptotic lower bound that applies to all methods, regardless of their computational complexity. Combined, these results show that the compressive binary search is within a double logarithmic factor of the optimal performance.

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Mark A. Davenport, Ery Arias-Castro. 2012-05-31. Compressive binary search. https://arxiv.org/abs/1202.0937

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