Compressive binary search
Information Theory
2012-06-01 v2 math.IT
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.
Cite
@article{arxiv.1202.0937,
title = {Compressive binary search},
author = {Mark A. Davenport and Ery Arias-Castro},
journal= {arXiv preprint arXiv:1202.0937},
year = {2012}
}