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May 2019 Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals
Rui M. Castro, Ervin Tánczos
Bernoulli 25(2): 977-1012 (May 2019). DOI: 10.3150/17-BEJ1010

Abstract

In this paper, we investigate the problem of detecting dynamically evolving signals. We model the signal as an $n$ dimensional vector that is either zero or has $s$ non-zero components. At each time step $t\in\mathbb{N}$ the nonzero components change their location independently with probability $p$. The statistical problem is to decide whether the signal is a zero vector or in fact it has non-zero components. This decision is based on $m$ noisy observations of individual signal components collected at times $t=1,\ldots,m$. We consider two different sensing paradigms, namely adaptive and non-adaptive sensing. For non-adaptive sensing, the choice of components to measure has to be decided before the data collection process started, while for adaptive sensing one can adjust the sensing process based on observations collected earlier. We characterize the difficulty of this detection problem in both sensing paradigms in terms of the aforementioned parameters, with special interest to the speed of change of the active components. In addition, we provide an adaptive sensing algorithm for this problem and contrast its performance to that of non-adaptive detection algorithms.

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Rui M. Castro. Ervin Tánczos. "Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals." Bernoulli 25 (2) 977 - 1012, May 2019. https://doi.org/10.3150/17-BEJ1010

Information

Received: 1 February 2017; Revised: 1 November 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049397
MathSciNet: MR3920363
Digital Object Identifier: 10.3150/17-BEJ1010

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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