Bernoulli

  • Bernoulli
  • Volume 25, Number 2 (2019), 977-1012.

Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals

Rui M. Castro and Ervin Tánczos

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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.

Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 977-1012.

Dates
Received: February 2017
Revised: November 2017
First available in Project Euclid: 6 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1551862841

Digital Object Identifier
doi:10.3150/17-BEJ1010

Mathematical Reviews number (MathSciNet)
MR3920363

Zentralblatt MATH identifier
07049397

Keywords
adaptive sensing dynamically evolving signals sequential experimental design sparse signals

Citation

Castro, Rui M.; Tánczos, Ervin. Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals. Bernoulli 25 (2019), no. 2, 977--1012. doi:10.3150/17-BEJ1010. https://projecteuclid.org/euclid.bj/1551862841


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