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

## TL;DR

This paper studies the challenge of detecting signals that change over time using adaptive and non-adaptive sensing, providing theoretical insights and an adaptive algorithm for improved detection of evolving sparse signals.

## Contribution

It introduces a formal model for detecting dynamically changing sparse signals and proposes an adaptive sensing algorithm that outperforms non-adaptive methods.

## Key findings

- Adaptive sensing improves detection performance over non-adaptive methods.
- The difficulty of detection depends on the speed of signal component changes.
- The paper provides theoretical characterization of detection limits in both paradigms.

## 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 non-zero 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.