Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation

TL;DR

This paper introduces Distilled Sensing, an adaptive sampling method that significantly improves the detection and localization of sparse signals in noise, surpassing the limitations of non-adaptive sampling.

Contribution

The paper proposes and analyzes Distilled Sensing, a multi-stage adaptive sampling technique that enables detection and localization of weaker signals than previously possible.

Findings

Adaptive sampling allows detection of signals with constant amplitude.

Localization is achievable when signal amplitude exceeds any slowly growing function of dimension.

Distilled Sensing outperforms non-adaptive methods in sparse signal recovery.

Abstract

Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of multi-stage experimental design and testing. Because of the adaptive nature of the data collection, DS can detect and localize far weaker signals than possible from non-adaptive measurements. In particular, reliable detection and localization (support estimation) using non-adaptive samples is possible only if the signal amplitudes grow logarithmically with the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the amplitude exceeds a constant, and localization is possible when the amplitude exceeds any arbitrarily slowly growing function of the dimension.