Distilled sensing: Adaptive sampling for sparse detection and estimation

Jarvis Haupt, Rui M. Castro, Robert Nowak

Research output: Contribution to journalArticle

101 Scopus citations

Abstract

Adaptive sampling results in significant 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 multistage 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.

Original languageEnglish (US)
Article number6006586
Pages (from-to)6222-6235
Number of pages14
JournalIEEE Transactions on Information Theory
Volume57
Issue number9
DOIs
StatePublished - Sep 1 2011

Keywords

  • Adaptive sampling
  • experimental design
  • multiple hypothesis testing
  • sequential sensing
  • sparse recovery

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