Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation

Jarvis Haupt; Rui Castro; Robert Nowak

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arXiv · 1001.5311

Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation

Jarvis Haupt·Rui Castro·Robert Nowak

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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.

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BibTeX RIS

Jarvis Haupt, Rui Castro, Robert Nowak. 2010-05-27. Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation. https://arxiv.org/abs/1001.5311

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