Fundamental limits for support recovery of tree-sparse signals from noisy compressive samples

Akshay Soni, Jarvis Haupt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a sparse representation in some basis. Subsequent efforts have shown that the performance of CS can be improved by exploiting structure in the locations of the nonzero signal coefficients during inference, or by utilizing some form of data-dependent adaptive measurement scheme during the sensing process. Our previous work established that an adaptive sensing strategy specifically tailored to signals that are tree-sparse can significantly outperform adaptive and non-adaptive sensing strategies that are agnostic to the underlying structure in noisy support recovery tasks. In this paper we establish corresponding fundamental performance limits for these support recovery tasks, in settings where measurements may be obtained either non-adaptively (using a randomized Gaussian measurement strategy motivated by initial CS investigations) or by any adaptive sensing strategy. Our main results here imply that the adaptive tree sensing procedure analyzed in our previous work is nearly optimal, in the sense that no other sensing and estimation strategy can perform fundamentally better for identifying the support of tree-sparse signals.

Original languageEnglish (US)
Title of host publication2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
Pages961-964
Number of pages4
DOIs
StatePublished - 2013
Event2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Austin, TX, United States
Duration: Dec 3 2013Dec 5 2013

Publication series

Name2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings

Other

Other2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013
CountryUnited States
CityAustin, TX
Period12/3/1312/5/13

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