TY - GEN
T1 - Fundamental limits for support recovery of tree-sparse signals from noisy compressive samples
AU - Soni, Akshay
AU - Haupt, Jarvis
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84897731189&partnerID=8YFLogxK
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U2 - 10.1109/GlobalSIP.2013.6737052
DO - 10.1109/GlobalSIP.2013.6737052
M3 - Conference contribution
AN - SCOPUS:84897731189
SN - 9781479902484
T3 - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
SP - 961
EP - 964
BT - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
T2 - 2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013
Y2 - 3 December 2013 through 5 December 2013
ER -