TY - GEN
T1 - Improved bounds for sparse recovery from adaptive measurements
AU - Haupt, Jarvis
AU - Castro, Rui
AU - Nowak, Robert
PY - 2010
Y1 - 2010
N2 - It is shown here that adaptivity in sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. An adaptive sampling-and-refinement procedure called distilled sensing is discussed and analyzed, resulting in fundamental new asymptotic scaling relationships in terms of the minimum feature strength required for reliable signal detection or localization (support recovery). In particular, reliable detection and localization using non-adaptive samples is possible only if the feature strength grows logarithmically in the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the feature strength exceeds a constant, and localization is possible when the feature strength exceeds any (arbitrarily slowly) growing function of the problem dimension.
AB - It is shown here that adaptivity in sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. An adaptive sampling-and-refinement procedure called distilled sensing is discussed and analyzed, resulting in fundamental new asymptotic scaling relationships in terms of the minimum feature strength required for reliable signal detection or localization (support recovery). In particular, reliable detection and localization using non-adaptive samples is possible only if the feature strength grows logarithmically in the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the feature strength exceeds a constant, and localization is possible when the feature strength exceeds any (arbitrarily slowly) growing function of the problem dimension.
UR - http://www.scopus.com/inward/record.url?scp=77955671530&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2010.5513489
DO - 10.1109/ISIT.2010.5513489
M3 - Conference contribution
AN - SCOPUS:77955671530
SN - 9781424469604
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1563
EP - 1567
BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010
Y2 - 13 June 2010 through 18 June 2010
ER -