Distilled sensing: selective sampling for sparse signal recovery
Jarvis Haupt, Rui Castro, Robert Nowak; JMLR W&CP 5:216-223, 2009.
A selective sampling methodology called Distilled Sensing (DS) is proposed for recovering sparse signals in noise. DS exploits the fact that it is often easier to rule out locations that do not contain signal than it is to detect the locations of non-zero signal components. We formalize this observation and use it to devise a sequential selective sensing strategy that focuses sensing/measurement resources towards the signal subspace. This adaptivity in sensing results in rather surprising gains in sparse signal recovery compared to non-adaptive sensing. We show that exponentially weaker sparse signals can be recovered via DS compared with conventional non-adaptive sensing.