4,022 research outputs found
Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets
This paper investigates the problem of recovering the support of structured
signals via adaptive compressive sensing. We examine several classes of
structured support sets, and characterize the fundamental limits of accurately
recovering such sets through compressive measurements, while simultaneously
providing adaptive support recovery protocols that perform near optimally for
these classes. We show that by adaptively designing the sensing matrix we can
attain significant performance gains over non-adaptive protocols. These gains
arise from the fact that adaptive sensing can: (i) better mitigate the effects
of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor
Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation
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.Comment: 23 pages, 2 figures. Revision includes minor clarifications, along
with more illustrative experimental results (cf. Figure 2
- …