2013 | OriginalPaper | Chapter
Search for Sparse Active Inputs: A Review
Author : Mikhail Malyutov
Published in: Information Theory, Combinatorics, and Search Theory
Publisher: Springer Berlin Heidelberg
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The theory of Compressed Sensing (highly popular in recent years) has a close relative that was developed around thirty years earlier and has been almost forgotten since – the design of screening experiments. For both problems, the main assumption is sparsity of active inputs, and the fundamental feature in both theories is the threshold phenomenon: reliable recovery of sparse active inputs is possible when the rate of design is less than the so-called capacity threshold, and impossible with higher rates.
Another close relative of both theories is
multi-access information transmission
. We survey a collection of tight and almost tight screening capacity bounds for both
adaptive
and
non-adaptive
strategies which correspond to either having or not having feedback in information transmission. These bounds are inspired by results from multi-access capacity theory. We also compare these bounds with the simulated performance of two analysis methods: (i) linear programming relaxation methods akin to basis pursuit used in compressed sensing, and (ii) greedy methods of low complexity for both non-adaptive and adaptive strategies.