Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction

Details Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction

2009-11-22

arxiv.org/abs/0911.4219v1

Computer Science

Information Theory

5 pages, IEEE Information Theory Workshop, Cairo 2010

Scientific paper

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP, for approximate message passing. This is the first of two conference papers describing the derivation of these algorithms, connection with the related literature, extensions of the original framework, and new empirical evidence. In particular, the present paper outlines the derivation of AMP from standard sum-product belief propagation, and its extension in several directions. We also discuss relations with formal calculations based on statistical mechanics methods.

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