Graphical Models Concepts in Compressed Sensing

Details Graphical Models Concepts in Compressed Sensing Graphical Models Concepts in Compressed Sensing

2010-11-18

arxiv.org/abs/1011.4328v3

Computer Science

Information Theory

43 pages, 22 eps figures, typos corrected

Scientific paper

This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via ell_1 penalized least-squares (known as LASSO or BPDN). We discuss how to derive fast approximate message passing algorithms to solve this problem. Surprisingly, the analysis of such algorithms allows to prove exact high-dimensional limit results for the LASSO risk. This paper will appear as a chapter in a book on `Compressed Sensing' edited by Yonina Eldar and Gitta Kutyniok.

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