# Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction

@article{Barbier2012CompressedSO, title={Compressed sensing of approximately-sparse signals: Phase transitions and optimal reconstruction}, author={Jean Barbier and F. Krzakala and M. M{\'e}zard and L. Zdeborov{\'a}}, journal={2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)}, year={2012}, pages={800-807} }

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only “approximately sparse”, i.e. even though the signal contains only a small fraction of relevant (large) components the other components are not strictly equal to zero, but are only close to zero. In this paper we model the approximately sparse signal with a Gaussian distribution of small components, and we study its compressed sensing with dense random matrices. We… Expand

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