Stable signal recovery from incomplete observations

Emmanuel Candes; Justin Romberg

doi:10.1117/12.620143

17 September 2005 Stable signal recovery from incomplete observations

Emmanuel Candes, Justin Romberg

Proceedings Volume 5914, Wavelets XI; 59140S (2005) https://doi.org/10.1117/12.620143
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

A widespread problem in the applied sciences is to recover an object of interest from a limited number of measurements. Recently, a series of exciting results have shown that it is possible to recover sparse (or approximately sparse) signals with high accuracy from a surprisingly small number of such measurements. The recovery procedure consists of solving a tractable convex program. Moreover, the procedure is robust to measurement error; adding a perturbation of size ε to the measurements will not induce a recovery error of more than a small constant times ε. In this paper, we will briefly overview these results, describe how stable recovery via convex optimization can be implemented in an efficient manner, and present some numerical results illustrating the practicality of the procedure.

Citation Download Citation

Emmanuel Candes and Justin Romberg "Stable signal recovery from incomplete observations", Proc. SPIE 5914, Wavelets XI, 59140S (17 September 2005); https://doi.org/10.1117/12.620143

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