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.

Date Published: 17 September 2005
PDF: 6 pages
Proc. SPIE 5914, Wavelets XI, 59140S (17 September 2005); doi: 10.1117/12.620143

Published in SPIE Proceedings Vol. 5914:
Wavelets XI
Manos Papadakis; Andrew F. Laine; Michael A. Unser, Editor(s)