DocumentCode :
2916591
Title :
A uniform uncertainty principle for Gaussian circulant matrices
Author :
Romberg, Justin
Author_Institution :
Sch. of Elec. & Comp. Eng., Georgia Tech, Atlanta, GA, USA
fYear :
2009
fDate :
5-7 July 2009
Firstpage :
1
Lastpage :
5
Abstract :
This paper considers the problem of estimating a discrete signal from its convolution with a pulse consisting of a sequence of independent and identically distributed Gaussian random variables. We derive lower bounds on the length of a random pulse needed to stably reconstruct a signal supported on [1, n]. We will show that a general signal can be stably recovered from convolution with a pulse of length m gsim n log5 n, and a sparse signal which can be closely approximated using s lsim n/log5 n terms can be stably recovered with a pulse of length n.
Keywords :
Gaussian processes; convolution; matrix algebra; signal reconstruction; Gaussian circulant matrices; convolution; discrete signal; distributed Gaussian random variables; signal reconstruction; sparse signal; uniform uncertainty principle; Channel estimation; Convolution; Digital communication; Image reconstruction; Inverse problems; Radar applications; Radar signal processing; Random variables; Signal processing; Uncertainty;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Digital Signal Processing, 2009 16th International Conference on
Conference_Location :
Santorini-Hellas
Print_ISBN :
978-1-4244-3297-4
Electronic_ISBN :
978-1-4244-3298-1
Type :
conf
DOI :
10.1109/ICDSP.2009.5201083
Filename :
5201083
Link To Document :
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