Keywords

Convergence, Least squares

Abstract

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of simulation results strongly confirming the utility of their approach, they did not rigorously establish the convergence properties of their algorithm. In this paper, we introduce prior information on the support of the sparse domain of the solution into the algorithm of Daubechies et al. We then provide a rigorous proof of the convergence of the resulting algorithm.

Notes

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Graduation Date

2011

Semester

Fall

Advisor

Li, Xin

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0004154

URL

http://purl.fcla.edu/fcla/etd/CFE0004154

Language

English

Release Date

December 2011

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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