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Iteratively Reweighted Least Squares Minimization with Prior Information: A New Approach

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Date Issued:
2011
Abstract/Description:
Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1-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.
Title: Iteratively Reweighted Least Squares Minimization with Prior Information: A New Approach.
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Name(s): Popov, Dmitriy, Author
Li, Xin, Committee Chair
Moore, Brian, Committee Member
Mikusinski, Piotr, Committee Member
, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2011
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1-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.
Identifier: CFE0004154 (IID), ucf:49082 (fedora)
Note(s): 2011-12-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): iteratively reweighted least squares -- prior information -- convergence
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0004154
Restrictions on Access: public 2011-12-15
Host Institution: UCF

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