Sparsity Maximization under a Quadratic Constraint with Applications in Filter Design
Name
Wei-2010-Sparsity Maximization under a Quadratic Constraint with Applications in Filter Design.pdf
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228.29 KB
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Adobe PDF
Checksum (MD5)
353954213fc16180a6ca1b91ab51cae6
Author(s)
Wei, Dennis
Oppenheim, Alan V.
Date Issued
June 2010
Journal
IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2010
Publisher
Institute of Electrical and Electronics Engineers
Citation
Wei, D., and A.V. Oppenheim. “Sparsity maximization under a quadratic constraint with applications in filter design.” Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on. 2010. 3686-3689. ©2010 Institute of Electrical and Electronics Engineers.
Version
Final published version
Abstract
This paper considers two problems in sparse filter design, the first involving a least-squares constraint on the frequency response, and the second a constraint on signal-to-noise ratio relevant to signal detection. It is shown that both problems can be recast as the minimization of the number of non-zero elements in a vector subject to a quadratic constraint. A solution is obtained for the case in which the matrix in the quadratic constraint is diagonal. For the more difficult non-diagonal case, a relaxation based on the substitution of a diagonal matrix is developed. Numerical simulations show that this diagonal relaxation is tighter than a linear relaxation under a wide range of conditions. The diagonal relaxation is therefore a promising candidate for inclusion in branch-and-bound algorithms.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ICASSP.2010.5495892
