Sparsity Maximization under a Quadratic Constraint with Applications in Filter Design
Author(s)Wei, Dennis; Oppenheim, Alan V.
DownloadWei-2010-Sparsity Maximization under a Quadratic Constraint with Applications in Filter Design.pdf (228.2Kb)
MetadataShow full item record
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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2010
Institute of Electrical and Electronics Engineers
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.
Final published version
INSPEC Accession Number: 11540848