Sparsity amplified

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The L1 norm is often used as a penalty function to obtain a sparse approximate solution to a system of linear equations, but it often underestimates the true values. This paper proposes a different type of penalty that (1) estimates sparse solutions more accurately and (2) maintains the convexity of the cost function. The new penalty is a multivariate generalization of the minimax-concave (MC) penalty. To define the generalized MC (GMC) penalty we first define a multivariate generalized Huber function. The resulting cost function can be minimized by proximal algorithms comprising simple computations. The effectiveness of the GMC penalty is illustrated in a denoising example.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4356-4360
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Fingerprint

Cost functions
Linear equations

Keywords

  • basis pursuit denoising
  • convex optimization
  • Sparse regularization
  • sparse-regularized linear least squares

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Selesnick, I. (2017). Sparsity amplified. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings (pp. 4356-4360). [7952979] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2017.7952979

Sparsity amplified. / Selesnick, Ivan.

2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. p. 4356-4360 7952979.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Selesnick, I 2017, Sparsity amplified. in 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings., 7952979, Institute of Electrical and Electronics Engineers Inc., pp. 4356-4360, 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017, New Orleans, United States, 3/5/17. https://doi.org/10.1109/ICASSP.2017.7952979
Selesnick I. Sparsity amplified. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 4356-4360. 7952979 https://doi.org/10.1109/ICASSP.2017.7952979
Selesnick, Ivan. / Sparsity amplified. 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 4356-4360
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