Convex fused lasso denoising with non-convex regularization and its use for pulse detection

Ankit Parekh, Ivan W. Selesnick

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

Abstract

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation. Originally, the 1 norm was used as a sparsity-inducing convex penalty function for the fused lasso signal approximation problem. However, the 1 norm underestimates signal values. Non-convex sparsity-inducing penalty functions better estimate signal values. In this paper, we show how to ensure the convexity of the fused lasso signal approximation problem with non-convex penalty functions. We further derive a computationally efficient algorithm using the majorization-minimization technique. We apply the proposed fused lasso method for the detection of pulses.

Original languageEnglish (US)
Title of host publication2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Print)9781509013500
DOIs
StatePublished - Feb 11 2016
EventIEEE Signal Processing in Medicine and Biology Symposium - Philadelphia, United States
Duration: Dec 12 2015 → …

Conference

ConferenceIEEE Signal Processing in Medicine and Biology Symposium
CountryUnited States
CityPhiladelphia
Period12/12/15 → …

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Observation
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Keywords

  • fused lasso
  • non-convex regularization
  • pulse detection
  • Sparse signal
  • total variation denoising

ASJC Scopus subject areas

  • Biomedical Engineering
  • Signal Processing
  • Radiology Nuclear Medicine and imaging
  • Health Informatics

Cite this

Parekh, A., & Selesnick, I. W. (2016). Convex fused lasso denoising with non-convex regularization and its use for pulse detection. In 2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings [7405474] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SPMB.2015.7405474

Convex fused lasso denoising with non-convex regularization and its use for pulse detection. / Parekh, Ankit; Selesnick, Ivan W.

2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2016. 7405474.

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

Parekh, A & Selesnick, IW 2016, Convex fused lasso denoising with non-convex regularization and its use for pulse detection. in 2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings., 7405474, Institute of Electrical and Electronics Engineers Inc., IEEE Signal Processing in Medicine and Biology Symposium, Philadelphia, United States, 12/12/15. https://doi.org/10.1109/SPMB.2015.7405474
Parekh A, Selesnick IW. Convex fused lasso denoising with non-convex regularization and its use for pulse detection. In 2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2016. 7405474 https://doi.org/10.1109/SPMB.2015.7405474
Parekh, Ankit ; Selesnick, Ivan W. / Convex fused lasso denoising with non-convex regularization and its use for pulse detection. 2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2016.
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