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On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters

Andersson, Fredrik LU ; Carlsson, Marcus LU and Wendt, Herwig (2016) 24th European Signal Processing Conference, EUSIPCO 2016 In 2016 24th European Signal Processing Conference, EUSIPCO p.326-330
Abstract

We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this... (More)

We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this is the case.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Fixed-point algorithms, Low rank approximation, Structured matrices
in
2016 24th European Signal Processing Conference, EUSIPCO
pages
5 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
24th European Signal Processing Conference, EUSIPCO 2016
external identifiers
  • scopus:85006073740
ISBN
9780992862657
DOI
10.1109/EUSIPCO.2016.7760263
language
English
LU publication?
yes
id
8422e8c8-ce26-478c-9d59-5307dc14f42b
date added to LUP
2016-12-30 08:35:36
date last changed
2017-01-01 08:44:52
@inproceedings{8422e8c8-ce26-478c-9d59-5307dc14f42b,
  abstract     = {<p>We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this is the case.</p>},
  author       = {Andersson, Fredrik and Carlsson, Marcus and Wendt, Herwig},
  booktitle    = {2016 24th European Signal Processing Conference, EUSIPCO },
  isbn         = {9780992862657},
  keyword      = {Fixed-point algorithms,Low rank approximation,Structured matrices},
  language     = {eng},
  month        = {11},
  pages        = {326--330},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters},
  url          = {http://dx.doi.org/10.1109/EUSIPCO.2016.7760263},
  year         = {2016},
}