On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters
(2016) 24th European Signal Processing Conference, EUSIPCO 2016 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.
(Less)
- author
- Andersson, Fredrik LU ; Carlsson, Marcus LU and Wendt, Herwig
- organization
- publishing date
- 2016-11-28
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Fixed-point algorithms, Low rank approximation, Structured matrices
- host publication
- 2016 24th European Signal Processing Conference, EUSIPCO
- article number
- 7760263
- pages
- 5 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 24th European Signal Processing Conference, EUSIPCO 2016
- conference location
- Budapest, Hungary
- conference dates
- 2016-08-28 - 2016-09-02
- 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
- 2022-03-01 18:31:55
@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}}, keywords = {{Fixed-point algorithms; Low rank approximation; Structured matrices}}, language = {{eng}}, month = {{11}}, pages = {{326--330}}, publisher = {{IEEE - 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}}, doi = {{10.1109/EUSIPCO.2016.7760263}}, year = {{2016}}, }