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

Andersson, Fredrik and Carlsson, Marcus and Wendt, Herwig On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters. (2016) In: 24th European Signal Processing Conference (EUSIPCO 2016), 29 August 2016 - 2 September 2016 (Budapest, Hungary).

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Official URL: http://dx.doi.org/10.1109/EUSIPCO.2016.7760263


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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of EUSIPCO 2016 Electronic ISBN: 978-0-9928-6265-7 The original PDF is available at: http://ieeexplore.ieee.org/document/7760263/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01447346
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Lund University (SWEDEN)
Laboratory name:
Deposited On:17 Jan 2017 14:48

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