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Enhancing Prony’s method by nuclear norm penalization and extension to missing data

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Abstract

Prony’s method is a widely used method for modelling signals using a finite sum of exponential terms. It has innumerable applications in weather modelling, finance, medical signal analysis, image compression, time series analysis, power grids, etc. Prony’s method has, however, the reputation of being unstable with respect to noise perturbations. The goal of the present paper is to assess the potential improvements of a nuclear-norm-penalized regularization of Prony’s method. The nuclear norm regularization is a standard technique for improving the performance when processing noisy signals with low-rank underlying structure such as in matrix completion, matrix compressed sensing, hidden variable models. We consider both the standard setting and the case of missing data. We provide a fast estimation algorithm for the nuclear-norm-penalized least-squares minimization. Monte Carlo experiments show that regularization can significantly enhance the performance of Prony’s method with and without missing data.

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Notes

  1. Otherwise, replace r by \(r-1\) until this condition is satisfied.

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Acknowledgements

The research leading to this paper is part of the European Metrology Research Programme (EMRP), which is jointly funded by participating countries within EURAMET and the EU.

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Author notes

  1. Basad Al Sarray

    Present address: Computer Science Department, College of Science, University of Baghdad/Jadirya, 10071, Baghdad, Iraq

Authors and Affiliations

  1. Université de Franche Comté, 16 Route de Gray, 25030, Besançon, France

    Basad Al Sarray

  2. National Physical Laboratory, Hampton Road, Teddington, TW11 0LW, UK

    Stéphane Chrétien & Paul Clarkson

  3. Département Automatique Et Systèmes, Université de Franche Comté, Micro-Mécatroniques MINAROB, TEMIS, 24 R Alain Savary, 25000, Besançon, France

    Guillaume Cottez

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  1. Basad Al Sarray
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  2. Stéphane Chrétien
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  4. Guillaume Cottez
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Correspondence to Stéphane Chrétien.

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Sarray, B.A., Chrétien, S., Clarkson, P. et al. Enhancing Prony’s method by nuclear norm penalization and extension to missing data. SIViP 11, 1089–1096 (2017). https://doi.org/10.1007/s11760-017-1062-2

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  • DOI: https://doi.org/10.1007/s11760-017-1062-2

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