L_p-norm minimization for stochastic process power spectrum estimation subject to incomplete data

verfasst von

Yuanjin Zhang, Liam Comerford, Ioannis A. Kougioumtzoglou, Michael Beer

Abstract

A general L_p norm (0<p≤1) minimization approach is proposed for estimating stochastic process power spectra subject to realizations with incomplete/missing data. Specifically, relying on the assumption that the recorded incomplete data exhibit a significant degree of sparsity in a given domain, employing appropriate Fourier and wavelet bases, and focusing on the L₁ and L_1/2 norms, it is shown that the approach can satisfactorily estimate the spectral content of the underlying process. Further, the accuracy of the approach is significantly enhanced by utilizing an adaptive basis re-weighting scheme. Finally, the effect of the chosen norm on the power spectrum estimation error is investigated, and it is shown that the L_1/2 norm provides almost always a sparser solution than the L₁ norm. Numerical examples consider several stationary, non-stationary, and multi-dimensional processes for demonstrating the accuracy and robustness of the approach, even in cases of up to 80% missing data.

Organisationseinheit(en)

Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

The University of Liverpool
Tongji University
Columbia University

Typ

Artikel

Journal

Mechanical Systems and Signal Processing

Band

101

Seiten

361-376

Anzahl der Seiten

16

ISSN

0888-3270

Publikationsdatum

15.02.2018

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Steuerungs- und Systemtechnik, Signalverarbeitung, Tief- und Ingenieurbau, Luft- und Raumfahrttechnik, Maschinenbau, Angewandte Informatik

Elektronische Version(en)

https://www.sciencedirect.com/science/article/am/pii/S0888327017304430 (Zugang: Offen)
https://doi.org/10.1016/j.ymssp.2017.08.017 (Zugang: Geschlossen)