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

authored by

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.

Organisation(s)

Institute for Risk and Reliability

External Organisation(s)

University of Liverpool
Tongji University
Columbia University

Type

Article

Journal

Mechanical Systems and Signal Processing

Volume

101

Pages

361-376

No. of pages

16

ISSN

0888-3270

Publication date

15.02.2018

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications

Electronic version(s)

https://www.sciencedirect.com/science/article/am/pii/S0888327017304430 (Access: Open)
https://doi.org/10.1016/j.ymssp.2017.08.017 (Access: Closed)