<i>L_p</i>-norm minimization for stochastic process power spectrum estimation subject to incomplete data

Zhang, Yuanjin, Comerford, Liam, Kougioumtzoglou, Ioannis A and Beer, Michael ORCID: 0000-0002-0611-0345 (2018) <i>L_p</i>-norm minimization for stochastic process power spectrum estimation subject to incomplete data. MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 101. pp. 361-376.

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Abstract

A general Lp 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 L1/2 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 L1/2 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.

Item Type:	Article
Uncontrolled Keywords:	Norm minimization, Stochastic process, Evolutionary power spectrum, Missing data, Compressive sensing
Depositing User:	Symplectic Admin
Date Deposited:	17 Oct 2017 06:43
Last Modified:	05 Oct 2023 16:51
DOI:	10.1016/j.ymssp.2017.08.017
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3010237