Details
| Original language | English |
|---|---|
| Pages (from-to) | 361-376 |
| Number of pages | 16 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 101 |
| Early online date | 23 Sept 2017 |
| Publication status | Published - 15 Feb 2018 |
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.
Keywords
- Compressive sensing, Evolutionary power spectrum, Missing data, Norm minimization, Stochastic process
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 101, 15.02.2018, p. 361-376.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lp-norm minimization for stochastic process power spectrum estimation subject to incomplete data
AU - Zhang, Yuanjin
AU - Comerford, Liam
AU - Kougioumtzoglou, Ioannis A.
AU - Beer, Michael
N1 - Funding Information: The first author gratefully acknowledges the financial support from China Scholarship Council. The third author gratefully acknowledges the support by the CMMI Division of the National Science Foundation , USA (Award number: 1724930 ).
PY - 2018/2/15
Y1 - 2018/2/15
N2 - A general Lp norm (01 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.
AB - A general Lp norm (01 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.
KW - Compressive sensing
KW - Evolutionary power spectrum
KW - Missing data
KW - Norm minimization
KW - Stochastic process
UR - http://www.scopus.com/inward/record.url?scp=85029715692&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2017.08.017
DO - 10.1016/j.ymssp.2017.08.017
M3 - Article
AN - SCOPUS:85029715692
VL - 101
SP - 361
EP - 376
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
ER -