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

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 L-1 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 L-1 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. (C) 2017 Elsevier Ltd. All rights reserved.