Regularized spectral analysis of unevenly spaced data

High resolution spectral analysis has recently been addressed as an inverse problem, and solutions are currently proposed through the regularization framework. In this paper, we focus on regularized spectral analysis of unevenly sampled data for line spectra estimation. First, we study the structural differences of the model between regular sampling, missing data (where the sampling is regular, but with missing data) and irregular sampling cases. Then, consequences for the computation of the solution are emphasized. We propose an approximation of the irregular sampling model to compute the nonquadratic regularization solution at a cost comparable to the other sampling cases. Finally, algorithmic implementation is discussed and applications to simulated data are presented.