Sparse estimation of spectroscopic signals

This work considers the semi-parametric estimation of sparse spectroscopic signals, aiming to form a detailed spectral representation of both the frequency content and the spectral line widths of the occurring signals. Extending on the recent FOCUSS-based SLIM algorithm, we propose an alternative prior for a Bayesian formulation of this sparse reconstruction method, exploiting a proposed suitable prior for the noise variance. Examining three common models for spectroscopic signals, the introduced technique allows for reliable estimation of the characteristics of these models. Numerical simulations illustrate the improved performance of the proposed technique.