Relax-based estimation of Voigt lineshapes

Most spectroscopic signals are well described as having either a Lorentzian or Gaussian lineshape, and the recent literature contains a variety of estimation approaches for such models. However, several experimental works indicate that such signals can be better described as having the more general Voigt lineshape, formed as the combination of the two. Due to the inherent complexity of this model, there exist few techniques to form estimates of the parameters of the Voigt model, with a numerical search of the multidimensional nonlinear least squares (LS) cost function being the typical solution. In this paper, we propose a parametric relax-based estimator that estimates the lineshape parameters recursively, one spectral line at a time. Numerical simulations using both simulated and real measurement data illustrate the performance gain of the proposed methods.