Baseline spectrum estimation using half-quadratic minimization

In this paper, we propose a method to estimate the spectrum baseline. Basically, it consists in finding a low-order polynomial that minimizes the non-quadratic cost function. The optimization problem is solved using half-quadratic minimization. Two different cost functions are considered: firstly, the hyperbolic function which can be minimized using the algorithm ARTUR; secondly, the asymmetric truncated quadratic, which is minimized with the algorithm LEGEND. The latter gives the best results. This can be attributed to its asymmetric shape and its constant part for high positive values, making it better adapted to the problem than the hyperbolic function. The performances of these approaches are illustrated both on a real and simulated spectra and the choice of the hyperparameters is also discussed.