Background removal from spectra by designing and minimising a non-quadratic cost function

In this paper, the problem of estimating the background of a spectrum is addressed. We propose to fit this background to a low-order polynomial, but rather than determining the polynomial parameters that minimise a least-squares criterion (i.e. a quadratic cost function), non-quadratic cost functions well adapted to the problem are proposed. To minimise these cost functions, we use the half-quadratic minimisation. It yields a fast and simple method, which can be applied to a wide range of spectroscopic signal. Guidelines for the choice of the design parameters are given and illustrated on simulated spectra. Finally, the effectiveness of the method is shown by processing experimental infrared and Raman spectra.