Robust fitting of spectra to splines with variable knots

Spectra consist of continuum features that vary over many channels, and peaks that vary over few channels. In a fit to the continuum the peaks appear as outliers. Robust methods in which the weights associated with the peaks are reduced allow the continuum to be fitted almost independently of the peaks. This requires a very smooth background. Cubic splines, which are continuous with continuous first and second derivatives, are a good choice for this task when the locations of the discontinuities in the third derivatives, the knots, are included in the parameters optimized in the fitting process. An extension to the Marquardt method allows a Newton-Raphson method to be used in this optimization.