Automatic smoothing by optimal splines

Abstract

We propose a method that is capable to filter out noise as well as suppress outliers of sampled real functions under fairly general conditions. From an a priori selection of the number of knots that define the adjusting spline, but not their location in that curve, the method automatically determines the adjusting cubic spline in a least-squares optimal sense. The method is fast and easily allows for selection of various possible number of knots, adding a desirable flexibility to the procedure. As an illustration, we apply the method to some typical situations found in geophysical problems.