On the use of Steiner’s weights in inversion-based Fourier transformation: robustification of a previously published algorithm

Abstract

In our previous paper (Dobróka et al. Acta Geod Geophys Hung 47(2):185–196, 2012) we proposed a new robust algorithm for the inversion-based Fourier transformation. It was presented that the Fourier transform and its variants responds very sensitively to any little measurement noise affected an input data set. The continuous Fourier spectra are assumed as a series expansion with the scaled Hermite functions. The expansion coefficients are determined by solving an over-determined inverse problem. Here, we use the new Steiner’s weights (previously called the weights of most frequent values or abbreviated as MFV), where the scale parameter can be determined in an internal iteration process. This method results a very efficient robust inversion method in which we calculate the Steiner weights from iteration to iteration into an IRLS procedure. The new method using the Steiner’s weights is also numerically tested by using synthetic data.