A New Robust Inversion Method Using Cauchy-Steiner Weights – And Its Application in Data Processing

The Fourier-transform (FT) often results noisy Fourier spectrum because this operation is linear and contaminate noise in time domain dataset appear in the frequency domain also. Especially, in case of non-Gaussian nature of the noise distribution (for example outliers in the data sets) can cause appreciable distortions in the Fourier spectra. If we treat the FT as an over-determined inverse problem, the noise effect on the Fourier spectrum can be greatly reduced. The geophysical series inversion was used for the discretization. The scaled Hermite functions - note that they are eigen-functions of the FT - were chosen as basis function. During the inversion process by using the Steiner-weights we get a highly robust inversional FT method. Numerical tests show the significant noise rejection capability of the new inversion based FT algorithm.