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

On the use of Steiner’s weights in inversion-based Fourier transformation: robustification of a... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Geodaetica et Geophysica" Springer Journals

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

"Acta Geodaetica et Geophysica" , Volume 49 (1): 10 – Mar 1, 2014

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Publisher
Springer Journals
Copyright
2014 Akadémiai Kiadó, Budapest, Hungary
ISSN
2213-5812
eISSN
2213-5820
DOI
10.1007/s40328-014-0041-0
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

"Acta Geodaetica et Geophysica"Springer Journals

Published: Mar 1, 2014

References