In this paper, a new, robust and resistant, inversion based 2D Fourier transformation is presented where the spectrum is discretized by series expansion (S-IRLS-FT). The series expansion coefficients as model parameters are given by the solution of the inverse problem. Since it is advantageous to use squared-integrable, full, orthogonal and normed basis functions, Hermite-functions are chosen as basis functions of the inversion based Fourier transformation. Taking advantage of the beneficial properties of Hermite polynomials, that they are the eigenfunctions of the inverse Fourier transformation, the elements of the Jacobian matrix can be calculated fast and easily, without integration. The procedure can be robustified using Iteratively Reweighted Least Squares (IRLS) method with Steiner weights. The advantage of the Steiner weights is that the scale parameters ( 2) can be determined from the statistic of the measured data set in an inner iteration process. Thus, a very effective robust and resistant inversion procedure can be defined. Its applicability using magnetic data calculated above a square and “L”-shape object is proved.


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