The Wilson-Burg method of spectral factorization with application to helical filtering

Published as Geophysical Prospecting, 51, 409-420 (2003)

The Wilson-Burg method of spectral factorization
with application to helical filtering

Sergey Fomel, Paul Sava, James Rickett, and Jon F. Claerbout

Abstract:

Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform.

To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behavior in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.

The Wilson-Burg method of spectral factorization with application to helical filtering