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

with application to helical filtering

**Sergey Fomel ^{},
Paul Sava^{},
James Rickett^{},
and Jon F. Claerbout^{}**

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.

- Introduction
- Method description

- Application of spectral factorization:

Regularizing smooth data with splines in tension- Mathematical theory of splines in tension
- Finite differences and spectral factorization
- Regularization example

- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

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

2014-02-15