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

Conclusions

The Wilson-Burg spectral factorization method, presented in this paper, allows one to construct stable recursive filters. The method appears to have attractive computational properties and can be significantly more efficient than alternative spectral factorization algorithms. It is particularly suitable for the multidimensional case, where recursive filtering is enabled by the helix transform.

We have illustrated an application of the Wilson-Burg method for efficient smooth data regularization. A constrained approach to smooth data regularization leads to splines in tension. The constraint is embedded in a user-specified tension parameter. The two boundary values of tension correspond to cubic and linear interpolation. By applying the method of spectral factorization on a helix, we have been able to define a family of two-dimensional minimum-phase filters, which correspond to the spline interpolation problem with different values of tension. We have used these filters for accelerating data-regularization problems with smooth surfaces by recursive preconditioning. In general, they are applicable for preconditioning acceleration in various estimation problems with smooth models.

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