The autocorrelation of the helix derivative filter **H** is the
negative of the finite-difference representation of the Laplacian
operator ,

(1) |

The helix low-cut filter *H*/*D* is designed by doing two spectral
factorizations, one for the numerator of *H*, and another for the
denominator of *D*. It is expressed by

(2) |

Both the filters do not remove the zero frequency completely, degrading
the contrast and details of the roughened image.
A way to solve this problem as suggested by Claerbout, is to rescale
all the coefficients of *H* with nonzero lags by *a*.
If *s* is the sum of all the coefficients with nonzero lag (which are
all negative), *a* is expressed by

(3) |

Now I have the enhanced helix derivative with adjustable parameters
*n*_{a} and , the enhanced helix low-cut filter with *n*_{a}, *k _{0}*
and . Here

Compared with the conventional helix filters, the enhanced filters have a new adjustable parameter, .

4/20/1999