The autocorrelation of the helix derivative filter H is the negative of the finite-difference representation of the Laplacian operator ,
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
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
Now I have the enhanced helix derivative with adjustable parameters na and , the enhanced helix low-cut filter with na, k0 and . Here na is the half length of the helix filter.
Compared with the conventional helix filters, the enhanced filters have a new adjustable parameter, .