The autocorrelation of the helix derivative filter H is the
negative of the finite-difference representation of the Laplacian
operator ,
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(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
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(3) |
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, .