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![]() | Nonlinear structure-enhancing filtering using plane-wave prediction | ![]() |
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In this appendix, we review lower-upper-middle (LUM)
filters introduced by Hardie and Boncelet (1993). Consider a window function
containing a set of samples centered about the sample
. We
assume
to be odd. This set of observations will be denoted by
. The rank-ordered set can be written as
The estimate of the center sample will be denoted .
Thus, the output of the lower-upper-middle (LUM)
smoother is if
. If
, then
the output of the LUM smoother is
. Otherwise the output
of the LUM smoother is simply
.
Then, the output of the lower-upper-middle (LUM)
sharpener with parameter is given by
Thus, if
, then
is shifted outward to
or
according to which is closest to
. Otherwise the sample
is unmodified. By changing the
parameter
, various levels of sharpening can be achieved. In the
case where
, no sharpening occurs and the
lower-upper-middle (LUM) sharpener is simply an
identity filter. In the case where
, a maximum amount of
sharpening is achieved since
is being shifted to one of the
extreme-order statistics
or
.
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![]() | Nonlinear structure-enhancing filtering using plane-wave prediction | ![]() |
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