Natural alternatives for one dimensional median filtering

Abstract

For practical purposes median smoothers have often
been considered the basic components for the construction of simple non-linear
smoothers for removing impulsive noise before any subsequent linear signal
extraction from a 
sequence. Alternatives exist that are computationally convenient,
conceptually simpler and provide significant insight into the removal of
impulsive noise of chosen briefness. Deriving these, so called LULU-operators, from the simplest rank
selectors provides a simpler proof structure that provides significant
additional insight for analysis and comparison of similar smoothers. From an
algebraic point of view, an interesting finite, partially ordered, idempotent semigroup arises.


Mathematics Subject
Classification (2000):
65D10, 94A08, 06D99, 06E30, 20M99.



Key words: Nonlinear smoothing and image
processing, median filtering; stack filters; Boolean normal forms; minimal
transversals; distributive lattice; finite semigroup
of idempotent min-max operators; fix points of min-max operators; canonical
forms of min-max operators.



Quaestiones
Mathematicae 25 (2002), 135-162