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 LU LU-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.

Keywords: 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

Document Type: Research article