Decomposition and order statistics in filtering

The paper investigates a three stage filtering scheme, namely: 1) signal decomposition, 2) filtering and 3) signal reconstruction. If marginal rank order filtering is used in step 2, the derived filtering scheme generalizes the classical order statistics one. Based on this idea, a new family of nonlinear filters, called decomposition filters, is proposed and investigated. The most interesting feature of the new filters is their dependency on signal decomposition. Three decomposition procedures that exhibit certain minimum and symmetry properties are investigated. They are the canonical decomposition of functions, the Jordan decomposition of bounded variation functions and the parity decomposition, respectively. The properties of the derived filters are discussed.