Title :
Decomposition and order statistics in filtering
Author :
Coltuc, Dinu ; Bolon, Philippe
Author_Institution :
LAMII-CESALP, Univ. of Savoie, Annecy, France
Abstract :
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.
Keywords :
filtering theory; nonlinear filters; signal reconstruction; statistical analysis; Jordan decomposition; bounded variation functions; canonical decomposition; classical order statistics; decomposition filters; marginal rank order filtering; nonlinear filters; parity decomposition; signal decomposition; signal reconstruction; symmetry property; three stage filtering scheme; Computational complexity; Filtering theory; Frequency modulation; Image processing; Noise; Noise measurement; Signal resolution;
Conference_Titel :
Signal Processing Conference (EUSIPCO 1998), 9th European
Conference_Location :
Rhodes
Print_ISBN :
978-960-7620-06-4