Design of permutation order statistic filters through group coloring.pdf

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI I ANALOG AND DIGITAL SIGNAL PROCESSING Design of Permutation Order Statistic Filters Through Group Colorings Kenneth E Barner Member IEEE and Gonzalo R Arce Senior Member IEEE A bstract In this pap er we develop a group theoretic N lter this results in at least N dierent observation metho d for reducing the class cardinality of Permutation s pro ducing identical outputs Clearly rankorder based P lters P lters are a recently intro duced class of non linear lters that have their ro ots in p ermutation theory lters fail to exploit the temp oral context of a sequence and are based on the mapping x x r where x and x r are Many generalizations of rankorder lters have b een pro temp oralordered and rankordered observation vectors re p osed that incorp orate some form of temp oral information sp ectively While P lters contain as a prop er subset a large Still due to their constrained nature these b o dy of nonlinear lters prop osed to date and have shown to b e eective at estimating nonstationary pro cesses in metho ds do not fully utilize the information contained in nonGaussian environments the large numb er of parame b oth the temp oral and rank ordering of the observed data ters required to dene a P lter limits the lters practical Recently several ltering metho ds that op erate on the window size Also the information required to formulate an acceptable estimate is often only a subset of that con full information contained in the temp oral to rank map tained in the p ermutation mapping x x r To reduce in ping x x r have b een develop ed These lters a exible and systematic