Ranking in R(p) and its Use in Multivariate Image Estimation

The extension of ranking a set of elements In R to ranking a set of vectors In a p'th dimensional space RP is considered. In the approach presented here vector making reduces to ordering vectors according to a sorted list of vector distances. A statistical analysis of this vector ranking Is presented, and these vector ranking concepts are then used to develop ranked-order type estimators for multivariate image fields. A class of vector filters are developed, which am efficient smoothers in additive noise and can be designed to have detail-preserving characteristics. A statistical analysis is developed for the class of filters and a number of simulations were performed in order to quantitatively evaluate their performance. These simulations involve the estimation of both stationary multivariate random signals and color images in additive noise.