Ranking in Rp 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 R^p is considered. In the approach presented here vector ranking 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 is developed, which are 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.