Ranking in R/sup p/ and its use in multivariate image estimation
- 1 June 1991
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems for Video Technology
- Vol. 1 (2) , 197-209
- https://doi.org/10.1109/76.97975
Abstract
The extension of ranking a set of elements in R to ranking a set of vectors in a p'th dimensional space R/sup 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.Keywords
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