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Ranking in Rp and its use in multivariate image estimation

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2 Author(s)
Hardie, R.C. ; Dept. of Electr. Eng., Delaware Univ., Newark, DE, USA ; Arce, G.R.

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 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.

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Circuits and Systems for Video Technology, IEEE Transactions on  (Volume:1 ,  Issue: 2 )