Adaptive-neighborhood best mean rank vector filter for impulsive noise removal

Rank-order based filters are usually implemented using reduced ordering, since there is no natural way to order vector data, such as color pixel values. This paper proposes a new statistics for multivariate data which is a mean rank obtained by aggregating partial ordering ranks. This statistics is then used for the reduced ordering of vector data; the median statistic is characterized by the best mean rank vector (BMRV). We devise two filtering structures based on the BMRV statistics: one that uses a classical square neighborhood, and one which is based on adaptive neighborhoods. We show that the proposed filters are highly effective for filtering color images heavily corrupted by impulsive noise, and compare favorably to state-of-the-art filtering structures.