Recursive algorithms and VLSI implementations for median filtering

Median filters and the more general order-statistic-based filters have proven very useful in filtering signals corrupted by noise with heavier tails than the Gaussian, in filtering signals with jumps or edges, or in situations where both occur. The author presents two simple recursive definitions for the kth order statistic taken from n samples. From these recursive expressions, some simple inequalities satisfied by order statistics are presented. Formulas for computing distributions of order statistics are derived. Finally, a series of VLSI implementations for computing both a fixed-order statistic (e.g. the median) or all-order statistics is presented.<>