Weighted Median Filters for Multichannel Signals

Weighted medians over multichannel signals are not uniquely defined. Due to its simplicity, Astola ´s Vector Median (VM) has received considerable attention particularly in image processing applications. In this paper, we show that the VM and its direct extension the Weighted VM are limited as they do not fully utilize the cross-channel correlation. In fact, VM treats all sub-channel components independent of each other. By revisiting the principles of Maximum Likelihood estimation of location in a multivariate signal space, we propose two new and conceptually simple multichannel weighted median filters which can capture cross-channel information effectively. Their optimal filter derivations are also presented, followed by a series of simulations from color image denoising to array signal processing where the advantages of the new filtering structures are illustrated