Median Based Idempotent Filters

Idempotent filters produce a root signal in a single filter pass, i.e. the filter output is invariant to further filterings with the same filter. In this paper median based idempotent filter structures are introduced. Two approaches to generate these filters are studied: weighted median filters and median filter cascades. Two subclasses of n-dimensional idempotent weighted median filters, called Class 1 and Class 2 filters in the paper, are introduced. It is shown that both Class 1 and Class 2 filters suppress impulsive noise from n-dimensional input signals and yet have almost no effect on the non-corrupted parts of the signal. These filters are therefore well-suited for example for preprocessing purposes. An application to speech processing is described. Other likely applications of these filters are in image processing and, also, in image sequence processing, where the filter mask is typically 3-dimensional. Sufficient conditions for a filter cascade to be idempotent are given. Two idempotent median filter cascades and their advantages are discussed.