Generating idempotent filters

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, 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 noncorrupted parts of the signal. These filters are therefore well suited for preprocessing purposes. Likely applications of these filters are in speech processing, image processing, and image sequence processing, where the filter mask is typically three-dimensional. Sufficient conditions for a filter cascade to be idempotent are given. Two idempotent median filter cascades and their advantages are discussed.<>