ABSTRACT
FMH filters combine the desirable properties of the FIR filter for noise removal in constant signals and the capability of median filters to preserve edges, and can be written as [44]
x median x x xˆ , , ,k k k M k1 2 ( )( ) ( ) ( )= Φ Φ Φ (4.1) where Φi is the ith FIR subfilter operating on the input signal. The length k and number M of FIR subfilters are selected to allow for an acceptable compromise between noise reduction and edge preservation. Typically, M is kept small in Equation (4.1) to allow for simple implementation. The large number of compare and swap operations needed by the median filter is eliminated in the FMH filter by taking the median over the outputs of a few FIR substructures. FMH filters are much faster than median filters of the same length. The median filter is a special case of the FMH filter where the lengths of all the FIR substructures are 1.
