Decimated rank-order filtering

Rank-order filters are used for a wide range of applications. They are noted for their ability to remove impulsive noise and to preserve sharp changes in the signal. However, there is a tradeoff between noise removing capability and edge retention. When impulsive noise and sharp edges in the signal coincide, edges are no longer preserved. Another tradeoff is noise removal versus computational cost. The increase in the number of operations is proportional to the noise-removal capability. The authors introduce a new filter (the decimated rank-order filter) that achieves large amount of noise removal with much less detail and edge smoothing as compared with the standard rank-order filter. Furthermore, this is possible at a reduced computational burden. The decimated median filter is a particular example of this class. The authors investigate its deterministic and statistical properties and show that it compares favorably with the standard median filter in terms of impulsive noise removal, especially in the neighborhood of edges. They extend the structure of decimated rank-order filters. They find all rank orders of the signal to obtain the decimated sorter and show that the decimated sorter is the bitonic sorter used in switching networks. They point out the connection between their research and concepts in sorting and switching structures