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 trade-off between noise removing capability and edge retention. When impulsive noise and sharp edges in the signal coincide, edges are no longer preserved. Another trade-off is noise removal versus computational cost: The increase in the number of operations is proportional to the noise removal capability. We introduce a new filter, the decimated rank order filter (DROF) 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. In this thesis, we define and analyze the DROF and focus on applications that demonstrate its strength.The decimated median filter (DMF) is a particular example of this class. We investigate its deterministic and statistical properties. We show that it has the same root signals as a standard median filter with the same window size. The output statistics point out that the DMF compares favorably with the standard median filter in terms of impulsive noise removal, especially in the neighborhood of edges.The adaptive decimated median filter (ADMF) is another application that achieves better impulse noise removal and edge retention with lower computational complexity. We compare the ADMF with the adaptive median filter and show that it has better performance based on statistical arguments and results of tests on standard images.We extend the structure of the DROF to find all rank orders of the signal and obtain the decimated sorter. We show that the decimated sorter is the bitonic sorter used in switching networks. We point out the connection between our research and concepts in sorting and switching structures.