A structure for adaptive order statistics filtering

In applications such as smoothing and enhancement of images, adaptive filtering techniques offer the flexibility needed for good performance with non-stationary observations. Many adaptive schemes can be based on the idea of determining the local statistics of the signal through appropriate tests on the data, to aid in the selection of a filtering procedure that is suited to the data. In the paper, the authors consider decision-directed or data-dependent adaptive filtering schemes that are based on order statistics. A general formulation for such a class of adaptive order statistics filters is presented. Approximate statistical performance analysis, especially in the presence of edges, may be carried out for this entire class of filters. The authors give examples of some existing filters that fit into this framework. The formulation also accommodates filters that employ multiple windows in their operation. To illustrate the potential of this class of multiple window (MW) filters, they construct and analyze simple filters, like the triple window median (TW-MED) and the triple window median of means (TW-MOM) filters, that are shown to yield useful performance. The class of mean-median hybrid (MMH) filters is also presented as a simple example which may be extended to give interesting performance