Double-window Hodges-Lehman (D) filter and hybrid D-median filter for robust image smoothing

The double window Hodges-Lehman filter (DWD-filter) and a hybrid D-median filter (HDM-filter) for robust image smoothing are proposed. An adaptive mixture of the median and the D-filter, the HDM filter first makes decisions about the presence of edges on the basis of a two-way classification of pixels near and around the pixel to be filtered. Subsequently, straightforward D-filtering is used in the absence of edges, and median filtering is used in the presence of edges. The DWD filter uses two windows and D-filtering. The smaller window is used to preserve the details, then the larger window to provide for sufficient smoothing. Detailed simulation results show that the HDM-filter, while retaining all the good properties of the DWD filter, consistently performs better, in terms of signal-to-noise ratio, than the DWD filter and a number of other filters, including the median filter. The DWD filter is shown to have simpler structure, although not necessarily lesser computational complexity