Double-Window Hodges-Lehman (D) Filter and Hybrid D-Median Filter for Robust Image Smoothing

In this correspondence, we have proposed two new niters: the Double Window Hodges-Lehman filter (DWD filter) and a hybrid D-median filter (HDM filter) for robust image smoothing. Schematically, the Hodges-Lehman D-filter is the median of the averages of symmetrically placed order statistics of a sample. This filter is well known in the statistical literature for its robust signal smoothing efficiency and good tolerance to outliers. However, sharp variation of signals, i.e., edges, are not preserved. 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 2-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 other new filter—the DWD filter—uses two windows and D-filtering. The smaller window is employed to preserve the details, and 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 SNR, than the DWD filter and a host of other filters including the median filter. The DWD filter, on the other hand, is shown to have simpler structure although not necessarily lesser computational complexity.