<title>Generalized adaptive median filters and their application in computed tomography</title>

Abstract

ABSTRACT A generalized adaptive median filter (GAMF) is intrOdUced for more robust noise suppression and edge preservation incomputedtomography. TheGAMFemployes asetofadapdvelinearfiltersinconjunction with an adaptivemedian filter. Eachlinear filter is designed to preserve a feature in one orientation. The window sizes of these filters are adaptive to the localstatistics. The outputofthe GAMF is selected from the linear filter outputset that is closest to the adaptive median filter. Thisfilter has been successfully utilized in the computed tomography to combatsevere streaking artifacts resulting from excessivex-ray quantum noise. Its effectiveness has been demonstrated in phantom tests and clinical studies. In addition, little impacton system resolution can be observed.Keywords: Computed Tomography, median filter, adaptive filter, generalized adaptive median filter, system resolution INTRODUCTION In many applications, the requirement ofsimultaneously removing high frequency noise components and preserving the edgestructure ofthe signal has broughtmany interests in non—linear filtering techniques. One ofthe most famous non—linear filtersis the median filter inlroduced by Tukey.1 The popularity of the median filter comes from its simplicity and efficiency.However, it has been shown that median filter contains some undesired characteHstics such as blotching or false contouring.2It often fails to provide sufficient smoothing for non—impulsive noises. To overcome these shortcomings, many extensionshave been introduced. This includes the introduction of a generalized median ifiter by Bovik et al.3 The output of the filteris given by alinear combination ofthe order statistics of the input sequence. Based on the observation that the noise removalcapability increases with increasing median filter window length, and the fact that a larger window length leads to a moresmoothing of signal details and edges, median filters with variable window size were presented.4 To overcome its inferiorperformance in suppressing Gaussian white noise as compared to the average operator, Lee and Kassam described a doublewindow modified trimmed mean filter (DWMTM).5 The DWMTM filter selects the median from a small size window andaverage those samples inside a larger window close to the median. To further improve the performance ofthese filters in edgeshifting, some sophisticated algorithms were proposed. For example, the decimated rank-order filter (DROF) and multilevelnonlinear filter TheDROF employes a signal decimation technique to keep the window size of the median filter