Adaptive Order Statistic Filters for Noise Characterization and Suppression without a Noise-Free Reference

Several adaptive order statistic filters (OSF) are developed and compared for channel characterization and noise suppression in images and 3-D CT data. Emphasis has been put on the situation when a noisefree reference image is not available but instead we can have a sequence of two noisy versions of the same image (or a 3-D data slice). One of the noisy images is used as the reference in the OSF. The adaptive updating formula for the filter coefficients is derived. It is shown theoretically that if noises are not correlated, the expected values of the derived filter coefficients will be equal to those coefficients derived using a noise-free reference. Experiments using the noisy reference image yield comparable results to those methods using a noise-free reference image and also better results than those of median, Gaussian, averaging and Wiener filters.