An adaptive rank-conditioned median filter for edge-preserving image smoothing

Median filter (MF) is a powerful tool for impulsive noise removal in digital signals and images: noisy samples do not affect its output, but are discarded as outliers. The basic scheme of median filter has been specialized to remove noisy spikes with little distortion, that is without modifying noise-free pixels, like the rank-conditioned median (RCM) filter, recently introduced by the authors. In this work a spatially adaptive RCM scheme (ARCM) is proposed with the aim at extending its filtering capability also to additive and multiplicative noise models. Accordingly, only pixels having botndary ranks are adaptively replaced with the sample median, while the others are left unaltered: pixel replacements are conditioned to their ranks, i.e., positions of their values after sorting in ascending order, based on an estimate of local SNR and on the response of a simple detector of structured edges. An adaptivity function is empirically designed, and a unified framework is developed to deal with both additive and multiplicative noise models. Results are presented on images corrupted with several noise models, as well as on true Synthetic Aperture Radar (SAR) images affected by speckle noise.