Noise-adaptive rational filter

A new rational filter (RF), called noise-adaptive rational filter (NARF), is de- veloped in this thesis to deal with image smoothing in non-impulsive noise (e.g., Gaussian noise) environment. In our development, one-dimensional optimal NARF is first derived that yields the least mean-square error. For image processing, the derived one-dimensional filter is then extended to two-dimensional optimal NARF. Since the optimal NARF is not feasible due to its involvement on the original signal samples, the performance can only be considered as the theoretical reference. In practice, a nonlinear term is proposed to approximate those unavailable signal sam- plesMaster of Science (Signal Processing