Noise adaptive rational filter

A new rational filter (RF), called the noise adaptive rational filter (NARF), is developed for removing non-impulsive noise, such as Gaussian noise concerned in this paper. The optimal NARF, in the least mean-square (LMS) error sense, is first derived for the one-dimensional signal, followed by its extension to the two-dimensional signal through a separable approach for image denoising. Due to the feasibility issue encountered in the derived optimal closed form, a feasible (thus, sub-optimal) NARF is then proposed, which exploits noise variance (or power) to adapt to signal transitions. The vector NARF is also proposed for color image denoising. Extensive simulation results show that our proposed NARF outperforms the RF on both objective evaluation in peak signal-to-noise ratio (PSNR) measurement and subjective evaluation through visual quality assessment. Furthermore, how to exploit the proposed NARF for denoising a noisy image corrupted by a mixture of impulse noise and non-impulsive noise using a two-stage cascading approach is also discussed with some simulation results.