Bayesian inference for neighborhood filters with application in denoising

Range-weighted neighborhood filters are useful and popular for their edge-preserving property and simplicity, but they are originally proposed as intuitive tools. Previous works needed to connect them to other tools or models for indirect property reasoning or parameter estimation. In this paper, we introduce a unified empirical Bayesian framework to do both directly. A neighborhood noise model is proposed to reason and infer the Yaroslavsky, bilateral, and modified non-local means filters. An EM+ algorithm is devised to estimate the essential parameter, range variance, via the model fitting to empirical distributions. Finally, we apply this framework to color-image denoising. Experimental results show that the proposed model fits noisy images well and the range variance is estimated successfully. The image quality can also be improved by a proposed recursive fitting and filtering scheme.