Bayesian Inference for Neighborhood Filters With Application in Denoising

Area of Science:

• Computer Vision
• Image Processing
• Statistical Modeling

Background:

• Range-weighted neighborhood filters are popular for edge preservation but lack direct property reasoning and parameter estimation.
• Previous methods required indirect connections to other models for analysis.

Purpose of the Study:

• To introduce a unified empirical Bayesian framework for direct reasoning and parameter estimation of neighborhood filters.
• To develop an efficient algorithm for estimating the essential parameter, range variance.

Main Methods:

• A neighborhood noise model was proposed for inferring Yaroslavsky, bilateral, and modified non-local means filters using joint maximum a posteriori and maximum likelihood estimation.
• Range variance estimation was achieved via model fitting to an empirical distribution of a chi scale mixture variable.
• An expectation-maximization and quasi-Newton optimization algorithm was devised for efficient model fitting.

Main Results:

• The proposed framework successfully fits noisy images and efficiently estimates range variance.
• Extensive experiments demonstrated the framework's effectiveness across various configurations (kernel functions, filter types, noise types).
• A recursive fitting and filtering scheme improved color-image denoising quality.

Conclusions:

• The unified empirical Bayesian framework provides a direct and efficient method for neighborhood filter analysis and parameter estimation.
• This approach significantly enhances image denoising performance, particularly for color images.