A Unified Designing Framework for Nonlinear Digital Filters and Behavior Analysis
Wen Shao · Chinese Journal of Computers · 2007
A unified designing framework for nonlinear digital filters is discussed in the paper.Based on robust statistics and the idea of bilateral filtering,a unified and robust energy functional for image restoration is firstly constructed,which incorporates both the double-weighting idea of bilateral filtering and the robustness of robust ρ-functions for edge-outlier processing,and hence behaves much better in edge-preservation.The unified designing framework for nonlinear digital filters is subsequently derived,through solving the Euler-Lagrange equation of the unified energy functional.Under the unified designing framework,bilateral filtering,digital TV filtering,and adaptive smoothing can be expanded correspondingly.The robustness of various robust ρ-functions in edge-preservation is also compared systematically,and a novel edge-preserving robust ρ-function is proposed in the paper,that is,ρ(x)=-σ 2(1+｜x｜/σ)exp｛-｜x｜/σ｝+σ 2.Numerous experiment results demonstrate the rationality of the unified designing framework and edge-preservation of the novel robust ρ-function,both in the visual effect and the PSNR value.