摘要
文章旨在研究非线性数字滤波器的统一设计框架问题.基于稳健统计理论和双边滤波思想,首先建立了一种鲁棒的图像复原统一能量泛函.该能量泛函充分融合了双边滤波的双重异性加权机制和稳健ρ-函数对边缘奇异点的鲁棒性处理机制,因而具有更强的边缘保持能力.随后,基于图像复原统一能量泛函的欧拉-拉格朗日方程,导出一种非线性数字滤波器的统一设计框架.特别地,在此统一框架下,双边滤波、数字TV滤波以及自适应平滑均可进行相应的扩展.同时,文中系统比较了各种稳健ρ-函数在边缘保持方面的鲁棒性,并提出一种新型边缘保持性稳健ρ-函数,即ρ(x)=-σ2(1+|x|/σ)exp(-|x|/σ)+σ2.不论是视觉效果方面还是峰值信噪比方面,大量实验结果验证了文中统一设计框架的合理性和新型稳健ρ-函数的边缘保持性.
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.
出处
《计算机学报》
EI
CSCD
北大核心
2007年第1期91-102,共12页
Chinese Journal of Computers
关键词
稳健估计
双边滤波
各向异性扩散
非线性滤波
奇异点
outlier robust estimation
bilateral filtering
anisotropic diffusion
nonlinear filtering
outlier
