数字双边全变差滤波及非线性去噪

Digital Bilateral TV Filtering and Nonlinear Denoising

为了更好地滤噪,在研究基于数字滤波器的图像去噪问题的基础上,首先简洁地建立了双边滤波与最优能量泛函之间的理论联系,同时导出一类广义双边滤波器;然后基于双边滤波在阶数大邻域中的双重异性加权滤波机制,推广了Chan提出的数字全变差(TV)模型,提出了一种数字双边TV模型;随后,建立了基于数字双边TV模型的最优能量泛函,并且导出了适于高斯噪声和脉冲噪声两种情形的非线性数字双边全变差滤波器。实验结果显示,无论是在视觉效果方面,还是去噪后图像的峰值信噪比方面,双边全变差滤波都是对双边滤波和全变差滤波极为合理而有效的推广。尤其对于脉冲噪声,该双边全变差滤波的去噪性能明显优于中值滤波器,具有重要的实用价值。

The paper mainly focuses on the problem of filtering-based noise removal. First of all, the theoretical relationship between bilateral filtering and an optimization functional is concisely constructed, and meanwhile with a kind of generalized bilateral filtering derived. Through combining the idea of bilateral filtering with the digital TV model proposed by Chan, a new regularization term is proposed, based on which a unified optimization functional is subsequently constructed in both cases of Gaussian noise and impulse noise. Finally, a digital bilateral TV filtering is deduced by solving the Euler-Lagrange equation of the optimization functional. Experiment results demonstrate that the digital bilateral TV filtering is a reasonable and effective generalization of both the bilateral filtering and digital TV filtering. Especially for the impulse noise, digital bilateral TV filtering behaves much better than Median filtering, and hence it is a good method for the actual application.