Digital Bilateral TV Filtering and Nonlinear Denoising
数字双边全变差滤波及非线性去噪

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.