Anisotropic Variational Models for Image Denoising Based on Directional Hessian

Guangyu Yang, Weibo Wei, Zhenkuan Pan

Abstract: Anisotropic and high-order diffusion variational models have excellent performances in image coherence and smoothness preserving, respectively. In order to preserve these merits simultaneously in one variational model for image restoration, we propose three second-order anisotropic variational models making use of directional Hessian. The first one is the double-orientational bounded Hessian (DOBH) model; it is an extension to the isotropic bounded Hessian (BH) model. The second is the double-orientational total generalized variation (DOTGV), which is an extension to the total generalized variation (TGV) model. The third is the double-orientational total variation and bounded Hessian (DOTBH) model, which is a hybrid one combining the first-order and second-order directional regularizers. The second-order directional derivatives are designed by Hession and directional vectors which are derived from classic structure tensors. In order to cope with complex calculations of these models, alternating direction method of multipliers (ADMM) algorithms are designed, respectively. Thus, the proposed models can be decomposed into a set of simple sub-problems of optimization, which can be solved by fast FFT method or soft thresholding formulas. In order to improve computational efficiency, fast ADMM algorithms with restart strategy are designed and implemented finally. Experimental results demonstrate better performances compared with previous classical models, especially in large-scale texture restoration.