PDE-based noise removal with geometrical mean diffusion of adaptive TV and Gauss curvature-driven diffusion

The adaptive TV model can keep sharp edges while remove noise. Some key structures that have low gradient magnitudes cannot be preserved by the adaptive TV model, and can be preserved by the Gauss curvature-driven diffusion model while removing noise that has a large Gauss curvature. However, one of the defects of the Gauss curvature-driven diffusion model is that it requires much iteration. Thus, a novel edge preserving model based on the geometrical mean value of the adaptive TV and the Gauss curvature is proposed in this paper. In the proposed model, the diffusion conductance is determined by combining the gradient and the Gauss curvature to preserve sharp edges and some key structures. Comparative results on two synthetic images and a medical image denoising demonstrate that the proposed model outperforms the Gauss curvature-driven diffusion model in terms of both mean square error (MSE) and peak signal-to-noise ratio (PSNR).