Based On Robust Statistical Image Modeling For Denoising

Image restoration is to reconstruct or restore original images from given degraded images or noise-polluted images with some priori knowledge. Traditional linear filtration will blur edges, lines, textures and other image features. This paper's research focus on denoising while preserving edges.By introducing and analyzing Perona and Mailik's anisotropic diffusion model, this paper establishes the connections and unification among Bayesian inference, the variational PDE models and robust statistic theory. This paper proposes the L_p normas fidelity from Maximum Likelihood Estimation. By fitting the histogram module of image gradient field, this paper gains the three potential functions as from three density functions: Gexi density function T density function and Weibull density function by Huber theorem respectively. Then, we propose corresponding model to denoise Gaussian noise and pulse noise. Experiments show that: 1) good denoising effect can be achieved for Gaussian noises when fidelity is L₂ norm, while we canachieve good denoising effect to pulse noise when fidelity is L₁ norm.2) The three potential functions deduced from density functions can achieve a better compromise between noise-suppressing and edge-preserving. The model with regularization term deduced from Gexi distribution has the strongest denoising capability.