Higher-order regularization based image restoration with automatic regularization parameter selection

Poisson and multiplicative Rayleigh noises often appear in medical imaging such as X-ray images, positron emission tomography, and ultrasound images. In this study, we propose novel variational models for removing Poisson/multiplicative Rayleigh noise. We make use of hybrid higher-order total variation as the regularization terms of our proposed models to eliminate staircasing artifacts. We also adopt the spatially adaptive parameter technique to adequately smooth homogenous regions while preserving the edges. The spatially adaptive parameter selection is closely related to local constraints through a local expected value estimator. We provide a convergence analysis, including the existence and uniqueness of solution, and the first order optimality conditions. We apply the alternating direction method of multipliers for solving the proposed models. Numerical experiments demonstrate that our models exhibit a better performance than that of state-of-the-art models in terms of edge preservation, smoothness of the homogenous regions, and various quality measures.