Nonconvex higher-order regularization based Rician noise removal with spatially adaptive parameters

• We utilize nonconvex higher-order regularization for Rician denoising and deblurring.
• A new spatially adaptive regularization parameter strategy is adopted.
• The models sufficiently denoise smooth regions while preserving textures and details.

In this article, we introduce a class of variational models for the restoration of images that are polluted by Rician noise and/or blurring. The novel energy functional consists of a convex fidelity term and a nonconvex higher-order regularization term. The regularization term enables us to efficiently denoise piecewise smooth images, by alleviating the staircasing effects that appear in total variation based models, and to preserve details and edges. Furthermore, we incorporate our nonconvex higher-order model with spatially adaptive regularization parameters; this further improves restoration results by sufficiently smoothing homogeneous regions while conserving edge parts. To handle the nonconvexity and nonsmoothness of our models, we adopt the iteratively reweighted ℓ1ℓ1 algorithm, and the alternating direction method of multipliers. This results in fast and efficient algorithms for solving our proposed models. Numerical experiments demonstrate the superiority of our models over the state-of-the-art methods, as well as the effectiveness of our algorithms.