Regularization is an essential term to suppress noise and artifacts in iterative reconstruction algorithms. The total variation (TV) is one of the most successful regularizations which can eliminate noise and streak artifacts while preserving edges. However, strong TV regularization usually produces staircase artifacts if the image contains non-constant regions. Recently, the mean curvature (MC) regularization based on the geometry-driven diffusion model has been proposed to solve image processing problems. In an aspect of geometry, minimizing the mean curvature to zero derives a linear surface. In this paper, we develop a linear convolution approximated mean curvature based on the local geometric properties of surfaces embedded in 3D space. We adopted the half window kernel technique and formulated a novel edge-preserving mean curvature (EPMC) regularization. Compared with the traditional curvature diffusion model that employs secondorder partial derivatives, the proposed method is efficient and concise. The ADMM algorithm can solve the optimization problem. We conducted a simulation study and compared the proposed EPMC regularization with TV. The results demonstrate that the proposed method is superior in noise suppression and edge preservation in linear regions while avoiding staircase artifacts.
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