This work presents a novel computed tomography (CT) reconstruction method for the few-view problem based on fractional calculus. To overcome the disadvantages of the total variation minimization method, we propose a fractional-order total variation-based image reconstruction method in this paper. The presented model adopts fractional-order total variation instead of traditional total variation. Different from traditional total variation, fractional-order total variation is derived by considering more neighboring image voxels such that the corresponding weights can be adaptively determined by the model, thus suppressing the over-smoothing effect. The discretization scheme of the fractional-order model is also given. Numerical and clinical experiments demonstrate that our method achieves better performance than existing reconstruction methods, including filtered back projection (FBP), the total variation-based projections onto convex sets method (TV-POCS), and soft-threshold filtering (STH).
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