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The exterior cone-beam computed tomography (CBCT) appears when the x-rays can only pass through the exterior region of an object due to the restriction of the size of the detector, the energy of x-rays and many other factors. The exterior CBCT is an ill-posed inverse problem due to the missing projection data. The distribution of artifacts in exterior CBCT is highly related to the direction of missing projection data. In order to reduce artifacts and reconstruct high quality image, an image reconstruction method based on weighted directional total variation in cylindrical coordinates (cWDTV)is presented in this paper. The directional total variation is calculated according to the direction of missing projection data. The weights are set to reduce artifacts and preserve edges. The convexity of cWDTV and the relationship between cWDTV and classical TV are also illustrated to explain the advantages of our method. Simulated experiments show that our method can improve the performance on artifact reduction and edge preserving.

Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates