Image reconstruction model for the exterior problem of computed tomography based on weighted directional total variation

The exterior problem of computed tomography (CT) is a special imaging modality and it is an important research issue in Non-Destructive Testing (NDT). In the exterior problem, the missing projection data vary with the position of the pixels. Furthermore, amounts of theoretical and experimental results showed that the edges that are tangent to the radial direction are much harder to be reconstructed than edges that are tangent to the angular direction. In this paper, a weighted directional total variation (WDTV) based regularization model was proposed to better deal with the exterior problem. By introducing the WDTV regularization term, our model can reconstruct high quality images. First, WDTV of an image also describes the sparsity of image gradient magnitude which can enforce the reconstructed result to be a nearly flat image. Second, our model can preserve edges and reduce artifacts near edges that are tangent to the radial direction. Third, a numerical implementation called SART+WDTV algorithm was developed to solve our model. Simulated and real experiments demonstrated that our model was more capable of suppressing artifacts and preserving edges.