Abel Transformation Based Adaptive Regularization Approach for Image Reconstruction

In this paper, we discuss an adaptive regularization approach for density reconstruction of axially symmetric object whose tomography comes from a single X-ray projection. The method we proposed is based on the combination of total variation regularization and high-order total variation regularization. Its main advantage is to reduce the staircase effect while keeping sharp edges and recovering smoothly varying regions. Moreover, it simplifies the use of parameters. We apply the augmented Lagrangian method to solve the optimization involved. Numerical results show that the proposed method has improved the accuracy of density edges and values. Besides, the method is not sensitive to the measured data noise.