Mumford-Shah-ATV functional for limited angle tomography

Limited angle tomography is a severely ill-posed problem yet practically significant in x-ray computed tomography. In recent development, limited angle tomography problem is casted in the form of convex optimization problem. In this paper, incorporating anisotropic total variation with Mumford-Shah functional, we propose a novel objective functional and develop the corresponding alternating optimization algorithm. The experimental results demonstrate the efficiency of Mumford-Shah functional minimization for limited angle tomography. Furthermore, we also get the segmentations of reconstructed images.