Binary Tomography with Deblurring

We study two scenarios of limited-angle binary tomography with data distorted with an unknown convolution: Either the projection data are taken from a blurred object, or the projection data themselves are blurred. These scenarios are relevant in case of scattering and due to a finite resolution of the detectors. Assuming that the unknown blurring process is adequately modeled by an isotropic Gaussian convolution kernel with unknown scale-parameter, we show that parameter estimation can be combined with the reconstruction process. To this end, a recently introduced Difference-of-Convex-Functions programming approach to limited-angle binary tomographic reconstruction is complemented with Expectation-Maximization iteration. Experimental results show that the resulting approach is able to cope with both ill-posed problems, limited-angle reconstruction and deblurring, simultaneously.