Combining interior tomography reconstruction and spatial regularization

Interior tomography, also called local or region-of-interest tomography is a special case of computed tomography, in which the object under study is larger than the detector. In this modality, reconstructing the tomography image is an even more ill-posed problem than standard tomography and characteristic artefacts are typically observed, even when a large number of measurements are taken. In this work we propose a reconstruction algorithm designed for interior tomography. We also investigate the case of under-sampled measurements in the case of gradient-sparse images. Our algorithm optimizes the sum of a spatial regularization terms for the image inside the region of interest, and a sinogram regularization term for the projection of the non-reconstructed part of the sample, using convex optimization techniques. We present results on simulated and real data.