A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing the X-ray tomography rather than on the conventional integral formulation. The quasi-reversibility method is applied. Convergence analysis is performed using a new Carleman estimate. Numerical results are presented and compared with the inversion of the Radon transform using the well-known filtered back projection algorithm. In addition, it is shown how to use our method to study the inversion of the attenuated X-ray transform for the same case of incomplete data.
Institute of Biomathematics and Biometry, Helmholtz Zentrum München, German Research Center for Environmental Health（生物数学与生物计量研究所，赫尔霍兹慕尼黑中心，德国环境健康研究中心）；Technische Universität München（慕尼黑工业大学）
Generative Prior-Guided Neural Interface Reconstruction for 3D Electrical Impedance Tomography
Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）；Department of Mathematics, School of Mechanical Engineering, Purdue University（帕克大学机械工程学院数学系）
