The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the recently discovered backprojection type inversion formulas for the case of spherical acquisition in 3D. A numerical simulation of the data acquisition with subsequent reconstructions are made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered. The results are compared with the implementation of a previously used approximate inversion formula.
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）
Limited Tomography Reconstruction via Tight Frame and Sinogram Extrapolation
Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；Beijing International Center for Mathematical Research Peking University（北京大学北京国际数学研究中心）；Institute of Natural Sciences, School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University（上海交通大学自然科学研究院、数学科学学院和教育部科学计算与工程应用重点实验室）
A Convex Functional for Image Denoising based on Patches with Constrained Overlaps and its vectorial application to Low Dose Differential Phase Tomography
the Ludwig Maximilians University, Physics Departement, 85748 Garching, Germany（慕尼黑大学物理系）；Ludwig Maximilians University, Departement of Clinical Radiology,80336 Munich, Germany（慕尼黑大学临床放射学系）
Stability estimates for the regularized inversion of the truncated Hilbert transform
Seminar for Applied Mathematics, ETH Zürich（苏黎世联邦理工学院应用数学研讨会）；Department of Nuclear Medicine, Vrije Universiteit Brussel（布鲁塞尔自由大学核医学系）；Department of Mathematics, University of Central Florida（中佛罗里达大学数学系）
