论文标题
Riemannian歧管上的大地断层扫描术问题
Geodesic tomography problems on Riemannian manifolds
论文作者
论文摘要
该博士学位论文与整体几何逆问题有关。地球射线变换是一个运算符，该操作员编码沿大地测量的函数的线积分。当此类信息确定唯一和稳定的功能时，论文就建立了许多条件。作为论文的一部分，创建了用于计算层析成像的新数值模型。论文的入门部分包含了与计算机断层扫描相关的反问题和数学模型的介绍。主要重点是对整体几何问题的定义，对相关文献进行调查以及介绍论文的主要结果。给出了积分几何学中重要的开放问题的列表。 论文的四篇文章（Arxiv：1705.10126，Arxiv：1901.03525，Arxiv：1906.05046，Arxiv：1909.00495）现在在各种期刊上发表，本文档的内容自2019年11月11日以来没有更新。这四本文档仅在此文档中被介绍，该文档仅包含该文档，该文档仅包含该文档，该文档仅包含该文档，该文档均包含该文档，该文档均包含该文档，该文档均包含该文档，该文档均包含该文档，该文档均包含该文档，该文档均已被遗漏，该文档均已被遗漏。在文档中以英语和芬兰语给出了扩展的摘要。
This PhD dissertation is concerned with integral geometric inverse problems. The geodesic ray transform is an operator that encodes the line integrals of a function along geodesics. The dissertation establishes many conditions when such information determines a function uniquely and stably. A new numerical model for computed tomography imaging is created as a part of the dissertation. The introductory part of the dissertation contains an introduction to inverse problems and mathematical models associated to computed tomography. The main focus is in definitions of integral geometry problems, survey of the related literature, and introducing the main results of the dissertation. A list of important open problems in integral geometry is given. The four articles of the dissertation (arXiv:1705.10126, arXiv:1901.03525, arXiv:1906.05046, arXiv:1909.00495) are now published in various journals and the content of the document has not been updated since November 11, 2019. These four articles are omitted from this document which contains only the introductory part. Extended abstracts are given in the document in English and Finnish.
