Geometric Inverse Problems
Geometric Inverse Problems
复制标题
几何反问题
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Salo
中科院分区：
文献类型：
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作者：
M. Salo
这最新的治疗几何反问题的最新发展介绍了研究生和研究人员的一个令人兴奋的研究领域。重点放在二维的情况下，涵盖的主题包括测地线X射线变换，边界刚度，张量层析成像，衰减X射线变换和卡尔德龙问题。该演示文稿是独立的，并开始与氡变换和径向声速作为激励的例子。所需的几何背景中详细开发的背景下，简单的流形的边界。深入分析了各种测地线X射线变换，以及相关的唯一性，稳定性，重建和范围表征结果。重点包括简单表面的边界刚性证明以及连接的散射刚性。最后一章讨论了当前的开放问题和相关主题。大量的练习和例子使这本书成为一个很好的自学资源或一个学期的课程或研讨会的文本。
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.