论文标题
重新访问反指数ra transform
Revisit to the Inverse Exponential Radon Transform
论文作者
论文摘要
该重新访问对逆指数ra变换的分析方法进行了调查，该方法在过去的三十年中已经从数学兴趣和医学应用（例如核医学排放成像）进行了研究。经典反转公式的推导是通过针对逆衰减变换而开发的最新参数。该派生允许指数参数是一个复杂的常数，这对于其他应用很有用，例如磁共振成像和张量现场成像。该调查还包括使用有限的希尔伯特变换来处理180度数据的精确重建的新技术。已经对两个实际上重要的主题支付了特殊待遇。一个是从半扫描和截短的扫描数据等部分测量中重建的确切重建，另一个是从发散梁数据中的重建。重建中的噪声传播是通过启发式讨论而不是数学推断所涉及的。包括几种经典重建算法的数值实现。总而言之，讨论了一些主题，以便将来进行更多调查。
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine emission imaging. The derivation of the classical inversion formula is through the recent argument developed for the inverse attenuated Radon transform. That derivation allows the exponential parameter to be a complex constant, which is useful to other applications such as magnetic resonance imaging and tensor field imaging. The survey also includes the new technique of using the finite Hilbert transform to handle the exact reconstruction from 180 degree data. Special treatment has been paid on two practically important subjects. One is the exact reconstruction from partial measurements such as half-scan and truncated-scan data, and the other is the reconstruction from diverging-beam data. The noise propagation in the reconstruction is touched upon with more heuristic discussions than mathematical inference. The numerical realizations of several classical reconstruction algorithms are included. In the conclusion, several topics are discussed for more investigations in the future.
