Mathematical Sciences: Computational Methods for Ill-Posed Inverse Problems

9622119 Vogel 该项目的主要目标是开发稳健、高效的计算方法来解决正则化反问题。 还需要解决的是正则化参数选择方案以及改进的正则化函数的开发。针对图像重建和参数识别中的重要问题开展应用。 逆问题出现在许多重要的应用中。其中最广为人知的可能是生物医学成像，例如 CAT 扫描和磁共振成像 (MRI)。其他示例包括基于卫星的地球（远程）传感和地震数据处理。这些问题往往高度不稳定，即数据中的小错误可能会导致解决方案中的巨大错误。它们也往往非常大——涉及数千甚至数百万个未知数。该项目的目标是开发稳定且高效的计算技术来解决此类问题。这一目标的实现将极大增强一些重要技术。

9622119 Vogel The primary goal of this project is to develop robust, efficient computational methods for the solution of regularized inverse problems. Also to be addressed are regularization parameter selection schemes, and the development of improved regularization functionals. Applications will be carried out for important problems in image reconstruction and parameter identification. Inverse problems arise in a number of important applications. Perhaps the most well know of these is biomedical imaging, e.g., CAT scans and Magnetic Resonance Imaging (MRI). Other examples include satellite- based (remote) sensing of the earth and seismic data processing. These problems tend to be highly unstable, i.e., small errors in the data may give rise to enormous errors in the solution. They also tend to be very large--- involving thousands or even millions of unknowns. The goal of this project is to develop computational techniques to solve such problems which are both stable and efficient. The attainment of this goal will greatly enhance a number of important technologies.