Mathematical Sciences: Computational Methods for Ill-Posed Inverse Problems

9622119 Vogel这个项目的主要目标是为正则化逆问题的求解开发鲁棒、高效的计算方法。还将讨论正则化参数选择方案，以及改进正则化函数的开发。应用将在图像重建和参数识别的重要问题进行。逆问题出现在许多重要的应用中。也许其中最广为人知的是生物医学成像，例如CAT扫描和磁共振成像（MRI）。其他的例子包括基于卫星的地球遥感和地震数据处理。这些问题往往是高度不稳定的，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计算技术来解决这些问题，既稳定又高效。这一目标的实现将大大提高一些重要技术。

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.