Mathematical Sciences: Computational Methods for Ill-Posed Inverse Problems

小行星9622119 该项目的主要目标是开发强大、高效的 正则化反问题的求解方法。 也要解决的是正则化参数选择方案， 改进的正则化泛函的发展。应用将 针对图像重建中的重要问题进行， 参数识别 反问题出现在一些重要的应用。也许 其中最公知的是生物医学成像，例如，CAT扫描和 磁共振成像（MRI）。其他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 在解决方案中产生巨大的错误。它们也往往是非常大的-涉及数千甚至数百万的未知数。这个项目的目标 是发展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 一些重要的技术。

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.