Mathematical Sciences: Mathematical Tools for Imaging Reconstruction

这个项目将处理反问题， 图像重建 低能的衰减和散射 未知介质探测，孤子理论应用于切片 磁共振成像中的选择和组的应用 将考虑信号处理的表示。 在 此外，还将作出巨大努力， 开发PI引入的技术以获得第二等级 某些偏微分方程的解。 这 技术避免了使用复杂的代数几何方法。 这个项目的动机是， 成像重建过程，例如X射线和磁 共振 要发展的数学有直接的 在构建算法和使用的设备的影响 在医学成像中。

This project will deal with inverse problems arising in image reconstruction. Attenuation and scattering of low energy probes by unknown media, soliton theory applied to slice selection in magnetic resonance imaging, and application of group representation to signal processing will be considered. In addition, considerable effort will be placed in further developing a technique introduced by the PI to obtain rank two solutions to certain partial differential equations. This technique avoids using complicated algebraic geometry methods. This project has been motivated by problems arising in imaging reconstruction processes such as X rays and magnetic resonance. The mathematics to be developed has direct implications in the construction of algorithms and devices used in medical imaging.