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.
