Title:  Prospective and Retrospective Retooling of Magnetic Resonance Imaging and Reconstruction

Committee: 

Dr. Romberg, Advisor

Dr. Hu, Co-Advisor        

Dr. Rozell, Chair

Dr. Oshinski

Abstract: The objective of the proposed research is to tackle medical image reconstruction both retrospectively and prospectively. Convex relaxations of sparse priors have given birth to strident improvements in the way signals are recovered from under determined systems. In the retrospective vein of image reconstruction, we seek to extend the benefits afforded by sparse regularization through the use of non convex sparse priors. We develop a novel algorithmic solution for the analysis based non convex sparse prior for linear inverse problems. This framework can be implicitly applied to under-determined signal recovery, single image super-resolution, image denoising and blind deconvolution. We demonstrate that these non convex formulations can outperform their convex counterparts even when they converge to local minima. In order to truly alter reconstruction, a more prospective approach is necessary where the data acquisition methodology and reconstruction pipeline are jointly constructed. Speed of imaging is of great concern in magnetic resonance imaging (MRI). In MR systems, faster imaging translates to a range of benefits from increased temporal / spatial resolution to reduced motion artifacts. We develop a novel MR data acquisition and reconstruction framework to accelerate MR imaging beyond what is currently commercially available. This is done by leveraging existing hardware that is under utilized during the data acquisition process thereby affording better control over the spectral distribution of the underlying encoding operator. We demonstrate the efficacy of this method using both simulations and empirical testing on MR human scanners. Finally, our methodology forms a generalized framework that allows for seamless transition between 2D and 3D MR imaging.