| In this dissertation, we focus on the problems of fast and accurate reconstruction of undersampled dynamic MRI data sets. Our approaches make use of the natural sparsity of images and belong to the family of compressed sensing algorithms. The compressed sensing theory relies on random sampling. In reality, people prefer non-Cartesian MRI sampling trajectories such as radial or spiral ones in order to mimic random cases. First, we propose a novel NUFFT scheme to reconstruct Non-Cartesian MRI dataset with high accuracy and low memory demands. Second, we develop a unified framework for nonlocal mean regularization algorithms to finely recover the MRI images from undersampled datasets. Finally, we show that our algorithms siginicantly improved the Cardiac MRI reconstruction in both signal to noise ratio and visual effects. |
