Reconstruction methods for fast magnetic resonance imaging

Magnetic Resonance Imaging (MRI) is a very successful method for imaging the body, due in large part to the excellent soft tissue contrast that can be obtained. A major challenge for MRI is reducing the long scan times that can be required to obtain an image. Fast Magnetic Resonance Imaging uses sophisticated encoding techniques, such as non-Cartesian k-space trajectories and parallel imaging, to reduce the scan times required for MRI and requires advanced MRI scanner hardware and reconstruction methods.; This work focuses on reconstruction methods for fast MRI. In this dissertation, improvements that can be made to the gridding method for reconstructing MR images encoded using non-Cartesian k-space trajectories are described. In addition, a new method called Anti-aliasing Partially Parallel Encoded Acquisition Reconstruction (APPEAR) is introduced and developed for reconstructing magnetic resonance images encoded using non-Cartesian k-space trajectories and parallel imaging.; The improvements to the gridding method described in this work include using a minimal oversampling ratio, improved design for a sampled convolution kernel, reduced field-of-view reconstruction and using block grid storage. Used together, these improvements can result in a three-fold reduction in computation memory requirements and can reduce the reconstruction time by a factor of approximately thirty times for three-dimensional (3-D) image reconstruction, compared to the use of a Kaiser-Bessel convolution kernel on a 2X oversampled grid using conventional line-by-line and slice-by-slice grid storage.; The APPEAR method is a parallel imaging reconstruction method that can be used with arbitrary k-space trajectories, is non-iterative and does not peed to estimate coil sensitivity functions. In this work, the mathematical framework for parallel imaging reconstruction is extended and this extended framework is used to develop and justify the APPEAR method. The concept of correlation values is introduced and used to improve the efficiency of the APPEAR method. Phantom and in-vivo results are shown for 1-D non-Cartesian k-space trajectories and variable-density spiral k-space trajectories.