Magnetic resonance (MR) imaging is a non-invasive medical imaging tech- nique to visualize detailed internal structure. Magnetic resonance imaging (MRI) provides great soft tissue contrast compared with other imaging modalities, which makes it especially useful in imaging the brain, the heart, and the musculoskeletal system. Magnetic resonance imaging speed is important especially in dynamic cardiac applications, which involve respiratory motion and heart motion. Patient safety considerations limit further use of faster gradients or higher RF power to speed up the pulse sequence beyond current technology.

With the introduction of reduced-data MR imaging methods, increasing acquisi- tion speed has become possible without requiring a higher gradient system. Reduced- data MR imaging techniques have significantly reduced acquisition time, decreased motion artifacts, and increased spatial or temporal resolution. Various reduced-data imaging methods utilize data redundancy to increase imaging speed, but carry a price for higher imaging speed. This may be a signal-to-noise ratio (SNR) penalty, reduced resolution, or a combination of both. Many methods sacrifice edge information in favor of SNR gain, which is not preferable for applications which require accurate detection of myocardial boundaries.

This thesis presents a novel reduced-data imaging method, PINOT (Parallel Imaging and NOquist in Tandem), to accelerate MR imaging. PINOT does not apply any filter or interpolation, therefore preserves the edge details, with exibility of improving SNR by regularization. A sampling scheme is designed for this method and the noise behavior is analyzed using the pseudo-replica method. The Conjugate-gradient (CG) method is used to alleviate the computational cost. Additional time savings is achieved by providing a favorable initial estimate. Regularized PINOT uses Tikhonov regularization on highly accelerated MRI to relieve the noise penalty.

Another contribution is to exploit the data redundancy from parallel imaging, rFOV and partial Fourier methods. A Gerchberg Reduced Iterative System (GRIS), implemented with the Gerchberg-Papoulis (GP) iterative algorithm is introduced. Under the GRIS, which utilizes a temporal band-limitation constraint in the image reconstruction, a variant of Noquist called iterative implementation iNoquist (iterative Noquist) is proposed. Utilizing a different source of prior information, first combining iNoquist and Partial Fourier technique (phase-constrained iNoquist) and further integrating with parallel imaging methods (PINOT-GRIS) are presented to achieve additional acceleration gains.