Regularized Estimation of Main and RF Field Inhomogeneity and Longitudinal Relaxation Rate in Magnetic Resonance Imaging

Regularized Estimation of Main and RF Field Inhomogeneity and Longitudinal Relaxation Rate in Magnetic Resonance Imaging by Amanda K. Funai Chair: Jeffrey A. Fessler In designing pulses and algorithms for magnetic resonance imaging, several simplifications to the Bloch equation are used. However, as magnetic resonance (MR) imaging requires higher temporal resolution and faster pulses are used, simplifications such as uniform main field (B0) strength and uniform radio-frequency (RF) transmit coil field (B + 1 ) strength no longer apply. Ignoring these non-uniformities can cause significant distortions. Accurate maps of the main and RF transmit coil field inhomogeneity are required for accurate pulse design and imaging. Standard estimation methods yield noisy maps, particularly in image regions having low spin density, and ignore other important factors, such as slice selection effects in B1 mapping and T2 effects in B0 mapping. This thesis uses more accurate signal models for the MR scans to derive iterative regularized estimators that show improvements over the conventional unregularized methods through Cramér-Rao Bound analysis, simulations, and real MR data. In fast MR imaging with long readout times, field inhomogeneity causes image distortion and blurring. This thesis first describes regularized methods for estimation of the off-resonance frequency at each voxel from two or more MR scans having different echo