Self-calibrated Interpolation of Undersampled Non-Cartesian Magnetic Resonance Imaging Data

Abstract

Effective image reconstructions from undersampled data have enabled acceleration of Magnetic Resonance Imaging (MRI) data acquisitions. Among them, the k-space reconstruction method such as Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) has been an active area of research. The k-space reconstruction of non-Cartesian sampling requires Region-specific Interpolation Kernels (RIKs) due to irregular undersampling patterns, while other types of kernels such as angularly independent/readout dependent were found to provide degraded reconstructions. The conventional strategy for calculating RIKs needs additional calibration scans, thereby increasing total scan time. The main contribution of this thesis is to obtain RIKs without additional calibration data. The proposed method, Self-calibrated Interpolation of Non-Cartesian data with GRAPPA (SING), generates autocalibrating signal (ACS) for calibrations of different RIKs with distinct geometry patterns. A local signal-to-noise (SNR) regularization is proposed to solve linear calibration systems via regularized least-squares. The proposed regularization motivated by the inherent regularization effect of noise in through time (TT)-GRAPPA, enables a balance between the contributions of signal and noise in the estimation of the RIKs. The SING method is validated using simulation and in vivo data, which include 2D cine, 3D whole-heart coronary, and dynamic contrast enhanced MRI prostate data. SING is also compared to reconstruction methods including gridding, TT-GRAPPA, conjugate gradient (CG)-SENSE, and compressed sensing (CS). The experimental results show that SING has similar reconstruction performance with TT-GRAPPA without using additional calibration scans. SING enables improved reconstructions compared to gridding, CG-SENSE, and CS.