On optimality and efficiency of parallel magnetic resonance imaging reconstruction: challenges and solutions

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Nana, Roger
Hu, Xiaoping
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Imaging speed is an important issue in magnetic resonance imaging (MRI), as subject motion during image acquisition is liable to produce artifacts in the image. However, the speed at which data can be collected in conventional MRI is fundamentally limited by physical and physiological constraints. Parallel MRI is a technique that utilizes multiple receiver coils to increase the imaging speed beyond previous limits by reducing the amount of acquired data without degrading the image quality. In order to remove the image aliasing due to k-space undersampling, parallel MRI reconstructions invert the encoding matrix that describes the net effect of the magnetic field gradient encoding and the coil sensitivity profiles. The accuracy, stability, and efficiency of a matrix inversion strategy largely dictate the quality of the reconstructed image. This thesis addresses five specific issues pertaining to this linear inverse problem with practical solutions to improve clinical and research applications. First, for reconstruction algorithms adopting a k-space interpolation approach to the linear inverse problem, two methods are introduced that automatically select the optimal k-space subset samples participating in the synthesis of a missing datum, guaranteeing an optimal compromise between accuracy and stability, i.e. the best balance between artifacts and signal-to-noise ratio (SNR). While the former is based on cross-validation re-sampling technique, the second utilizes a newly introduced data consistency error (DCE) metric that exploits the shift invariance property of the reconstruction kernel to provide a goodness measure of k-space interpolation in parallel MRI. Additionally, the utility of DCE as a metric for characterizing and comparing reconstruction methods is demonstrated. Second, a DCE-based strategy is introduced to improve reconstruction efficiency in real time parallel dynamic MRI. Third, an efficient and reliable reconstruction method that operates on gridded k-space for parallel MRI using non-Cartesian trajectories is introduced with a significant computational gain for applications involving repetitive measurements. Finally, a pulse sequence that combines parallel MRI and multi-echo strategy is introduced for improving SNR and reducing the geometric distortion in diffusion tensor imaging. In addition, the sequence inherently provides a T2 map, complementing information that can be useful for some applications.
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