Application of Recovery of Parametric Manifold from Reduced Measurements to Magnetic Resonance Parameter Mapping
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In the past two decades, a bunch of groups show great interest in magnetic resonance (MR) quantitative imaging including MR parameter mapping, diffusion tensor imaging, and dynamic cardiac perfusion because of the great potential of MR quantitative imaging in clinical application. The conventional methods require the acquisition of a sequence of images at different time points to extract the quantitative parameters. However, these methods are facing the challenge of the tradeoff between spatial resolution and temporal resolution, because the amount of data required increases exponentially as the physical dimension increases. To address this problem, a number of methods have been proposed. In this thesis, we propose a novel manifold recovery approach that obtains the quantitative map from highly reduced measurements. The performance of the proposed method is demonstrated by the comparison to the existing method using simulated and real datasets on MR parametric mapping.