Splines on disk and cylindrical domains with application to MRI reconstruction

Date

2017-05

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Abstract

MRI is an accurate and non-invasive imaging technique used for a wide range of disease diagnosis. A problem remaining in MRI is the long scanning time which results in image motion artifact and patient discomfort. Techniques that can reduce acquisition time by sampling less data are usually accompanied with the reduction in image quality. This thesis is thus aiming to develop advanced reconstruction algorithm that can support data acquisition technique with low sampling rate. We cast the problem as a penalized weighted regression with a penalty term. We build a novel algorithm to construct the Kimeldorf-Wahba representation on both unit disk domain and cylindrical domain, which can be applied to the reconstruction of 2D MRI and 3D MRI, respectively.

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Keywords

Magnetic resonance imaging, Low sampling rate, Reproducing kernel Hilbert space, Cubic spline, Linear spline

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