Abstract
Motivated by work in the area of dynamic magnetic resonance imaging (MRI), we develop a new approach to the problem of reduced-order MRI acquisition. Efforts in this field have concentrated on the use of Fourier and singular value decomposition (SVD) methods to obtain low-order representations of an entire image plane. We augment this work to the case of imaging an arbitrarily-shaped region of interest (ROI) embedded within the full image. After developing a natural error metric for this problem, we show that determining the minimal order required to meet a prescribed error level is in general intractable, but can be solved under certain assumptions. We then develop an optimization approach to the related problem of minimizing the error for a given order. Finally, we demonstrate the utility of this approach and its advantages over existing Fourier and SVD methods on a number of MRI images.
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