Direct calculation of MRF dictionaries can be prohibitive when high resolution or multi-component chemical exchange effects are taken into account. To address this problem, we propose a new approach based on the randomized SVD (rSVD) to generate a low rank approximation of the large sized dictionary without the need of pre-calculating, storing, or loading the dictionary. This in return saves significant amounts of memory, and speeds up the template matching process of MRF. In addition, when combined with polynomial fitting, one can generate MRF maps with arbitrary high resolution dictionaries.
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