Selection of arbitrary 3D Cartesian sampling patterns for support-contrained MRI, parallel MRI, and dynamic MRI can be heuristical, and g-factor calculations require a computationally expensive simulation. To provide theoretical guidance and a method to optimize 3D Cartesian sampling, a novel concept of a differential distribution is introduced to represent a distribution of pairwise differences between sample locations, and is related to point-spread-functions. Its relationship to noise amplification in a generalized sensitivity encoding model and linear reconstruction is then used to efficiently optimize multidimensional k-space sampling. Examples in support-constrained MRI, parallel MRI, and dynamic MRI demonstrate reduced noise amplification
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