Creating a library of generalized Fourier sampling patterns for irregular 2D regions of support

Multiple-region MRI (mrMRI) represents a generalization of the Shannon sampling theorem to permit sparse k-space sampling whenever the scanned object or its high-contrast edges are confined to multiple known regions. Use of an optimal mrMRI sampling pattern produces an image with root-mean-squared (RMS) noise over the supporting regions equal to the RMS noise in a conventional Fourier image with the same total area of support. Analytical solutions for such sampling patterns have been described previously for all arrangements of two or three (noncollinear) supporting regions. This work describes a robust numerical method for creating a library of optimal and near-optimal mrMRI sampling patterns for more complicated geometries. The average noise amplification over all sampling patterns in the demonstration library was only 4%, with 30% of the sampling patterns resulting in no noise amplification whatsoever.