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

Multiple-region MRI (mrMRI) represents a generalization of the Shannon samp ling theorem to permit sparse k-space sampling whenever the scanned object or its high-contrast edges are confined to multiple known regions. Use of a n optimal mrMRI sampling pattern produces an image with root-mean-squared ( RMS) noise over the supporting regions equal to the RMS noise in a conventi onal Fourier image with the same total area of support. Analytical solution s for such sampling patterns have been described previously for all arrange ments of two or three (noncollinear) supporting regions. This work describe s a robust numerical method for creating a library of optimal and near-opti mal mrMRI sampling patterns for more complicated geometries. The average no ise amplification over all sampling patterns in the demonstration library w as only 4%, with 30% of the sampling patterns resulting in no noise amplifi cation whatsoever. (C) 2001 Wiley-Liss, Inc.