Iterative reconstructions for multi-contrast multidimensional non-Cartesian MRI can require considerable computation time, with a large fraction dedicated to non-uniform fast Fourier transforms (NUFFTs). The Toeplitz approach has been previously shown to allow NUFFT operations to be replaced by computationally efficient fast Fourier transforms (FFTs) without loss of accuracy. Herein, we combine this approach with a 3D multi-contrast low-rank cardiac-motion-corrected radial reconstruction with low-rank patch-based regularisation to achieve a ~13.3-fold computational speed-up.
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