Direct reconstruction of non-Cartesian k-space data using a nonuniform fast Fourier transform

An algorithm of Dutt and Rokhlin (SIAM J Sci Comput 1993;14: 1368-1383) for the computation of a fast Fourier transform (FFT) of nonuniformly-spaced d ata samples has been extended to two dimensions for application to MRI imag e reconstruction. The 2D nonuniform or generalized FFT (GFFT) was applied t o the reconstruction of simulated MRI data collected on radially oriented s inusoidal excursions in k-space (ROSE) and spiral k-space trajectories. The GFFT was compared to conventional Kaiser-Bessel kernel convolution regridd ing reconstruction in terms of image reconstruction quality and speed of co mputation. images reconstructed with the GFFT were similar in quality to th e Kaiser-Bessel kernel reconstructions for 256(2) pixel image reconstructio ns, and were more accurate for smaller 64(2) pixel image reconstructions. C lose inspection of the GFFT reveals it to be equivalent to a convolution re gridding method with a Gaussian kernel. The Gaussian kernel had been dismis sed in earlier literature as nonoptimal compared to the Kaiser-Bessel kerne l, but a theorem for the GFFT, bounding the approximation error, and the re sults of the numerical experiments presented here show that this dismissal was based on a nonoptimal selection of Gaussian function. (C) 2001 Wiley-Li ss, Inc.