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 data samples has been extended to two dimensions for application to MRI image reconstruction. The 2D nonuniform or generalized FFT (GFFT) was applied to the reconstruction of simulated MRI data collected on radially oriented sinusoidal excursions in k-space (ROSE) and spiral k-space trajectories. The GFFT was compared to conventional Kaiser-Bessel kernel convolution regridding reconstruction in terms of image reconstruction quality and speed of computation. Images reconstructed with the GFFT were similar in quality to the Kaiser-Bessel kernel reconstructions for 256(2) pixel image reconstructions, and were more accurate for smaller 64(2) pixel image reconstructions. Close inspection of the GFFT reveals it to be equivalent to a convolution regridding method with a Gaussian kernel. The Gaussian kernel had been dismissed in earlier literature as nonoptimal compared to the Kaiser-Bessel kernel, but a theorem for the GFFT, bounding the approximation error, and the results of the numerical experiments presented here show that this dismissal was based on a nonoptimal selection of Gaussian function.