An accurate nonuniform fourier transform for SPRITE magnetic resonance imaging data

A new algorithm is proposed for computing the discrete Fourier Transform (DFT) of purely phase encoded data acquired during Magnetic Resonance Imaging (MRI) experiments. These experiments use the SPRITE (Single Point Ramped Imaging with T1 Enhancement) method and multiple-point acquisition, sampling data in a nonuniform manner that prohibits reconstruction by fast Fourier transform. The chirp z-transform algorithm of Rabiner, Schafer, and Rader can be combined with phase corrections to compute the DFT of this data to extremely high accuracy. This algorithm outperforms the interpolation methods that are traditionally used to process nonuniform data, both in terms of execution time and in terms of accuracy as compared to the DFT.