Non-Uniform Sampling Methods for MRI

Simple Cartesian scans, which collect Fourier transform data on a uniformly-spaced grid in the frequency domain, are by far the most common in MRI. But non-Cartesian trajectories such as spirals and radial scans have become popular for their speed and for other benefits, like making motion-correction easier [12]. A major problem in such scans, however, is reconstructing from nonuniform data, which cannot be performed by a standard fast Fourier transform (FFT) as in the Cartesian case. Here, we briefly describe the most common reconstruction methods and the non-uniform fast Fourier transform (NFFT) needed to complete the computations quickly. We then give an overview of several current methods for choosing a density compensation function (DCF) and suggest some possible improvements.