Polar sampling in k‐space: Reconstruction effects

Magnetic resonance images are most commonly computed by taking the inverse Fourier transform of the k-space data. This transformation can potentially create artifacts in the image, depending on the reconstruction algorithm used. For equally spaced radial and azimuthal k-space polar sampling, both gridding and convolution backprojection are applicable. However, these algorithms potentially can yield different resolution, signal-to-noise ratio, and aliasing characteristics in the reconstructed image. Here, these effects are analyzed and their tradeoffs are discussed. It is shown that, provided the modulation transfer function and the signal-to-noise ratio are considered together, these algorithms perform similarly. In contrast, their aliasing behavior is different, since their respective point spread functions (PSF) differ. In gridding, the PSF is composed of the mainlobe and ringlobes that lead to aliasing. Conversely, there are no ringlobes in the convolution backprojection PSF, thus radial aliasing effects are minimized. Also, a hybrid gridding and convolution backprojection reconstruction is presented for radially nonequidistant k-space polar sampling.