Iterative reconstruction of magnetic resonance images from arbitrary samples in k-space

In magnetic resonance (MR) imaging, methods that use a non-Cartesian (e.g. spiral) sampling grid in k-space are becoming increasingly important. Reconstruction is then usually performed by resampling the data on a Cartesian grid, followed by FFT (gridding). In gridding, the weighting of the data to compensate for the varying density of the sampling scheme can lead to degradation of image quality. An iterative approach that avoids this problem is proposed. The two methods were compared using spiral k-space trajectories. Simulations were performed and showed better image quality and higher SNR in comparison to gridding based reconstruction.