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 fast Fourier transforms (gridding). In gridding, the weighting of the data to compensate for the varying density of the sampling scheme can lead to a 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 signal-to-noise ratio in comparison to gridding based reconstruction.