An algorithm for numerical calculation of the l-space data-weighting for polarly sampled trajectories: Application to spiral imaging

Image reconstruction of data sampled into a non-uniform k-space grid requires appropriate data weighting and, for spiral-scan raw data, this weighting is usually calculated analytically under the assumption of uniform radial k-space sampling. This paper presents a simple and efficient algorithm for explicit numerical calculation of the data weighting for generalised polarly sampled k-space trajectories. The algorithm has been tested against both simulated data and data from experimental spiral-scan imaging and clearly provides significant improvements in image reconstruction when the radial uniformity of the k-space trajectory is poor.