WARF: a weighted-sum approach to radial MRI image reconstruction with a rotating RF coil

The recently developed single-element surface rotating radio-frequency coil (RRFC) for magnetic resonance imaging (MRI) is able to acquire signals from around the subject in the manner of a multi-coil array, while exhibiting simplified construction and no coil size restrictions. Herein, we present a novel image reconstruction algorithm for data acquired with the RRFC, which we label WARF (a weighted-sum approach to radial MRI image reconstruction with a rotating RF coil). The algorithm approaches the reconstruction problem by considering each image pixel to be a weighted sum of all acquired k-space data, which is already the case implicitly in several established methods. The problem is thus posed as one of solving for the appropriate weights directly. The theory underlying WARF is presented, and several measures to improve the computational efficiency of a practical implementation are considered. We note that while still computationally expensive, the calculation of the weights themselves would not necessarily need to be repeated each time the algorithm is applied. MR data are simulated for imaging schemes involving the rotating RF coil with both ideal and variable angular velocities, and for the case where the k-space locations of the radial trajectory are deviated from their intended positions. The WARF reconstruction algorithm is applied to each simulated data set, and compared with reconstructions from existing methods, where it is seen to demonstrate a robustness to velocity variation and the suppression of artefacts arising from a deviated trajectory. Finally, WARF is applied to experimental rotating RF coil data, where it is shown to yield good quality images.