WARF: A WeightedSum Approach to Radial MRI Image Reconstruction With a Rotating RF Coil The recently developed singleelement surface rotating radiofrequency coil (RRFC) for magnetic resonance imaging (MRI) is able to acquire signals from around the subject in the manner of a multicoil 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 weightedsum 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 kspace 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 kspace 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.

Compressed Sensing: From Research to Clinical Practice With Deep Neural Networks: Shortening Scan Times for Magnetic Resonance Imaging Compressed sensing (CS) reconstruction methods leverage sparse structure in underlying signals to recover highresolution images from highly undersampled measurements. When applied to magnetic resonance imaging (MRI), CS has the potential to dramatically shorten MRI scan times, increase diagnostic value, and improve the overall patient experience. However, CS has several shortcomings that limit its clinical translation. These include 1) artifacts arising from inaccurate sparse modeling assumptions, 2) extensive parameter tuning required for each clinical application, and 3) clinically infeasible reconstruction times. Recently, CS has been extended to incorporate deep neural networks as a way of learning complex image priors from historical exam data. Commonly referred to as unrolled neural networks, these techniques have proven to be a compelling and practical approach to address the challenges of sparse CS. In this tutorial, we review the classical CS formulation and outline steps needed to transform this formulation into a deeplearningbased reconstruction framework. Supplementary opensource code in Python is used to demonstrate this approach with open databases. Further, we discuss considerations in applying unrolled neural networks in the clinical setting.