Simple auto-calibrated gradient delay estimation from few spokes using Radial Intersections (RING)

Purpose: To develop a simple and robust tool for the estimation of gradient delays from highly undersampled radial k-space data. Theory: In radial imaging gradient delays induce parallel and orthogonal trajectory shifts, which can be described using an ellipse model. The intersection points of the radial spokes, which can be estimated by spoke-by-spoke comparison of k-space samples, distinctly determine the parameters of the ellipse. Using the proposed method (RING), these parameters can be obtained using a least-squares fit and utilized for the correction of gradient delays. Methods: The functionality and accuracy of the proposed RING method is validated and compared to correlation-based gradient-delay estimation from opposing spokes using numerical simulations, phantom and in vivo heart measurements. Results: In all experiments, RING robustly provides accurate gradient delay estimations even for as few as three radial spokes. Conclusions: The simple and straightforward to implement RING method provides accurate gradient delay estimation for highly undersampled radial imaging.