Single‐step quantitative susceptibility mapping with variational penalties. (22nd June 2016) - Chatnuntawech, Itthi; McDaniel, Patrick; Cauley, Stephen F.; Gagoski, Borjan A.; Langkammer, Christian; Martin, Adrian; Grant, P. Ellen; Wald, Lawrence L.; Setsompop, Kawin; Adalsteinsson, Elfar; Bilgic, Berkin
Abstract : Quantitative susceptibility mapping (QSM) estimates the underlying tissue magnetic susceptibility from the gradient echo (GRE) phase signal through background phase removal and dipole inversion steps. Each of these steps typically requires the solution of an ill‐posed inverse problem and thus necessitates additional regularization. Recently developed single‐step QSM algorithms directly relate the unprocessed GRE phase to the unknown susceptibility distribution, thereby requiring the solution of a single inverse problem. In this work, we show that such a holistic approach provides susceptibility estimation with artifact mitigation and develop efficient algorithms that involve simple analytical solutions for all of the optimization steps. Our methods employ total variation (TV) and total generalized variation (TGV) to jointly perform the background removal and dipole inversion in a single step. Using multiple spherical mean value (SMV) kernels of varying radii permits high‐fidelity background removal whilst retaining the phase information in the cortex. Using numerical simulations, we demonstrate that the proposed single‐step methods reduce the reconstruction error by up to 66% relative to the multi‐step methods that involve SMV background filtering with the same number of SMV kernels, followed by TV‐ or TGV‐regularized dipole inversion. In vivo single‐step experiments demonstrate a dramatic reduction in dipole streaking artifacts and improved homogeneity of image contrast. These acquisitions employ the rapid three‐dimensional echo planar imaging (3D EPI) and Wave‐CAIPI (controlled aliasing in parallel imaging) trajectories for signal‐to‐noise ratio‐efficient whole‐brain imaging. Herein, we also demonstrate the multi‐echo capability of the Wave‐CAIPI sequence for the first time, and introduce an automated, phase‐sensitive coil sensitivity estimation scheme based on a 4‐s calibration acquisition. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : The tissue susceptibility distribution is directly estimated from the raw phase of a gradient echo acquisition by solving total variation (TV) and total generalized variation (TGV) regularized optimization problems. Efficient algorithms for the proposed single‐step quantitative susceptibility mapping (QSM) reconstructions, which permit analytical solutions to all the subproblems, are developed based on the alternating direction method of multipliers (ADMM). A dramatic reduction in dipole streaking artifacts and improved homogeneity of image contrast over conventional QSM are demonstrated using numerical simulations and in vivo experiments that were acquired using signal‐to‐noise ratio (SNR)‐efficient acquisitions including multi‐echo Wave‐CAIPI (controlled aliasing in parallel imaging) and three‐dimensional echo planar imaging (3D EPI).