Youngwook Kee1, Kofi Deh2, Alexey Dimov3, Pascal Spincemaille1, Yi Wang1,3. 1. Department of Radiology, Weill Cornell Medical College, New York, New York, USA. 2. Department of Physiology, Systems Biology and Biophysics, Weill Cornell Medical College, New York, New York, USA. 3. Department of Biomedical Engineering, Cornell University, Ithaca, New York, USA.
Abstract
PURPOSE: To investigate the computational aspects of the prior term in quantitative susceptibility mapping (QSM) by (i) comparing the Gauss-Newton conjugate gradient (GNCG) algorithm that uses numerical conditioning (ie, modifies the prior term) with a primal-dual (PD) formulation that avoids this, and (ii) carrying out a comparison between a central and forward difference scheme for the discretization of the prior term. THEORY AND METHODS: A spatially continuous formulation of the regularized QSM inversion problem and its PD formulation were derived. The Chambolle-Pock algorithm for PD was implemented and its convergence behavior was compared with that of GNCG for the original QSM. Forward and central difference schemes were compared in terms of the presence of checkerboard artifacts. All methods were tested and validated on a gadolinium phantom, ex vivo brain blocks, and in vivo brain MRI data with respect to COSMOS. RESULTS: The PD approach provided a faster convergence rate than GNCG. The GNCG convergence rate slowed considerably with smaller (more accurate) values of the conditioning parameter. Using a forward difference suppressed the checkerboard artifacts in QSM, as compared with the central difference. The accuracy of PD and GNCG were validated based on excellent correlation with COSMOS. CONCLUSIONS: The PD approach with forward difference for the gradient showed improved convergence and accuracy over the GNCG method using central difference. Magn Reson Med 78:2416-2427, 2017.
PURPOSE: To investigate the computational aspects of the prior term in quantitative susceptibility mapping (QSM) by (i) comparing the Gauss-Newton conjugate gradient (GNCG) algorithm that uses numerical conditioning (ie, modifies the prior term) with a primal-dual (PD) formulation that avoids this, and (ii) carrying out a comparison between a central and forward difference scheme for the discretization of the prior term. THEORY AND METHODS: A spatially continuous formulation of the regularized QSM inversion problem and its PD formulation were derived. The Chambolle-Pock algorithm for PD was implemented and its convergence behavior was compared with that of GNCG for the original QSM. Forward and central difference schemes were compared in terms of the presence of checkerboard artifacts. All methods were tested and validated on a gadolinium phantom, ex vivo brain blocks, and in vivo brain MRI data with respect to COSMOS. RESULTS: The PD approach provided a faster convergence rate than GNCG. The GNCG convergence rate slowed considerably with smaller (more accurate) values of the conditioning parameter. Using a forward difference suppressed the checkerboard artifacts in QSM, as compared with the central difference. The accuracy of PD and GNCG were validated based on excellent correlation with COSMOS. CONCLUSIONS: The PD approach with forward difference for the gradient showed improved convergence and accuracy over the GNCG method using central difference. Magn Reson Med 78:2416-2427, 2017.
Authors: Zhe Liu; Yan Wen; Pascal Spincemaille; Shun Zhang; Yihao Yao; Thanh D Nguyen; Yi Wang Journal: Magn Reson Med Date: 2019-08-11 Impact factor: 4.668
Authors: Christian Langkammer; Ferdinand Schweser; Karin Shmueli; Christian Kames; Xu Li; Li Guo; Carlos Milovic; Jinsuh Kim; Hongjiang Wei; Kristian Bredies; Sagar Buch; Yihao Guo; Zhe Liu; Jakob Meineke; Alexander Rauscher; José P Marques; Berkin Bilgic Journal: Magn Reson Med Date: 2017-07-31 Impact factor: 4.668