Back to Journals » Reports in Medical Imaging » Volume 7

Reconstructing brain magnetic susceptibility distributions from T2* phase images by TV-regularized 2-subproblem split Bregman iterations

Authors Chen Z, Calhoun V

Received 14 September 2013

Accepted for publication 4 November 2013

Published 24 March 2014 Volume 2014:7 Pages 41—53


Checked for plagiarism Yes

Review by Single anonymous peer review

Peer reviewer comments 5

Zikuan Chen,1 Vince D Calhoun1,2

1The Mind Research Network and LBERI, Albuquerque, NM, USA; 2University of New Mexico, ECE Dept, Albuquerque, NM, USA

Abstract: The underlying source of brain imaging by T2*-weighted magnetic resonance imaging (T2*MRI) is mainly due to the intracranial inhomogeneous magnetic susceptibility distribution (denoted by χ). We can reconstruct the source χ by two computational steps: first, calculate a fieldmap from a T2* phase image and then second, calculate a χ map from the fieldmap. The internal χ distribution reconstruction from observed T2* phase images is termed χ tomography, which connotes the digital source reproduction with spatial conformance by solving inverse problems in the context of medical imaging. In the small phase angle regime, the T2* phase image remains unwrapped (−π<phase angle<π) and it is linearly related to the fieldmap by a scaling factor. However, the second inverse step (calculating a χ map from a fieldmap) is a severely ill-posed 3D deconvolution problem due to an unusual bipolar-valued kernel (dipole field kernel). We have reported on a 3-subproblem split Bregman iteration algorithm for total variation-regularized 3D χ reconstruction; in this paper, we report on a 2-subproblem split Bregman iteration algorithm with easy implementation. We validate the 3D χ tomography algorithms by numerical simulations and phantom experiments. We also demonstrate the feasibility of 3D χ tomography for obtaining in vivo brain χ states at 2 mm spatial resolution.

Keywords: T2*-weighted MRI (T2*MRI), magnetic susceptibility tomography (χ tomography), dipole effect, 3D deconvolution, filter truncation, total variation (TV), split Bregman iteration, computed inverse magnetic resonance imaging (CIMRI)

Creative Commons License This work is published and licensed by Dove Medical Press Limited. The full terms of this license are available at and incorporate the Creative Commons Attribution - Non Commercial (unported, v3.0) License. By accessing the work you hereby accept the Terms. Non-commercial uses of the work are permitted without any further permission from Dove Medical Press Limited, provided the work is properly attributed. For permission for commercial use of this work, please see paragraphs 4.2 and 5 of our Terms.

Download Article [PDF]  View Full Text [HTML][Machine readable]