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

Abstract

The underlying source of brain imaging by T2&z.ast;-weighted magnetic resonance imaging (T2&z.ast;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&z.ast; phase image and then second, calculate a χ map from the fieldmap. The internal χ distribution reconstruction from observed T2&z.ast; phase images is termed χtomography, 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&z.ast; 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. © 2014 Chen and Calhoun. This work is published by Dove Medical Press Limited.