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*-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 algo- rithms 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)