An Efficient Reconstruction Algorithm Based on the Alternating Direction Method of Multipliers for Joint Estimation of ${R}_{{2}}^{*}$ and Off-Resonance in fMRI

R*
₂
mapping is a useful tool in blood-oxygen-level dependent fMRI due to its quantitative-nature. However, like T*
₂
-weighted imaging, standard R*
₂
mapping based on multi-echo EPI suffers from geometric distortion, due to strong off-resonance near the air-tissue interface. Joint mapping of R*
₂
and off-resonance can correct the geometric distortion and is less susceptible to motion artifacts. Single-shot joint mapping of R*
₂
and off-resonance is possible with a rosette trajectory due to its frequent sampling of the k-space center. However, the corresponding reconstruction is nonlinear, ill-conditioned, large-scale, and computationally inefficient with current algorithms. In this paper, we propose a novel algorithm for joint mapping of R*
₂
and off-resonance, using rosette k-space trajectories. The new algorithm, based on the alternating direction method of multipliers, improves the reconstruction efficiency by simplifying the original complicated cost function into a composition of simpler optimization steps. Compared with a recently developed trust region algorithm, the new algorithm achieves the same accuracy and an acceleration of threefold to sixfold in reconstruction time. Based on the new algorithm, we present simulation and in vivo data from single-shot, double-shot, and quadruple-shot rosettes and demonstrate the improved image quality and reduction of distortions in the reconstructed R*
₂
map.