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

Abstract

R* mapping is a useful tool in blood-oxygen-level dependent fMRI due to its quantitative-nature. However, like T*-weighted imaging, standard R* mapping based on multi-echo EPI suffers from geometric distortion, due to strong off-resonance near the air-tissue interface. Joint mapping of R* and off-resonance can correct the geometric distortion and is less susceptible to motion artifacts. Single-shot joint mapping of R* 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* 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* map.

Myocardial T1 and T2 quantification and water–fat separation using cardiac MR fingerprinting with rosette trajectories at 3T and 1.5T

“…This signal cancellation can lead to a suppression of the signal from these off‐resonance spins. Interested readers are referred to these excellent works 9,40‐45,47,48 for more details on the spectral properties of rosette trajectories.…”

“…off-resonance spins. Interested readers are referred to these excellent works 9,[40][41][42][43][44][45]47,48 for more details on the spectral properties of rosette trajectories.…”

SUPER: A blockwise curve‐fitting method for accelerating MR parametric mapping with fast reconstruction

“…Model‐based reconstruction is another broad type of acceleration methods, which, in its simplest form, use an analytical model (e.g., mono‐exponential model for T 1 mapping) as a constraint for the multi‐contrast data to reduce the k‐space sampling . Additionally, model‐based reconstruction was often combined with Tikhonov regularization, low‐rank constraints, or compressed sensing to further improve the k‐space undersampling rate.…”

3D whole-heart isotropic sub-millimeter resolution coronary magnetic resonance angiography with non-rigid motion-compensated PROST

“…The positive parameter μ controls the tradeoff between the regularization and the fidelity of the reconstructed motion-corrected 3D CMRA image with regard to the acquired data, whereas λ controls the denoising level. Similar to [29,36], Eq. (1) can be efficiently solved by operator-splitting via alternating direction method of multipliers (ADMM), which divides the optimization process into three iterative simpler sub-problems:…”