Joint k-TE Space Image Reconstruction and Data Fitting for T2 Mapping

Objectives: To develop a joint k-TE reconstruction algorithm to reconstruct the T2-weighted (T2W) images and T2 map simultaneously. Materials and Methods: The joint k-TE reconstruction model was formulated as an optimization problem subject to a self-consistency condition of the exponential decay relationship between the T2W images and T2 map. The objective function included a data fidelity term enforcing the agreement between the solution and the measured k-space data, together with a spatial regularization term on image properties of the T2W images. The optimization problem was solved using Alternating-Direction Method of Multipliers (ADMM). We tested the joint k-TE method in phantom data and healthy volunteer scans with fully-sampled and under-sampled k-space lines. Image quality of the reconstructed T2W images and T2 map, and the accuracy of T2 measurements derived by the joint k- TE and the conventional signal fitting method were compared. Results: The proposed method improved image quality with reduced noise and less artifacts on both T2W images and T2 map, and increased measurement consistency in T2 relaxation time measurements compared with the conventional method in all data sets. Conclusions: The proposed reconstruction method outperformed the conventional magnitude image-based signal fitting method in image quality and stability of quantitative T2 measurements