  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
