  In parallel magnetic resonance imaging (pMRI), to find a joint solution for
the image and coil sensitivity functions is a nonlinear and nonconvex problem.
A class of algorithms reconstruct sensitivity encoded images of the coils first
followed by the magnitude only image reconstruction, e.g. GRAPPA. It is shown
in this paper that, if only the magnitude image is reconstructed, there exists
a convex solution space for the magnitude image and sensitivity encoded images.
This solution space enables formulation of a regularized convex optimization
problem and leads to a globally optimal and unique solution for the magnitude
image reconstruction. Its applications to in-vivo MRI data sets result in
superior reconstruction performance compared with other algorithms.
