Optimal parallel MRI reconstruction over a convex solution space

In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem in the existing literature. 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 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.