Parallel MRI Reconstruction by Convex Optimization

TL;DR

This paper introduces a convex optimization approach for parallel MRI reconstruction that guarantees a globally optimal solution for the magnitude image, improving reconstruction quality over existing methods.

Contribution

It formulates a convex optimization problem for magnitude image reconstruction in pMRI, providing a unique and globally optimal solution, unlike traditional nonconvex methods.

Findings

Convex formulation yields a unique solution.

Superior reconstruction performance on in-vivo data.

Outperforms existing algorithms like GRAPPA.

Abstract

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.