We present a method for combining the data retrieved by multiple coils of a
Magnetic Resonance Imaging (MRI) system with the a priori assumption of
compressed sensing to reconstruct a single image. The final image is the result
of an optimization problem that only includes constraints based on fundamental
physics (Maxwell's equations and the Biot-Savart law) and accepted phenomena
(e.g. sparsity in the Wavelet domain). The problem is solved using an
alternating minimization approach: two convex optimization problems are
alternately solved, one with the Fast Iterative Shrinkage Threshold Algorithm
(FISTA) and the other with the Primal-Dual Hybrid Gradient (PDHG) method. We
show results on simulated data as well as data of the knee, brain, and ankle.
In all cases studied, results from the new algorithm show higher quality and
increased detail when compared to conventional reconstruction algorithms