A computer-implemented method for reconstructing magnetic resonance images using a parallel computing platform comprising a host unit and a graphical processing device includes receiving a plurality of coil data sets from a magnetic resonance imaging system, each respective coil data set comprising scanner data and a coil sensitivity map associated with a distinct coil included in the magnetic resonance imaging system. An iterative compressed-sensing reconstruction process is applied to reconstruct an image based on the plurality of coil data sets. Each iteration of the iterative compressed-sensing reconstruction process comprises: individually transferring the plurality of coil data sets from the host unit to the graphical processing device using a plurality of asynchronous data streams, overlapping with transfer of the plurality of coil data sets, optimizing a plurality of data fidelity values on the graphical processing device, each respective data fidelity value corresponding to a distinct coil data set, and computing an estimated image on the graphical processing device based on the plurality of data fidelity values.