A method of reconstructing magnetic resonance (MR) image data from k-space data. The method includes obtaining k-space data of an image region of a subject; and reconstructing, using a sparse image coding procedure, the MR image data from the k-space data by performing an iterative optimization method. The optimization method includes a data consistency iteration step and a denoising iteration step applied to MR image data generated by the data consistency iteration step. The denoising iteration step incorporates a sparsifying operation to provide a sparse representation of the MR image data for the imaged region as an input to the data consistency iteration step.