1. A method for producing a sequence of magnetic resonance imaging (MRI) images, comprising: a. acquiring an acquired plurality of k-space data sets, wherein the acquired plurality of k-space data sets are acquired during a corresponding plurality of MRI scans taken over a corresponding plurality of time periods; b. reconstructing a sequence of MRI images from the acquired plurality of k-space data sets, wherein each MRI image of the sequence of MRI images is reconstructed from a corresponding k-space data set of the plurality of k-space data sets; c. applying a constraint to the sequence of MRI images in the image domain, wherein the constraint is applied to a portion of each MRI image that is slow-moving, wherein application of the constraint to the sequence of MRI images in the image domain modifies the sequence of MRI images; d. projecting each of the modified sequence of MRI images into k-space to create a projected plurality of k-space data sets; e. applying a fidelity operator to the projected plurality of k-space data sets, wherein the fidelity operator replaces at least a portion of the k-space data in the k-space data sets of the projected plurality of k-space data sets with the corresponding k-space data from the acquired plurality of k-space data sets, wherein the replacement of at least a portion of the k-space data in the projected plurality of k-space data sets further modifies the projected plurality of k-space data sets; and f. reconstructing an output sequence of MRI images from the modified projected plurality of k-space data sets.