1. A system for reconstructing an image from undersampled, multi-image k-space data, the system comprising: an imaging apparatus configured to generate a first undersampled image dataset defined in a first dimension and to generate a second undersampled image dataset defined in the first dimension; a computer-readable medium having computer-readable instructions stored therein which are programmed to (a) receive the first undersampled image dataset; (b) receive the second undersampled image dataset, the first undersampled image dataset and the second undersampled image dataset defining a multi-image dimension; (c) define an ordering for a plurality of pixels of the first dimension in the multi-image dimension; (d) sort the first undersampled image dataset and the second undersampled image dataset in the multi-image dimension based on the defined ordering; (e) define a first constraint in the first dimension using the unsorted first and second undersampled image datasets; (f) define a second constraint in the multi-image dimension using the sorted first and second undersampled image datasets; and (g) reconstruct an image using the applied first constraint and the applied second constraint while preserving fidelity to the first undersampled image dataset and the second undersampled image dataset; and a processor operably coupled to the computer-readable medium and configured to execute the instructions.