1. A method for reconstructing an image using a medical imaging system, the steps of the method comprising: a) acquiring data from a subject with the imaging system; b) initializing an image matrix having columns that each correspond to a different image; c) reconstructing at least one image of the subject from the data acquired in step a) by: i) minimizing a matrix rank of the image matrix; and ii) constraining the rank minimization of step c)i) subject to a consistency condition that promotes a forward projection of each column in the image matrix to be consistent with a different subset of the acquired data, each subset of the acquired data containing data that are consistent with each other while being inconsistent with data in other subsets of the acquired data.