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 corresponds to a different image; c) reconstructing at least one image of the subject from the data acquired in step a) by: i) performing a rank minimization to minimize 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; wherein each subset of the acquired data contains data that are consistent only with other data in that subset of the acquired data and are otherwise inconsistent with data in other subsets of the acquired data.