Described here is a system and method for image reconstruction that can automatically and iteratively produce multiple images from one set of acquired data, in which each of these multiple images corresponds to a subset of the acquired data that is self-consistent, but inconsistent with other subsets of the acquired data. The image reconstruction includes iteratively minimizing the rank of an image matrix whose columns each correspond to a different image. The rank minimization is constrained subject to a consistency condition that enforces consistency between the forward projection of each column in the image matrix and a respective subset of the acquired data that contains data that is consistent with data in the subset, but inconsistent with data not in the subset.