1. A method of reconstructing an image through solution of a data fitting problem, wherein the data fitting problem is not susceptible to efficient solution as a whole, comprising: gathering, via a computing device, k-space image data; selecting a data fitting problem solution algorithm for the k-space data; decomposing the data fitting problem solution into a plurality of sub-problem solutions each susceptible to efficient solution separately for the k-space data; obtaining, via the computing device, the plurality of sub-problem solutions far the k-space data; reconstructing, via the computing device, the image based upon a weighted average of the plurality of sub-problem solutions for the k-space