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, wherein decomposing the data fitting problem comprises splitting a first variable into at least two variables; obtaining, via the computing device, the plurality of sub-problem solutions for the k-space data, wherein obtaining the plurality of sub-problem solutions comprises performing operator splitting over each of the at least two variables independently; and reconstructing, via the computing device, the image based upon a weighted average of the plurality of sub-problem solutions for the k-space, wherein reconstructing the image comprises obtaining a solution for the first variable by a linear combination of the plurality of sub-problem solutions.