1. A magnetic resonance (MR) imaging water-fat separation method, comprising the steps of: operating an MR data acquisition device with a data acquisition sequence that causes separated in-phase image raw measurement data and out-of-phase image raw measurement data to be acquired; entering said in-phase image raw measurement data and said out-of-phase raw image measurement data into an electronic memory representing k-space according to a k-space trajectory, with undersamplinq of k-space that causes less than an entirety of k-space to be filled with said in-phase image raw measurement data and said out-of-phase image raw measurement data; in computer, generating a system matrix according to said k-space trajectory; in said computer, reconstructing an in-phase image and an out-of-phase image from said in-phase and out-of-phase raw measurement data using a penalty function regularized iterative reconstruction; algorithm that embodies sad system matrix; and in said computer, calculating a water image and a fat image from said in-phase image and out-of-phase image, and making said water image and said fat image available at an output of said computer in electronic form, as respective data files.