1. A method for generating a magnetic resonance (MR) image, the method comprising: a) acquiring k-space MR data; b) reconstructing an MR image from the k-space MR data by: i) using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes an optimization problem into subproblems; and ii) decomposing at least one of the subproblems based on a Woodbury matrix identity and using a diagonal preconditioner (PC) based on non-Toeplitz models.