1. A computer-implemented-method for rendering an image from a set of k-space data, comprising the steps of: constructing a cost functional based at least in part on said set of k-space data, said cost functional comprising 
 λ∥φ(ƒ)∥ 1 +∥W ( Aƒ−y )∥ 2 2 wherein ƒ is a vector representing said set of image-space data, λ is a Lagrange multiplier, y is a vector representing said set of k-space data, φ(ƒ) is an operator which transforms ƒ into a sparse representation, A is a Fourier operator which maps said set of image-space data into said set of k-space data, and W is said weighting matrix; iteratively solving for a set of image-space data, wherein said step of iteratively solving comprises the step of minimizing said cost functional; and, rendering said image from said set of image-space data.