This technology includes a method to reduce scanning time while retaining high image quality during MRI scans. A reconstructed image is rendered from a set of MRI data by first estimating an image with an area which does not contain artifacts or has an artifact with a relatively small magnitude. Corresponding data elements in the estimated image and a trial image are processed, for instance by multiplication, to generate an intermediate data set. The intermediate data set is transformed and minimized iteratively to generate a reconstructed image that is free or substantially free of artifacts. A sparsifying transformation may be applied to generate the reconstructed image.