1. A method for reconstructing an image of a subject from image data acquired with a medical imaging system, the steps comprising: a) acquiring, with the medical imaging system, image data from the subject; b) producing an estimate of a spatial support of the subject; c) producing an estimate image of the subject; and d) reconstructing an image of the subject using the produced estimate of the spatial support of the subject, the produced estimate image, and a compressed sensing algorithm; wherein the produced estimate of the spatial support of the subject is used in step d) by forming a matrix that when applied to the estimate image reduces a contribution of each pixel in the estimate image to the reconstructed image when that pixel is associated with a spatial location lying outside of the spatial support.