1. A method for enhancing signal-to-noise characteristics of an image, the steps of the method comprising: a) providing a previously reconstructed image to be enhanced; b) producing synthesized image data by performing a forward projection of the provided image; c) producing a prior image by filtering the provided image such that noise from the provided image is substantially suppressed in the prior image; d) subtracting the provided image and the prior image to produce a sparsified image; e) selecting an estimate image that is an estimate of an enhanced image having a higher signal-to-noise ratio than the provided image, wherein the estimate image is different than the provided image; and f) reconstructing the enhanced image by iteratively minimizing an objective function that includes a term containing the sparsified image and a term that includes a difference between a forward projection of the selected estimate image and the synthesized image data.