1. A method for constructing an image, comprising: acquiring image data in a first domain; transforming the acquired image data from the first domain into a second domain in which the acquired image data exhibits a high degree of sparsity; approximating an initial set of transform coefficients for transforming the image data from the second domain into a third domain in which the image may be displayed; updating the approximated initial set of transform coefficients based on a weighing of where substantial transform coefficients are likely to be located relative to the initial set of transform coefficients; constructing an image in the third domain based on the updated set of transform coefficients; and displaying the constructed image.