A method for constructing an image includes acquiring image data in a first domain. The acquired image data is transformed from the first domain into a second domain in which the acquired image data exhibits a high degree of sparsity. An initial set of transform coefficients is approximated for transforming the image data from the second domain into a third domain in which the image may be displayed. The approximated initial set of transform coefficients is updated based on a weighing of where substantial transform coefficients are likely to be located relative to the initial set of transform coefficients. An image is constructed in the third domain based on the updated set of transform coefficients. The constructed image is displayed.