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 higher degree of sparsity than exhibited in the first domain; approximating an initial set of transform coefficients for transforming the acquired 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 context information pertaining to the approximate 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, wherein the context information includes parent coefficients of the initial set of transform coefficients that has already been found within the image data in the second domain and a weighted sum of neighbor coefficients proximate to the initial set of transform coefficients that has already been found within the image data in the second domain, and wherein for each initial transform coefficient that has already been found, the parent coefficient is weighed equally, within the context information, with the sum of neighbor coefficients.