1. A method of acquiring and reconstructing an image, such method comprising the steps of: obtaining prior knowledge of the image, possibly by coarse sampling of the image; using the obtained prior knowledge of the image to identify relative locations of structures having relatively high contrast edges; prescribing a set of k-space locations based upon the relative locations of the structures in order to achieve comparable eigenvalues of a reconstruction matrix; sampling the k-space at the prescribed k-space locations to obtain k-space sample data; decomposing the k-space sample data into background data and edge data; Fourier transforming the background data to reconstruct a background image component; Fourier transforming subsets of the edge data and using the reconstruction matrix to form a linear combination of these Fourier transformations in order to reconstruct an edge image component; and combining the background image component and the edge image component to generate a final image.