Sampling and reconstruction of signals and images including mr images of

Abstract

A method and apparatus are provided for acquiring and reconstructing an image. The method includes the steps of obtaining prior knowledge of the image, possibly by coarse sampling of the image and using the obtained prior knowledge of the image to identify relative locations of structures having relatively high contrast edges. The method further includes the steps of 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 and sampling the k-space at the prescribed k-space locations to obtain k-space sample data. The k-space sample data are decomposed into background data and edge data. The background data are Fourier transformed to reconstruct a background image component. Similarly, subsets of the edge data are Fourier transformed and the reconstruction matrix is used to form a linear combination of these Fourier transformations in order to reconstruct an edge image component. Finally, the background image component and the edge image component are combined to generate a final image.