Conventional magnetic resonance images are reconstructed by Fourier transformation and have uniform spatial resolution across the entire field of view (FOV). This paper describes a way of creating MR images that have higher spatial resolution in some areas than in others. High resolution imaging can be confined to just those areas where it is necessary to resolve strong edges without truncation artifact. Such locally focused images can be acquired in less scan time than that required to image the entire FOV with uniformly high resolution. Images are reconstructed from a subset of the usual phase-encoded signals required to create a uniformly well-resolved image. The measured signals are usually nonuniformly scattered in k-space. Functional and interventional imaging may benefit from this technique, which makes it possible to acquire a rapid series of dynamical images that have high resolution in areas of expected change and lower resolution elsewhere. Spectroscopic images may be improved by using high resolution in the neighborhood of sharp edges (e.g., scalp lipids) that might otherwise cause truncation artifacts.