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 which have higher spatial resolution in some areas than others. High resolution imaging can be confined to just those areas where it is necessary to resolve strong edges without truncation artifacts. Such locally focused images can be acquired in less scan time than required to image the entire FOV with uniformly high resolution. After the user specifies the spatial resolution in each portion of the FOV, the algorithm automatically generates image basis functions which oscillate most rapidly in the regions with highest resolution. Images are reconstructed by summing image projection onto these basis functions. These projections are calculated from a subset of the usual phase-encoded signals required to create a uniformly well-resolved image. The algorithm also determines which phase-encodings are optimal for this purpose, and these are usually nonuniformly scattered in k-space. Thus, both data acquisition and image reconstruction are optimized. Functional and interventional imaging may benefit from this technique, which makes it possible to acquire a rapid series of dynamical images which have high resolution in areas of expected changes and lower resolution elsewhere. Spectroscopic images may be improved by using high resolution in the neighborhood of sharp edges which might otherwise cause truncation artifacts.