MR imaging with spatially variable resolution

Abstract

In some situations it may be advantageous to produce “locally focused” magnetic resonance images that have nonuniform spatial resolution matching the expected local rate of spatial variation in the object. Because such an image has fewer pixels than a conventional image with uniformly high resolution, it can be reconstructed from fewer signals, acquired in less time. This can be done by using a highly convergent representation of the image as a sum of orthonormal functions with slow (fast) spatial variation in relatively homogeneous (heterogeneous) parts of the object. Since this series is shorter than a conventional truncated Fourier series, its terms can be calculated from a subset of the usual array of phase‐encoded signals. The optimal choice of these phase encodings, which are usually scattered nonuniformly in k space, results in minimization of noise in the reconstructed image. The technique is illustrated by applying it to simulated data and to data from images of phantoms.