We describe a new theory of MR imaging that utilizes prior information
in the form of a set of ''training'' images thought to be similar to
the ''unknown'' objects to be scanned. First, the training images are
processed to find an orthonormal series representation of these images
that is more convergent than the usual Fourier series. The coefficien
ts in this new series can be calculated from a subset of the phase-enc
oded signals needed to construct the Fourier image representation. The
characteristics of the training images also determine exactly which p
hase-encoded signals should be measured in order to minimize error in
the image reconstruction. The optimal phase-encodings are usually scat
tered nonuniformly in k-space. Good results were obtained when this th
eory was applied to imaging data from simulated objects and to experim
ental data from phantom scans. This theory provides the basis for deve
loping efficient scanning and image reconstruction techniques that are
''tailored'' to each body part or to particular disease states.