Convex geometry for rapid tissue classification in MRI

We propose an efficient computational engine for solving linear combination problems that arise in tissue classification on dual-echo MRI data. In 2D feature space, each pure tissue class is represented by a central point, together with a circle representing a noise tolerance. A given unclassified voxel can be approximated by a linear combination of these pure tissue classes. With more than three tissue classes, multiple combinations can represent the same point, thus heuristics are employed to resolve this ambiguity. An optimised implementation is capable of classifying 1 million voxels per second into four tissue types on a 1.5 GHz Pentium 4 machine. Used within a region-growing application, it is found to be at least as robust and over 10 times faster than numerical optimization and linear programming methods.