Very High-Precision Inversion of Ill-Conditioned Matrices: A Medical Imaging
Volume 1, Issue 1
Marie Foley Kijewski, Stefan P. Mueller, Frank J. Rybicki and Paulo
A. Carvalho, Harvard Medical School and Brigham and Women's Hospital
Mathematical models of performance in diagnostic imaging tasks to be
used for design and evaluation of emission-computed tomographic systems
have been developed using Mathematica. The measure of performance
is the precision with which the level of radioactivity within a structure
can be estimated; the models are based on the Barankin lower bound on precision.
Since the models depend on physical properties of the imaging system as
well as on characteristics of the imaging task, they can be used for system
optimization. Derivation of the bound requires symbolic differentiation
and integration, as well as very high-precision numerical inversion of
large, ill-conditioned matrices.