Very High-Precision Inversion of Ill-Conditioned Matrices: A Medical Imaging Application

Volume 1, Issue 1
Summer 1990

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.