Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop­ ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.

Inhalt

1: Introduction to and Overview of the Field.- to integral transforms.- to discrete reconstruction methods in medical imaging.- Image structure.- Fundamentals of the Radon transform.- Regularization techniques in medical imaging.- Statistical methods in pattern recognition.- Image data compression techniques: A survey.- From 2D to 3D representation.- VLSI-intensive graphics systems.- Knowledge based interpretation of medical images.- 2: Selected Topics.- 2.1 Analytic Reconstruction Methods.- The attenuated Radon transform.- Inverse imaging with strong multiple scattering.- 2.2 Iterative Methods.- Possible criteria for choosing the number of iterations in some iterative reconstruction methods.- Initial performance of block-iterative reconstruction algorithms.- Maximum likelihood reconstruction in PET and TOFPET.- Maximum likelihood reconstruction for SPECT using Monte Carlo simulation.- X-ray coded source tomosynthesis.- Some mathematical aspects of electrical impedance tomography.- 2.3 Display and Evaluation.- Hierarchical figure-based shape description for medical imaging.- GIHS: A generalized color model and its use for the representation of multiparameter medical images.- The evaluation of image processing algorithms for use in medical imaging.- Focal lesions in medical images: A detection problem.- 2.4 Applications.- Time domain phase: A new tool in medical ultrasound imaging.- Performance of echographic equipment and potentials for tissue characterization.- Development of a model to predict the potential accuracy of vessel blood flow measurements from dynamic angiographic recordings.- The quantitative imaging potential of the HIDAC positron camera.- The use of cluster analysis and constrained optimisation techniques in factor analysis of dynamic structures.- Detection of elliptical contours.- Optimal non-linear filters for images with non-Gaussian differential distributions.- Participants.