IJPAM: Volume 40, No. 1 (2007)

STRUCTURE PROPERTIES OF THE CONE
BEAM TOMOGRAPHY MATRIX IN
CYLINDRICAL COORDINATES

Fabiana Zama
Department of Mathematics
University of Bologna
Piazza di Porta S. Donato, 5, Bologna, 40127, ITALY
e-mail: zama@dm.unibo.it


Abstract.Iterative regularization methods and algebraic techniques are very powerful in the solution of complex tomographic problems because of better noise tolerance and possibility of accurate modeling of physical phenomena. The main drawback of using algebraic routines in practical situations are high computational complexity and prohibitive storage requirements. In this work we show how the representation of the object by means of an alternative coordinate system, such as the cylindric system, gives raise to highly sparse block structured matrices. The structural properties of the projection matrix allow us to identify a minimum number of elements that must be computed and stored in order to operate on the whole matrix by means of efficient methods based on matrix vector products.

Received: August 2, 2007

AMS Subject Classification: 65F50

Key Words and Phrases: cone beam tomography, cylindric coordinates, block matrix, iterative regularization algorithms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1