Date of Award
Doctor of Philosophy
Electrical and Computer Engineering
During the last two decades, iterative computerized tomography (CT) algorithms, such as ART (Algebraic Reconstruction Technique) and SIRT (Simultaneous Iterative Reconstruction Technique), have been applied to the solution of overdetermined and underdetermined systems. These algorithms arrive at the least squares solution of normal equations. In theory, such algorithms converge to the minimum-norm solution when a system is underdetermined if there are no computational errors and the initial vector is chosen properly. In practice, computational errors may lead to failure to converge to a unique solution.;The dissertation introduces a method called the projection iterative reconstruction technique (PIRT) which differs from the other reconstruction algorithms used for solving underdetermined systems. Even though the differences between the method outlined in this dissertation and the algorithms proposed earlier are subtle, the proposed scheme guarantees convergence to a unique minimum-norm solution. Several acceleration techniques are discussed in the dissertation. Furthermore, the iterative algorithm can also be generalized and employed to solve other large and sparse linear systems.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Lu, Tongxin, "Tomographic reconstruction algorithms using optoelectronic devices " (1992). Retrospective Theses and Dissertations. 10330.