Software for algebraic iterative reconstruction methods often uses different discretization methods for the projection and the backprojection. Consequently, the two matrices that represent these operations are not each other’s transpose; they form an unmatched projector/backprojector pair. We study the influence of such an unmatched pair on the reconstruction problem through perturbation bounds and convergence analysis for the iterative methods, and we give numerical examples that illustrate our results. This is joint work with Tommy Elfving.

This presentation is part of Minisymposium “MS34 - Numerical Linear Algebra techniques for Image Restoration and Reconstruction (2 parts)”
organized by: Caterina Fenu (University of Cagliari) , Marco Donatelli (University of Insubria) .

Authors:

Per Christian Hansen (Technical University of Denmark)

Tommy Elfving (Linköping University)

Keywords:

algebraic iterative methods, computed tomography, convergence analysis, image reconstruction, inverse problems, numerical linear algebra, perturbation analysis, semi-convergence