Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector

Yiqiu Dong, Per Christian Hansen, Michiel E. Hochstenbach, Nicolai André Brogaard Riis

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6 Citations (Scopus)
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We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair, i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography.

Original languageEnglish
Pages (from-to)A1822-A1839
Number of pages18
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 1 Jan 2019


  • Algebraic iterative reconstruction
  • Computed tomography
  • Leftmost eigenvalue estimation
  • Perturbation theory
  • Unmatched transpose


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