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A hybrid Kaczmarz–Conjugate Gradient algorithm for image reconstruction

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  • Popa, Constantin

Abstract

The present paper is a theoretical contribution to the field of iterative methods for solving inconsistent linear least squares problems arising in image reconstruction from projections in computerized tomography. It consists on a hybrid algorithm which includes in each iteration a CG-like step for modifying the right-hand side and a Kaczmarz-like step for producing the approximate solution. We prove convergence of the hybrid algorithm for general inconsistent and rank-deficient least-squares problems. Although the new algorithm has potential for more applied experiments and comparisons, we restrict them in this paper to a regularized image reconstruction problem involving a 2D medical data set.

Suggested Citation

  • Popa, Constantin, 2010. "A hybrid Kaczmarz–Conjugate Gradient algorithm for image reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2272-2285.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:12:p:2272-2285
    DOI: 10.1016/j.matcom.2010.04.024
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    References listed on IDEAS

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    1. Popa, Constantin & Zdunek, Rafal, 2004. "Kaczmarz extended algorithm for tomographic image reconstruction from limited-data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(6), pages 579-598.
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