A hybrid Kaczmarz-Conjugate Gradient algorithm for image reconstruction

Authors:
Constantin Popa
Affiliations:
Ovidius University, Faculty of Mathematics and Computer Science, Blvd. Mamaia 124, 900527 Constanta, Romania
Venue:
Mathematics and Computers in Simulation
Year:
2010

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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.