A hybrid Kaczmarz-Conjugate Gradient algorithm for image reconstruction
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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
image reconstruction from projections inconsistent least squares problems kaczmarz extended algorithm conjugate gradient for least squares tikhonov regularization