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Towards an algebraic multigrid method for tomographic image reconstruction -- improving convergence of ART

In this paper we introduce a multigrid method for sparse, possibly rank-deficient and inconsistent least squares problems arising in the context of tomographic image reconstruction. The key idea is to construct a suitable AMG method using the Kaczmarz algorithm as smoother. We first present some theoretical results about the correction step and then show by our numerical experiments that we are able to reduce the computational time to achieve the same accuracy by using the multigrid method instead of the standard Kaczmarz algorithm.