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Classical iterative methods for tomographic reconstruction include the classof Algebraic Reconstruction Techniques (ART). Convergence of these stationarylinear iterative methods is however notably slow. In this paper we propose theuse of Krylov solvers for tomographic linear inversion problems. These advancediterative methods feature fast convergence at the expense of a highercomputational cost per iteration, causing them to be generally uncompetitivewithout the inclusion of a suitable preconditioner. Combining elements fromstandard multigrid (MG) solvers and the theory of wavelets, a novelwavelet-based multi-level (WMG) preconditioner is introduced, which is shown tosignificantly speed-up Krylov convergence. The performance of theWMG-preconditioned Krylov method is analyzed through a spectral analysis, andthe approach is compared to existing methods like the classical SimultaneousIterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methodson a 2D tomographic benchmark problem. Numerical experiments are promising,showing the method to be competitive with the classical AlgebraicReconstruction Techniques in terms of convergence speed and overall performance(CPU time) as well as precision of the reconstruction.

A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems