GMRES methods for tomographic reconstruction with an unmatched back projector

Unmatched pairs of forward and back projectors are common in X-ray CT computations for large-scale problems; they caused by the need fast algorithms that best utilize computer hardware, it is an interesting challenging task to develop easy-to-use these cases. Our approach use preconditioned GMRES, form AB- BA-GMRES algorithms, handle unmatched normal equations associated with pair. These simple implement, rely only on available projectors, do not require tuning any algorithm parameters. We show equivalent well-known LSQR LSMR case a matched projector. numerical experiments demonstrate exhibit desired semi-convergence behavior comparable LSQR/LSMR standard stopping rules work well. Hence, suited reconstruction problems noisy data projector pairs.