Alternating Minimization Multigrid Algorithms for Transmission Tomography

摘要

The problem of image formation for X-ray transmission tomography is formulated as a statistical inverse problem. The maximum likelihood estimate of the attenuation function is sought. Using convex optimization methods, maximizing the log-likelihood functional is equivalent to a double minimization of I-divergence, one of the minimizations being over the attenuation function. Restricting the minimization over the attenuation function to a coarse grid component forms the basis for a multigrid algorithm that is guaranteed to monotonically decrease the I-divergence at every iteration on every scale.