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16 December 1992 Nonlinear multigrid methods of optimization in Bayesian tomographic image reconstruction
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Bayesian estimation of transmission tomographic images presents formidable optimization tasks. Numerical solutions of this problem are limited in speed of convergence by the number of iterations required for the propagation of information across the grid. Edge-preserving prior models for tomographic images inject a nonlinear element into the Bayesian cost function, which limits the effectiveness of algorithms such as conjugate gradient, intended for linear problems. In this paper, we apply nonlinear multigrid optimization to Bayesian reconstruction of a two-dimensional function from integral projections. At each resolution, we apply Gauss-Seidel type iterations, which optimize locally with respect to individual pixel values. If the cost function is differentiable, the algorithm speeds convergence; if it is nonconvex and/or nondifferentiable, multigrid can yield improved estimates.
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Charles A. Bouman and Ken D. Sauer "Nonlinear multigrid methods of optimization in Bayesian tomographic image reconstruction", Proc. SPIE 1766, Neural and Stochastic Methods in Image and Signal Processing, (16 December 1992);

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