A local update strategy for iterative reconstruction from projections

A method for Bayesian reconstruction which relies on updates of single pixel values, rather than the entire image, at each iteration is presented. The technique is similar to Gauss-Seidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well suited to segmentation when the image is constrained to be discretely valued. It is shown that Bayesian segmentation using GS iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction. The convergence properties of gradient ascent and GS for reconstruction from integral projections are analyzed, and simulations of both maximum-likelihood and maximum a posteriori cases are included