A LOCAL UPDATE STRATEGY FOR ITERATIVE RECONSTRUCTION FROM PROJECTIONS

Iterative methods for computing tomographic reconstruction are computationally costly relative to convolution backprojection, but allow useful image reconstruction from sparse and noisy data. We present a method for Bayesian reconstruction which relies on updates of single pixel values, rather than the entire image, at each iteration. 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. We demonstrate that Bayesian segmentation using GS iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction. This paper includes analysis of the convergence properties of gradient ascent and GS for reconstruction from integral projections, and simulations of both maximum-likelihood and maximum a posteriori cases.