A primal-dual method for large-scale image reconstruction in emission tomography

In emission tomography, images can be reconstructed from a set of measured projections using a maximum likelihood( ML) criterion. In this paper, we pr esent a primal-dual algorithm for large-scale three-dimensional image recon struction. The primal-dual method is specialized to the ML reconstruction p roblem. The reconstruction problem is extremely large; in several of our da ta sets the Hessian of the objective function is the product of a 1.4 milli on by 63 million matrix and its scaled transpose. As such, we consider only approaches that are suitable for large-scale parallel computation. We appl y a stabilization technique to the system of equations for computing the pr imal direction and demonstrate the need for stabilization when approximatel y solving the system using an early-terminated conjugate gradient iteration . We demonstrate that the primal-dual method for this problem converges faste r than the logarithmic barrier method and considerably faster than the expe ctation maximization algorithm. The use of extrapolation in conjunction wit h the primal-dual method further reduces the overall computation required t o achieve convergence.