Preconditioning methods for improved convergence rates in iterative reconstructions

Because of the characteristics of the tomographic inversion problem, iterative reconstruction techniques often suffer from poor convergence rates-especially at high spatial frequencies. By using preconditioning methods, the convergence properties of most iterative methods can be greatly enhanced without changing their ultimate solution. To increase reconstruction speed, spatially invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques have been applied. In a sample application, reconstructions from noiseless, simulated projection data, were performed using preconditioned and conventional steepest-descent algorithms. The preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the assisted algorithms at the same iteration. Applications of these methods to regularized reconstructions from projection data containing Poisson noise showed similar, although not as dramatic, behavior