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, we have applied spatially-invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques. In a sample application, we performed reconstructions from noiseless, simulated projection data, using preconditioned and conventional steepest-descent algorithms. The preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the unassisted 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.