Scalable regularized tomography without repeated projections

Summary form only given. X-ray computerized tomography (CT) and related imaging modalities (e.g., PET) are notorious for their excessive computational demands, especially when noise-resistant probabilistic methods such as regularized tomography are used. The basic idea of regularized tomography is to compute a smooth image whose simulated projections (line integrals) approximate the observed, noisy X-ray projections. The computational expense in previous methods stems from explicitly applying a large sparse projection matrix to enforce these smoothness and data fidelity constraints during each of many iterations of the algorithm. Here we review our recent work in regularized tomography in which the smoothness constraint is analytically transformed from the image to the projection domain, before any computations begin. As a result, iterations take place entirely in the projection domain, avoiding the repeated sparse matrix-vector products. A more surprising benefit is the decoupling of a large system of regularization equations into many small systems of simpler independent equations, whose solution requires an "embarassingly parallel" computation. Here, we demonstrate that this method provides linear speedup of regularized tomography for up to 20 compute nodes (Pentium 4, 1.5 GHz) on a 100 Mb/s network using a Matlab MPI implementation.