A 2-level domain decomposition algorithm for inverse diffuse optical tomography

In this paper, we explore domain decomposition algorithms for the inverse DOT problem in order to reduce the computational complexity and accelerate the convergence of the optical image reconstruction. We propose a combination of a two-level multigrid algorithm with a modified multiplicative Schwarz algorithm, where a conjugate gradient is used as an accelerator to solve each sub-problem formulated on each of the partitioned sub-domains. For our experiments, simulated phantom configuration with two rectangular inclusions is used as a testbed to measure the computational efficiency of our algorithms. No a priori information about the configuration is assumed except for the source and detector locations. For the application of our modified Schwarz algorithm alone, we observe an increase in efficiency of 100% as compared to the conjugate gradient solution obtained for the full domain. With the addition of the coarse grid, this efficiency rises to 400%. The coarse grid also serves to improve the overall appearance of the reconstructed image at the boundaries of the inclusions.