A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains

We propose an efficient PDE based approach for solving the first-arrival traveltime tomography problem in irregular domains. consider mismatch functional on $L_1$ or $L_2$ fidelity term, respectively, and we compute both gradients with respect to sound speed by adjoint-state method. The novelty of proposed method consists two aspects. First, since is formulated domain, develop new level-set fast sweeping methods eikonal equations domain. Second, computed adjoint state associated a source singularity originated from gradient point solution, novel decomposition remove this singularity, which just requires same equation again but different boundary condition. Finally, show performance algorithm several numerical examples including synthetic data set ultrasound computerized tomography.