A globally accelerated numerical method for optical tomography with continuous wave source
It addresses the inverse problem of recovering unknown potential in elliptic equations, with applications to medical and battlefield imaging, but the method is domain-specific and incremental.
The paper proposes a globally convergent numerical method for optical tomography with a continuous wave source, validated through rigorous analysis and numerical experiments.
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured as the data for the inverse problem. A rigorous convergence analysis shows that this method converges globally, provided that the so-called tail function is approximated well. This approximation is verified in numerical experiments, so as the global convergence. Applications to medical imaging, imaging of targets on battlefields and to electrical impedance tomography are discussed.