In our terminology "globally convergent numerical method" means a numerical method, whose convergence to a good approximation for the correct solution is independent of the initial approximation. A new numerical imaging algorithm of reconstruction of optical absorption coefficients from near infrared light data with a continuous-wave has been purposed to solves a coefficient inverse problem for an elliptic equation with the data generated by the source running along a straight line. A regularization process, so-called "exterior forward problem", for preprocessing data with noise on the boundary has also been purpose for the problem related to matching fluid in experiment. A rigorous convergence analysis shows that this method converges globally. A heuristic approach for approximating "tail-function" which is a crucial part of our problem has been performed and verified in numerical experiments, so as the global convergence. Applications to both electrical impedance and optical tomography are discussed. Numerical experiments in the 2D case are presented.
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