In a paper by the first three authors a new algorithm for Optical Tomography (OT) in time domain was described and tested for the case of an uniform background medium. The goal of this paper is to test this method for the case where the background medium is an anatomically accurate optical map of the breast tissue obtained on the basis of a segmented Magnetic Resonance (MR) image. The key innovation of this imaging algorithm lies in a new approach for a novel linearized problem (LP). Such an LP is reduced to a boundary value problem for a coupled system of elliptic partial differential equations, rather than a conventional form of an ill-posed integral equation. The solution of this system in turn is done very rapidly. Thus, this is a fast imaging algorithm.