A non-iterative reconstruction method for bioluminescence tomography

Abstract

In this paper, we study an inverse source problem of the bioluminescence tomography in three dimensional case. Our aim is to reconstruct a bioluminescent source distribution within a body from the knowledge of the boundary measurements. The inverse source problem is reformulated as a topology optimization one minimizing an energy like type functional. It measures the difference between the solutions of two auxiliary boundary value problems. An asymptotic expansion of the considered functional with respect to a set of ball-shaped anomalies is computed using the topological sensitivity analysis method. The obtained theoretical result leads to build a non-iterative reconstruction algorithm. Finally, some numerical examples in 3D are presented in order to show the effectiveness of the devised reconstruction algorithm.