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.