  In this paper, we revisit the bioluminescence tomography (BLT) problem, where
one seeks to reconstruct bioluminescence signals (an internal light source)
from external measurements of the Cauchy data. As one kind of optical imaging,
the BLT has many merits such as high signal-to-noise ratio, non-destructivity
and cost-effectiveness etc., and has potential applications such as cancer
diagnosis, drug discovery and development as well as gene therapies and so on.
In the literature, BLT is extensively studied based on diffusion approximation
(DA) equation, where the distribution of peak sources is to be reconstructed
and no solution uniqueness is guaranteed without adequate a priori information.
Motivated by the solution uniqueness issue, several theoretical results are
explored. The major contributions in this work that are new to the literature
are two-fold: first, we show the theoretical uniqueness of the BLT problem
where the light sources are in the shape of $C^2$ domains or polyhedral- or
corona-shaped; second, we support our results with plenty of problem-orientated
numerical experiments.
