We consider in two dimensions, the inverse boundary problem of
reconstructing the absorption and scattering coefficient of an
inhomogeneous medium by probing it with diffuse light. The problem
is modeled as an inverse boundary problem for the stationary linear
Boltzmann equation. The information is encoded in the albedo operator.
We show that we can recover the absorption and the scattering kernel
from this information provided that the latter is small in an
appropriate topology. We also give stability estimates and propose
an approximate reconstruction procedure.