  In this article, we propose a non-parametric Bayesian level-set method for
simultaneous reconstruction of piecewise constant diffusion and absorption
coefficients in diffuse optical tomography (DOT). We show that the Bayesian
formulation of the corresponding inverse problem is well-posed and the
posterior measure as a solution to the inverse problem satisfies a Lipschitz
estimate with respect to the measured data in terms of Hellinger distance. We
reduce the problem to a shape-reconstruction problem and use level-set priors
for the parameters of interest. We demonstrate the efficacy of the proposed
method using numerical simulations by performing reconstructions of the
original phantom using two reconstruction methods. Posing the inverse problem
in a Bayesian paradigm allows us to do statistical inference for the parameters
of interest whereby we are able to quantify the uncertainty in the
reconstructions for both the methods. This illustrates a key advantage of
Bayesian methods over traditional algorithms.
