  In this paper, we propose a level set regularization approach combined with a
split strategy for the simultaneous identification of piecewise constant
diffusion and absorption coefficients from a finite set of optical tomography
data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse
problem combining together the exponential and mildly ill-posedness of
diffusion and absorption coefficients, respectively. We prove that the
parameter-to-measurement map satisfies sufficient conditions (continuity in the
$L^1$ topology) to guarantee regularization properties of the proposed level
set approach. On the other hand, numerical tests considering different
configurations bring new ideas on how to propose a convergent split strategy
for the simultaneous identification of the coefficients. The behavior and
performance of the proposed numerical strategy is illustrated with some
numerical examples.
