In this paper, we propose a level set regularization approach combined with a split strategy
for 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 diffu-
sion and absorption coefficients, respectively. We prove that the parameters-to-measurement
map satisfies sufficient conditions (continuity in the L1 -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. Therefore, the proposed numerical algorithm is
stable and convergent as shows in the presented examples as well as it saves computational
effort.