  Near-infrared spectroscopy (NIRS) including diffuse optical tomography is an
imaging modality which makes use of diffuse light propagation in random media.
When optical properties of a random medium is investigated from boundary
measurements of reflected or transmitted light, iterative inversion schemes
such as the Levenberg-Marquardt algorithm are known to fail when initial
guesses are not close to the true value of the coefficient to be reconstructed.
In this paper, we investigate how this weakness of iterative schemes is
overcome by the use of Markov chain Monte Carlo. Using time-resolved
measurements performed against a polyurethane-based phantom, we present a case
that the Levenberg-Marquardt algorithm fails to work but the proposed hybrid
method works well. Then with a toy model of diffuse optical tomography we
illustrate that the evenberg-Marquardt method fails when it is trapped by a
local minimum but the hybrid method can escape from local minima by using the
Metropolis-Hastings Markov chain Monte Carlo algorithm until it reaches the
valley of the global minimum. The proposed hybrid scheme can be applied to
different inverse problems in NIRS which are solved iteratively. We find that
for both numerical and phantom experiments optical properties such as the
absorption and reduced scattering coefficients can be retrieved without being
trapped by a local minimum when Monte Carlo simulation is run only about $100$
steps before switching to an iterative method. The hybrid method is compared
with simulated annealing. Although the Metropolis-Hastings MCMC arrives at the
steady state at about $10000$ Monte Carlo steps, in the hybrid method the Monte
Carlo simulation can be stopped way before the burn-in time.
