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

A hybrid inversion scheme combining Markov chain Monte Carlo and iterative methods for determining optical properties of random media