A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media

Abstract

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 Levenberg-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.

Special Issue on New Horizons in Time Domain Diffuse Optical Spectroscopy and Imaging

“…However, in these schemes, the initial guesses need to be close to the true values. Jiang et al propose a scheme combining Markov chain Monte Carlo and iterative methods to overcome this weakness in iterative schemes [24]. In TD DOT, regarding the datatypes obtained from the TPSF, such as temporal windows and Fourier transformations, determining which datatypes are used for image reconstruction is crucial for computational efficiency as well as for image quality.…”

Diffuse optical tomography by simulated annealing via a spin Hamiltonian

“…Statistical approaches have been developed in diffuse optical tomography [2,16]. To estimate parameters in coefficients of the diffusion equation or the radiative transport equation, which is approximated to the diffusion equation at large scales, the Metropolis-Hastings Monte Carlo algorithm was used [5,12,9]. However, only a few unknown parameters can be determined by the naive use of the Metropolis-Hastings Markov-chain Monte Carlo method.…”