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Open AccessFeature PaperArticle

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

School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
Institute for Medical Photonics Research, Hamamatsu University School of Medicine, Hamamatsu 431-3192, Japan
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(17), 3500;
Received: 31 July 2019 / Revised: 21 August 2019 / Accepted: 21 August 2019 / Published: 24 August 2019
(This article belongs to the Special Issue New Horizons in Time-Domain Diffuse Optical Spectroscopy and Imaging)
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 are 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 enough to the true value of the coefficient to be reconstructed. In this paper, we investigate how this weakness of iterative schemes is overcome using 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. Although the Metropolis–Hastings MCMC arrives at the steady state at about 10,000 Monte Carlo steps, in the hybrid method the Monte Carlo simulation can be stopped way before the burn-in time. View Full-Text
Keywords: near-infrared spectroscopy; diffuse light; inverse problems; optical tomography near-infrared spectroscopy; diffuse light; inverse problems; optical tomography
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Jiang, Y.; Hoshi, Y.; Machida, M.; Nakamura, G. A Hybrid Inversion Scheme Combining Markov Chain Monte Carlo and Iterative Methods for Determining Optical Properties of Random Media. Appl. Sci. 2019, 9, 3500.

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