Stochastic reconstruction techniques are developed for mapping the interior optical properties of tissues from exterior frequency-domain photon migration measurements at the air–tissue interface. Parameter fields of absorption cross section, fluorescence lifetime, and quantum efficiency are accurately reconstructed from simulated noisy measurements of phase shift and amplitude modulation by use of a recursive, Bayesian, minimum-variance estimator known as the approximate extended Kalman filter. Parameter field updates are followed by data-driven zonation to improve the accuracy, stability, and computational efficiency of the method by moving the system from an underdetermined toward an overdetermined set of equations. These methods were originally developed by Eppstein and Dougherty [Water Resources Res. 32, 3321 (1996)] for applications in geohydrology. Estimates are constrained to within feasible ranges by modeling of parameters as β-distributed random variables. No arbitrary smoothing, regularization, or interpolation is required. Results are compared with those determined by use of Newton–Raphson-based inversions. The speed and accuracy of these preliminary Bayesian reconstructions suggest the near-future application of this inversion technology to three-dimensional biomedical imaging with frequency-domain photon migration.
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