Frequency-domain diffusion imaging uses the magnitude and phase of modulated light propagating through a highly scattering medium to reconstruct an image of the spatially dependent scattering or absorption coefficients in the medium. An inversion algorithm is formulated in a Bayesian framework and an efficient optimization technique is presented for calculating the maximum a posteriori image. In this framework the data are modeled as a complex Gaussian random vector with shot-noise statistics, and the unknown image is modeled as a generalized Gaussian Markov random field. The shot-noise statistics provide correct weighting for the measurement, and the generalized Gaussian Markov random field prior enhances the reconstruction quality and retains edges in the reconstruction. A localized relaxation algorithm, the iterative-coordinate-descent algorithm, is employed as a computationally efficient optimization technique. Numerical results for two-dimensional images show that the Bayesian framework with the new optimization scheme outperforms conventional approaches in both speed and reconstruction quality.
© 1999 Optical Society of America
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6950) Image processing : Tomographic image processing
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(290.3200) Scattering : Inverse scattering
Jong Chul Ye, Kevin J. Webb, Charles A. Bouman, and R. P. Millane, "Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework," J. Opt. Soc. Am. A 16, 2400-2412 (1999)