25 June 1999 New approach for mathematical problems of the optical tomography of highly scattering (biological) objects
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We present a new method which we call the method of Photon Average Trajectory (PAT). This method provides an image reconstruction in real-time operation mode obtaining the images of superresolution quality. It is shown that time- resolved solutions of unsteady-state radiation transfer and diffusion equations permit to separate out in an explicit from the distribution function P for the probability density for a signal passage through various internal points of studied body while signal propagates from a source point to a detector point. The function P has a characteristic view of Baye's formula. Our analysis has allowed to establish a number of generalized rules of analytical derivation of the function P for highly scattering bodies of arbitrary shapes and for different measurement conditions. It is also shown that, the shadows at the body surface induced by internal macroinhomogeneities can be represented in terms of trajectory integral along the PAT. This approach for the optical tomography using multiply scattered light makes it similar to the conventional computer tomography. In this representation the integrated is the generalized distribution function of internal macroinhomogeneities averaged over the instantaneous values of the distribution P and normalized to the relative velocity of the center movement along the PAT of the distribution P.
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Vladimir V. Lyubimov, Vladimir V. Lyubimov, Olga V. Kravtsenyuk, Olga V. Kravtsenyuk, Alexander G. Murzin, Alexander G. Murzin, } "New approach for mathematical problems of the optical tomography of highly scattering (biological) objects", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351313; https://doi.org/10.1117/12.351313

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