Diffuse tomography

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Abstract
We propose a new method for reconstructing parameters of physiological interest within tissue. The novel aspect of this work is that we set out to determine not only the attenuation distribution but also the scattering characteristics of the unknown object. The model we propose contains, as a limiting case, the standard problem of X-ray tomography. In that case scattering (or diffusion) is usually ignored, and one only deals with straight paths between sources and detectors. The considerable increase in mathematical difficulty brought about by considering an unknown scattering distribution as part of the inversion problem is amply justified by the fact that at low energies - like those of an infrared laser - diffusion cannot be ignored. Numerical simulations based on a discretization of the appropriate equation describing the transport of photons through the medium are very encouraging.

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