[PDF][PDF] On forward and inverse models in optical tomography

M Schlottbom - 2011 - d-nb.info
2011d-nb.info
The present work deals with forward and inverse models in optical tomography. Optical
tomography is a non-invasive medical imaging method utilizing near-infrared light to probe
biological tissue in order to infer qualitative or quantitative information on the optical
properties of the tissue. The propagation of light in biological tissue is usually modeled by
the (time-harmonic) mono-chromatic radiative transfer equation. This equation is analyzed in
detail in this work. In particular, a mixed variational framework for the radiative transfer …
Abstract
The present work deals with forward and inverse models in optical tomography. Optical tomography is a non-invasive medical imaging method utilizing near-infrared light to probe biological tissue in order to infer qualitative or quantitative information on the optical properties of the tissue. The propagation of light in biological tissue is usually modeled by the (time-harmonic) mono-chromatic radiative transfer equation. This equation is analyzed in detail in this work. In particular, a mixed variational framework for the radiative transfer equation is derived. Within this framework, results on unique solvability of the radiative transfer equation are proven under mild assumptions on the parameters. The proofs of these results yield some insight into the stability of the problem, which will be exploited when deriving stable approximation schemes. Since the inverse problem of optical tomography, ie, the reconstruction of optical properties of the object of interest, is ill-posed, some standard regularization methods are presented. A detailed analysis of the forward model, ie, the relation of optical properties to actual measurements, allows the verification of the abstract assumptions of standard regularization theory, and in turn ensures the stability of our approach for reconstructing optical parameters.
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