In Diffuse Optical Tomography (DOT) near-infrared laser light is
used for imaging parts of the human body. The propagation of this
laser light in tissue is governed by a radiative transfer equation.
However, due to the numerical complexity of this mathematical model,
most of the inversion schemes developed so far employ instead the
easier to handle Diffusion Approximation (DA), which is well-known
to be inaccurate in certain situations. One of these situations is
the imaging of the human head, where so-called 'clear regions' are
present. We will report in this talk on some recent results which
we have achieved by using a full radiative transfer model (in 2D)
for the inversion task, in particular for the situation of imaging
the human head. The anomalies which we are looking for (which might
for example be tumors or hematomas) are assumed to be shapes with a
constant but possibly unknown parameter value inside, and some
known inhomogeneous parameter distribution outside.
Since the shapes which we are looking for can have a complicated
topological structure which is not known a priori, we employ a
level set strategy for representing and reconstructing these
shapes. We also will address in this talk possibilities to recover
in addition to the unknown inclusions the correct boundaries of
the 'clear regions', if they are only approximately known a priori.
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