  A two-step shape reconstruction method for diffuse optical tomography (DOT)
is presented which uses adjoint fields and level sets. The propagation of
near-infrared photons in tissue is modeled by the time-dependent linear
transport equation, of which the absorption parameter has to be reconstructed
from boundary measurements. In the shape reconstruction approach, it is assumed
that the inhomogeneous background absorption parameter and the values inside
the obstacles (which typically have a high contrast to the background) are
known, but that the number, sizes, shapes, and locations of these obstacles
have to be reconstructed from the data. An additional difficulty arises due to
the presence of so-called clear regions in the medium. The first step of the
reconstruction scheme is a transport-backtransport (TBT) method which provides
us with a low-contrast approximation to the sought objects. The second step
uses this result as an initial guess for solving the shape reconstruction
problem. A key point in this second step is the fusion of the 'level set
technique' for representing the shapes of the reconstructed obstacles, and an
'adjoint-field technique' for solving the nonlinear inverse problem. Numerical
experiments are presented which show that this novel method is able to recover
one or more objects very fast and with good accuracy.
