Optical tomography within the near-infrared (NIR) regime has
great potential in biological imaging applications. Here, one measures the
boundary photon density caused by an array of NIR light sources surrounding the
object under investication. However, due to the high scattering rate in
biological tissue, the resulting signal-to-noise ratio (SNR) is very poor, and
special care must be taken when using measured data to obtain reliable
reconstructions.
The mathematical problem in NIR imaging can be stated as follows: find
simultaneously the diffusion coefficient D > 0 and the absorption
coefficient μa
≥ 0 of a parabolic operator
Lu = ¶tu -
Ñx · (D
Ñxu) + μa
u
in a bounded domain Ω from some knowlegde
of the associated Dirichlet-to-Neumann map. We will present a new algorithm for
this ill-posed inverse problem, based on the well-known multiple signal
classification approach. We will discuss how this method can lead to a
significant increase in the SNR. Finally, we will show some numerical results of
our algorithm with both synthetic and measured data.
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