WIAS Preprint No. 427, (1998)

Optical Imaging: 3D Approximation and Perturbation Approaches for Time-domain Data


  • Hünlich, Rolf
  • Model, Regine
  • Orlt, Matthias
  • Walzel, Monika

2010 Mathematics Subject Classification

  • 35R30


  • Near-infrared imaging, diffusion model, time-resolved data, image reconstruction, perturbation approach, finite-element method


The reconstruction method presented here is based on the diffusion approximation for the light propagation in turbid media and on a minimization strategy for the output-least-squares problem. A perturbation approach is introduced for the optical properties. Here, the number of free variables of the inverse problem can be strongly reduced by exploiting a priori information such as the search for single inhomogeneities within a relatively homogeneous object, a typical situation for breast cancer detection. Higher accuracy and a considerable reduction of the computational effort are achieved by solving a parabolic differential equation for a perturbation density, i.e. the difference between the photon density in an inhomogeneous object and the density in the homogeneous case being given by an analytic expression. The calculations are performed by a 2D FEM algorithm, however, as a time-dependent correction factor is applied, the 3D situation is well approximated. The method was successfully tested by the University of Pennsylvania standard data set. Data noise was generated and taken into account in a modified data set. The influence of different noise on the reconstruction results is discussed.

Appeared in

  • Applied Optics, 37 (1998), pp. 7968-7976

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