WIAS Preprint No. 204, (1995)

Inverse problems in optical tomography


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


This preprint contains the revised version of two papers presented at the BiOS Europe '95 held at Barcelona in September 1995 (to appear in Proc. SPIE 2626). Both papers are devoted to inverse problems in optical tomography. The photon migration in highly scattering media is decribed by the diffusion equation including some absorption term and by suitable initial and boundary conditions. It represents a good approximation assuming scattering predominates over absorption. Algorithms for solving these inverse problems are an essential part in developing medical diagnostic methods based on transillumination of tissue.

In the first paper

  • R. Model, R. Huenlich: Parameter sensitivity in near infrared imaging, pp. 2-11
it is shown that the choice of boundary conditions sensitively affects the photon propagation and the output fluxes at the boundary of the object. A comparison between measurements (performed by H. Rinneberg, U. Sukowski, H. Wabnitz, Medical Measuring Techniques group of the PTB) of the time-resolved transmittance of ps laser pulses and numerical simulations leads to the result, that boundary conditions of the third kind must be used. Besides of the optical parameters the corresponding boundary parameters have been identified using an iteration method in analogy to the image reconstruction algorithm.

The second paper

  • M. Orlt, M. Walzel, R. Model: Transillumination imaging performance using time domain data, pp. 12-23
is concerned with the question of improving the image reconstruction algorithm itself. Improvements in reconstruction results may be achieved in two ways, first by adapting the detector arrangements and, secondly, by using a regularization strategy based on the Tikhonov regularization. The effectiveness of these methods is demonstrated by instructive examples concerned with the reconstruction of absorbers and scatterers, respectively.

Appeared in

  • Proc. SPIE, 2626 (1995), pp. 56-65

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