Recovery of piecewise constant coefficients in optical diffusion tomography

In optical diffusion tomography the reconstruction of the absorbtion and sc attering coefficients is conventionally carried out in a pixel basis. The r esulting number of unknowns makes the associated inverse problem severely i ll-posed. We have recently proposed a new approach in which the goal is to reconstruct boundaries of piecewise constant tissue regions as well as the diffusion and absorption coefficients within these regions. This method ass umes that there is a feasible initial guess on the domain boundaries. In th is paper we propose an extension to this approach in which the initial esti mate for the boundary and coefficient estimation is extracted from a conven tional pixel based reconstruction using standard image processing operation s. In the computation of the pixel based reconstruction the output least sq uares problem is augmented with an approximated total variation prior. The performance of the proposed approach is evaluated using simulated frequency domain data. It is shown that since the total variation type approach favo rs domains with constant coefficients it is well suited for the fixing of t he starting point for the actual boundary and coefficient reconstruction me thod. (C) 2000 Optical Society of America.