Open AccessRecovery of piecewise constant coefficients in optical diffusion tomography
Author(s) -
Ville Kolehmainen,
Marko Vauhkonen,
Jari P. Kaipio,
Simon R. Arridge
Publication year - 2000
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.7.000468
Subject(s) - piecewise , inverse problem , iterative reconstruction , constant (computer programming) , diffusion , boundary (topology) , computation , pixel , attenuation coefficient , least squares function approximation , mathematics , photon diffusion , algorithm , mathematical analysis , optics , computer science , physics , computer vision , light source , statistics , estimator , thermodynamics , programming language
In optical diffusion tomography the reconstruction of the absorbtion and scattering coefficients is conventionally carried out in a pixel basis. The resulting number of unknowns makes the associated inverse problem severely ill-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 assumes that there is a feasible initial guess on the domain boundaries. In this paper we propose an extension to this approach in which the initial estimate for the boundary and coefficient estimation is extracted from a conventional pixel based reconstruction using standard image processing operations. In the computation of the pixel based reconstruction the output least squares 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 favors domains with constant coefficients it is well suited for the fixing of the starting point for the actual boundary and coefficient reconstruction method.