Three-dimensional optical tomography based on even-parity finite-element formulation of the equation of radiative transfer

G. S. Abdoulaev, A. Bluestone, A. H. Hielscher

    Research output: Contribution to journalConference articlepeer-review


    In this work we present the first fully three-dimensional image reconstruction scheme for optical tomography that is based on the equation of radiative transfer. This scheme builds on the previously introduced concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an objective function, which is defined as the difference between predicted and measured data. The forward model is solved by using an even-parity approach to reduce the time-independent radiative transfer equation to an elliptic self-adjoint equation of second order. This equation is discretized using a finite element method, in which we apply a preconditioned conjugate gradient method with a multigrid-based preconditioner to solve the arising linear algebraic system. The gradient of the objective function is found by employing an adjoint differentiation method to the forward solver. Initial tests on synthetic data have shown robustness and good convergence of the algorithm.

    Original languageEnglish (US)
    Pages (from-to)53-60
    Number of pages8
    JournalProceedings of SPIE - The International Society for Optical Engineering
    StatePublished - 2001
    EventOptical Tomography and Spectroscopy of Tissue IV - San Jose, CA, United States
    Duration: Jan 21 2001Jan 23 2001


    • Even-parity model
    • Finite-element method
    • Optical tomography
    • Transport equation

    ASJC Scopus subject areas

    • Electronic, Optical and Magnetic Materials
    • Condensed Matter Physics
    • Computer Science Applications
    • Applied Mathematics
    • Electrical and Electronic Engineering


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