A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer

Hyun Keol Kim, Andreas H. Hielscher

    Research output: Contribution to journalArticlepeer-review

    Abstract

    It is well acknowledged that transport-theory-based reconstruction algorithm can provide the most accurate reconstruction results especially when small tissue volumes or high absorbing media are considered. However, these codes have a high computational burden and are often only slowly converging. Therefore, methods that accelerate the computation are highly desirable. To this end, we introduce in this work a partial-differential-equation (PDE) constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and inverse variables independently, which makes it possible to update the radiation intensities and the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate the performance of the proposed scheme with numerical and experimental data, and find that the rSQP scheme can reduce the computation time by a factor of 10-25, as compared to the commonly employed limited memory BFGS method. At the same time accuracy and robustness even in the presence of noise are not compromised.

    Original languageEnglish (US)
    Article number015010
    JournalInverse Problems
    Volume25
    Issue number1
    DOIs
    StatePublished - 2009

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Signal Processing
    • Mathematical Physics
    • Computer Science Applications
    • Applied Mathematics

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