Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

Wenwu Zhu, Yao Wang, Yuqi Yao, Jenghwa Chang, Harry L. Graber

Research output: Contribution to journalArticlepeer-review


We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [Y. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120], which solves a perturbation equation of the form WΔx ΔI. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data ΔI while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [WΔI] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method.

Original languageEnglish (US)
Pages (from-to)799-807
Number of pages9
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number4
StatePublished - Apr 1997


  • Conjugate gradient method
  • Image reconstruction
  • Medical optical tomography
  • Total least squares

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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