### Abstract

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 [W|ΔI] 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 language | English (US) |
---|---|

Pages (from-to) | 799-807 |

Number of pages | 9 |

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 14 |

Issue number | 4 |

State | Published - 1997 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Computer Vision and Pattern Recognition
- Engineering(all)

### Cite this

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*,

*14*(4), 799-807.

**Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method.** / Zhu, Wenwu; Wang, Yao; Yao, Yuqi; Chang, Jenghwa; Graber, Harry L.; Harbour, Randall L.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*, vol. 14, no. 4, pp. 799-807.

}

TY - JOUR

T1 - Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

AU - Zhu, Wenwu

AU - Wang, Yao

AU - Yao, Yuqi

AU - Chang, Jenghwa

AU - Graber, Harry L.

AU - Harbour, Randall L.

PY - 1997

Y1 - 1997

N2 - 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 [W|ΔI] 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.

AB - 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 [W|ΔI] 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.

KW - Conjugate gradient method

KW - Image reconstruction

KW - Medical optical tomography

KW - Total least squares

UR - http://www.scopus.com/inward/record.url?scp=0031106975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031106975&partnerID=8YFLogxK

M3 - Article

VL - 14

SP - 799

EP - 807

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 0740-3232

IS - 4

ER -