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Proceedings Paper

Total least squares approach for the solution of the perturbation equation
Author(s): Wenwu Zhu; Yao Wang; Jenghwa Chang; Harry L. Graber; Randall Locke Barbour
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Paper Abstract

This paper presents a new algorithm for solving the perturbation equation of the form W(Delta) x equals (Delta) I encountered in optical tomographic image reconstruction. The methods we developed previously are all based on the least squares formulation, which finds a solution that best fits the measurement (Delta) x while assuming the weight matrix W is accurate. In imaging problems, usually errors also occur in the weight matrix W. In this paper, we propose an iterative total least squares (ITLS) method which 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 associated with the minimal singular value. The proposed ITLS method obtains this solution using a conjugate gradient method which is particularly suitable for very large matrices. Experimental results have shown that the TLS method can yield a significantly more accurate result than the LS method when the perturbation equation is overdetermined.

Paper Details

Date Published: 30 May 1995
PDF: 11 pages
Proc. SPIE 2389, Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, (30 May 1995); doi: 10.1117/12.209992
Show Author Affiliations
Wenwu Zhu, Polytechnic Univ. (United States)
Yao Wang, Polytechnic Univ. (United States)
Jenghwa Chang, SUNY/Brooklyn (United States)
Harry L. Graber, SUNY/Brooklyn (United States)
Randall Locke Barbour, SUNY/Brooklyn (United States)


Published in SPIE Proceedings Vol. 2389:
Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation
Britton Chance; Robert R. Alfano, Editor(s)

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