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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 2 — Feb. 1, 2010
  • pp: 259–267

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

Hari M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu  »View Author Affiliations


JOSA A, Vol. 27, Issue 2, pp. 259-267 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000259


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Abstract

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Fréchet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography.

© 2010 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(170.0110) Medical optics and biotechnology : Imaging systems
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: September 23, 2009
Revised Manuscript: December 14, 2009
Manuscript Accepted: December 15, 2009
Published: January 22, 2010

Virtual Issues
Vol. 5, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Hari M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, "Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography," J. Opt. Soc. Am. A 27, 259-267 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-2-259

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