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

Varma, Hari M and Banerjee, B and Roy, D and Nandakumaran, AK and Vasu, RM (2010) Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography. In: Journal of the Optical Society of America A: Optics, Image Science, and Vision, 27 (2). pp. 259-267.

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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 Frechet 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. (C) 2010 Optical Society of America.

Item Type:	Journal Article
Publication:	Journal of the Optical Society of America A: Optics, Image Science, and Vision
Publisher:	Optical Society of America
Additional Information:	Copyright of this article belongs to Optical Society of America.
Department/Centre:	Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics Division of Mechanical Sciences > Civil Engineering Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	09 Mar 2010 07:23
Last Modified:	19 Sep 2010 05:55
URI:	http://eprints.iisc.ac.in/id/eprint/25790

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