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

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
Hari M VarmaR M Vasu

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.

References

Aug 28, 1995·Physical Review Letters·D A BoasA G Yodh
May 16, 2003·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Ville KolehmainenJari P Kaipio
Mar 19, 2005·Physics in Medicine and Biology·A P GibsonS R Arridge
May 23, 2006·Physical Review Letters·Sava Sakadzić, Lihong V Wang
Dec 18, 2008·Physics in Medicine and Biology·B BanerjeeR M Vasu
Jun 3, 2009·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Hari M VarmaR M Vasu

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Citations

Nov 4, 2011·Journal of the Optical Society of America. A, Optics, Image Science, and Vision·Hari M VarmaRam M Vasu

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