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Diffuse Optical Tomography through Solving a System of Quadratic Equations without Re-Estimating the Derivatives: the "Frozen-Newton" Method

Kanmani, B and Vasu, RM (2004) Diffuse Optical Tomography through Solving a System of Quadratic Equations without Re-Estimating the Derivatives: the "Frozen-Newton" Method. In: 2004 IEEE International Workshop on Biomedical Circuits and Systems, 1-3 December, Singapore, 17 -20.


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Optical tomography (OT) recovers the cross-sectional distribution of optical parameters inside a highly scattering medium from information contained in measurements that are performed on the boundary of the medium. The image reconstruction problem in OT can be considered as a large-scale optimization problem, in which an appropriately defined objective functional needs to be minimized. Most of earlier work is based on a forward model based iterative image reconstruction (MOBIIR) method. In this method, a Taylor series expansion of the forward propagation operator around the initial estimate, assumed to be close to the actual solution, is terminated at the first order term. The linearized perturbation equation is solved iteratively, re-estimating the first order term (or Jacobian) in each iteration, until a solution is reached. In this work we consider a nonlinear reconstruction problem, which has the second order term (Hessian) in addition to the first order. We show that in OT the Hessian is diagonally dominant and in this work an approximation involving the diagonal terms alone is used to formulate the nonlinear perturbation equation. This is solved using conjugate gradient search (CGS) without re-estimating either the Jacobian or the Hessian, resulting in reconstructions better than the original MOBIIR reconstruction. The computation time in this case is reduced by a factor of three.

Item Type: Conference Paper
Publisher: IEEE
Additional Information: �©1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited: 02 Dec 2005
Last Modified: 19 Sep 2010 04:21
URI: http://eprints.iisc.ac.in/id/eprint/4251

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