Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media

Hyvonen, N and Nandakumaran, AK and Varma, HM and Vasu, RM (2013) Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media. In: Mathematical Methods in the Applied Sciences, 36 (11). pp. 1447-1458.

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Abstract

We propose a novel numerical method based on a generalized eigenvalue decomposition for solving the diffusion equation governing the correlation diffusion of photons in turbid media. Medical imaging modalities such as diffuse correlation tomography and ultrasound-modulated optical tomography have the (elliptic) diffusion equation parameterized by a time variable as the forward model. Hitherto, for the computation of the correlation function, the diffusion equation is solved repeatedly over the time parameter. We show that the use of a certain time-independent generalized eigenfunction basis results in the decoupling of the spatial and time dependence of the correlation function, thus allowing greater computational efficiency in arriving at the forward solution. Besides presenting the mathematical analysis of the generalized eigenvalue problem on the basis of spectral theory, we put forth the numerical results that compare the proposed numerical method with the standard technique for solving the diffusion equation.

Item Type:	Journal Article
Publication:	Mathematical Methods in the Applied Sciences
Publisher:	Wiley-Blackwell
Additional Information:	Copyright of this article belongs to Wiley-Blackwell.
Keywords:	Generalized Eigenvalue Decomposition; Correlation Diffusion of Photons; Correlation Diffusion Equation; Ultrasound Modulated Optical Tomography; Diffuse Correlation Tomography
Department/Centre:	Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics
Date Deposited:	02 Sep 2013 06:25
Last Modified:	03 Sep 2013 06:45
URI:	http://eprints.iisc.ac.in/id/eprint/46953

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