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

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 th...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2013-07, Vol.36 (11), p.1447-1458
Main Authors: Hyvönen, N., Nandakumaran, A. K., Varma, H. M., Vasu, R. M.
Format: Article
Language:English
Subjects:
Correlation
correlation diffusion equation
correlation diffusion of photons
diffuse correlation tomography
Diffusion
Eigenvalues
generalized eigenvalue decomposition
Mathematical analysis
Mathematical models
Media
Numerical analysis
Photons
ultrasound modulated optical tomography
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Summary: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. Copyright © 2012 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.2697