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Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media
Author(s) -
Hyvönen N.,
Nandakumaran A. K.,
Varma H. M.,
Vasu R. M.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2697
Subject(s) - mathematics , eigenfunction , eigenvalues and eigenvectors , diffusion equation , photon diffusion , autocorrelation , mathematical analysis , helmholtz equation , diffusion , correlation function (quantum field theory) , parameterized complexity , basis function , convection–diffusion equation , boundary value problem , algorithm , physics , optics , quantum mechanics , statistics , light source , economy , spectral density , economics , service (business)
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.