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Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media
Authors:N Hyvönen  A K Nandakumaran  H M Varma  R M Vasu
Institution:1. Department of Mathematics and Systems Analysis, Aalto University, , FI‐00076 Aalto, Finland;2. Department of Mathematics, Indian Institute of Science, , Bangalore, 560012 India;3. ICFO – Institut de Ciències Fotòniques, , 08860 Castelldefels, Spain;4. Department of Instrumentation and Applied Physics, Indian Institute of Science, , Bangalore, 560012 India
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. Copyright © 2012 John Wiley & Sons, Ltd.
Keywords:generalized eigenvalue decomposition  correlation diffusion of photons  correlation diffusion equation  ultrasound modulated optical tomography  diffuse correlation tomography
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