30 May 1995 Modeling of noise for near-infrared transillumination imaging
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Models of light propagation in tissue fall into two general categories: stochastic such as Monte Carlo, or Random Walk, or deterministic, such as the diffusion approximation. The former attempts to model the discrete, particle, nature of light, and inherently includes noise via the random numbers used to generate steps. The latter models the continuous, wave nature of light via a partial differential equation. Considerable effort has gone into showing that the mean of a deterministic model equates to, and the mean of a stochastic model converges to, the mean of experimental data. Efficiency considerations lead to a Monte Carlo model that has reduced variance in the sense that sample mean more quickly converges to the expectation value. When considering image reconstruction problems it is vital to be able to predict the standard errors of data from any given measure. Unfortunately, variance reduction Monte Carlo models greatly underestimate the standard errors, and 'analog' Monte Carlo methods that give correct estimates are very inefficient. In this paper we derive standard error estimations from a deterministic model that is very much faster, and demostrate the equivalence of these estimates with stochastic methods. The application of reliable error-estimates to image reconstruction is shown.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Simon Robert Arridge, Simon Robert Arridge, Mutsuhisa Hiraoka, Mutsuhisa Hiraoka, Martin Schweiger, Martin Schweiger, "Modeling of noise for near-infrared transillumination imaging", Proc. SPIE 2389, Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, (30 May 1995); doi: 10.1117/12.209990; https://doi.org/10.1117/12.209990

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