Monte-Carlo (MC) simulations of photon migration are frequently used to build lookup tables modelling experimental results in Near-Infrared Spectroscopy. The optical properties of samples are inferred by minimizing χ²-deviation between MC model and experiment. Even for long MC simulations these lookup tables contain Poisson noise especially at high absorption or large source-detector separation. In these regimes the noise can cause the gradient of χ² to become discontinuous and complex, hindering retrieval of optical properties. Our simulation generates a large histogram of different but strongly correlated signals, differing in remission position, photon arrival time and acceptance angle. We apply singular value decomposition (SVD) to derive a low-rank-approximation of the lookup table. SVD helps us to harness the correlated signals, while rejecting uncorrelated noise. We found this approach to reduce noise and improve smoothness of χ²-planes, while preserving all features of the simulations exceeding noise-level. To enforce the smoothness of the χ²-planes we removed remaining noise in the singular vectors by a Savitzky-Golay-filtering. In contrast to the filtering of the whole high-dimensional lookup table, smoothing of a few singular vectors can be done in a mild, supervised way. As an additional benefit, the low rank approximation dramatically reduces the amount of memory needed to handle the table. This became especially important when treating lookup tables of high dimensionality created in multilayer simulations. Furthermore evaluation of interpolated MC-curves for intermediate optical properties and detector positions is simplified since it can be performed on the few singular vectors instead of the whole table.

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Thomas Gladytz, Heidrun Wabnitz, Lin Yang, and Dirk Grosenick, "Noise reduction and compression of Monte-Carlo lookup tables by singular value decomposition (Conference Presentation)," Proc. SPIE 10870, Design and Quality for Biomedical Technologies XII, 1087005 (Presented at SPIE BiOS: February 02, 2019; Published: 4 March 2019); https://doi.org/10.1117/12.2506035.6008541327001.