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Information about tissue oxygen saturation ($StO_2$) and other related important physiological parameters can be extracted from diffuse reflectance spectra measured through non-contact imaging. Three analytical optical reflectance models for homogeneous, semi-infinite, tissue have been proposed (Modified Beer-Lambert, Jacques 1999, Yudovsky 2009) but these have not been directly compared for tissue parameter extraction purposes. We compare these analytical models using Monte Carlo simulated diffuse reflectance spectra and controlled gelatin-based phantoms with measured diffuse reflectance spectra and known ground truth composition parameters. The Yudovsky model performed best against Monte Carlo simulations and measured spectra of tissue phantoms in terms of goodness of fit and parameter extraction accuracy followed closely by Jacques' model. In this study, Yudovsky's model appeared most robust, however our results demonstrated that both Yudovsky and Jacques models are suitable for modelling tissue that can be approximated as a single, homogeneous, semi-infinite slab., Comment: Main body: 15 pages, 5 figures, 5 tables. Supplementary: 8 pages, 5 figures, 4 tables

Hyperspectral imaging shows promise for surgical applications to non-invasively provide spatially-resolved, spectral information. For calibration purposes, a white reference image of a highly-reflective Lambertian surface should be obtained under the same imaging conditions. Standard white references are not sterilizable, and so are unsuitable for surgical environments. We demonstrate the necessity for in situ white references and address this by proposing a novel, sterile, synthetic reference construction algorithm. The use of references obtained at different distances and lighting conditions to the subject were examined. Spectral and color reconstructions were compared with standard measurements qualitatively and quantitatively, using $\Delta E$ and normalised RMSE respectively. The algorithm forms a composite image from a video of a standard sterile ruler, whose imperfect reflectivity is compensated for. The reference is modelled as the product of independent spatial and spectral components, and a scalar factor accounting for gain, exposure, and light intensity. Evaluation of synthetic references against ideal but non-sterile references is performed using the same metrics alongside pixel-by-pixel errors. Finally, intraoperative integration is assessed though cadaveric experiments. Improper white balancing leads to increases in all quantitative and qualitative errors. Synthetic references achieve median pixel-by-pixel errors lower than 6.5% and produce similar reconstructions and errors to an ideal reference. The algorithm integrated well into surgical workflow, achieving median pixel-by-pixel errors of 4.77%, while maintaining good spectral and color reconstruction., Comment: 22 pages, 10 figures

Integrating sphere (IS) techniques combined with an inverse adding doubling (IAD) algorithm have been widely used for determination of optical properties of ex vivo tissues. Semi-infinite samples are required in such cases. The aim of this study is to develop a methodology for calculating the optical absorption and reduced scattering of biological tissues of small size from IS measurements at 400-1800 nm. We propose a two-stage IAD algorithm to mitigate profound cross-talk effects in the estimation of the reduced scattering in the case of very high absorption. We developed a small sample adaptor kit to allow IS measurements of samples with small sizes using a commercial spectrophotometer. Results showed that: The two-stage IAD substantially eliminated the cross-talks in the reduced scattering spectra, thus rectifying absorption accordingly; and the small sized sample measurements led to systematically overestimated absorption values while the spectrum shape well preserved as compared to the normal port size measurements.

This paper considers the multi-agent reinforcement learning (MARL) problem for a networked (peer-to-peer) system in the presence of Byzantine agents. We build on an existing distributed $Q$-learning algorithm, and allow certain agents in the network to behave in an arbitrary and adversarial manner (as captured by the Byzantine attack model). Under the proposed algorithm, if the network topology is $(2F+1)$-robust and up to $F$ Byzantine agents exist in the neighborhood of each regular agent, we establish the almost sure convergence of all regular agents' value functions to the neighborhood of the optimal value function of all regular agents. For each state, if the optimal $Q$-values of all regular agents corresponding to different actions are sufficiently separated, our approach allows each regular agent to learn the optimal policy for all regular agents.