Stochastic optical tomography using beta-distributed parameters to model absorption, lifetime, and quantum efficiency
Biomedical Imaging: Reporters, Dyes, and Instrumentation, 3600, 230-237, 1999
Abstract: Stochastic methods originally devised for geophysical tomography are adapted to the biomedical optical tomography problem. Frequency domain measurements of modulated NIR light are inverted using a Bayesian approximate extended Kalman filter. Minimum variance updates for the linearized problem are calculated from explicit models of the parameters error covariance, the covariance of the system noise, and the measurement error covariance. The method is not iterative per se, but may be applied iteratively to account for strong nonlinearities. Data-driven zonation is used to dynamically reduce the parameterization for improved efficiency, sensitivity, and stability of the inversion. By modeling the parameters as beta distributed random variables, estimates are kept within feasible limits without ad hoc adjustments. In preliminary studies using synthetic domains we have successfully resolved spatially heterogeneous parameters such as absorption, fluorescence lifetime, and quantum efficiency. The method is shown to be much more accurate and computationally efficient than a more traditional Newton-Raphson method. On a 33 by 33 grid, distributed values of a single unknown parameter can be accurately identified in under 2 minutes on a 350 MHz Pentium.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).