Abstract: The approximate extended Kalman filter (AEKF) has been suggested as an appropriate inverse method for reconstructing fluorescent properties in large tissue samples from frequency domain data containing measurement error. The AEKF is an “optimal” estimator, in that it seeks to minimize the predicted error variances of the estimated optical properties in relation to measurement and system errors. However, due to non-linearities in the recursive estimation process, the updates are actually suboptimal. Furthermore, the computational overhead is large for the full AEKF algorithm when applied to large datasets. In this contribution we developed three hybrid forms of the AEKF algorithm that may improve the performance in frequency domain fluorescence tomography. Numerical results of image reconstruction from actual frequency domain emission data show that one hybrid form of the AEKF outperforms the traditional full AEKF in both image quality and computational efficiency for the two cases tested.
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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).