Measurement and Model Error Assessment of a Single Pixel, Frequency Domain Photon Migration Apparatus and Diffusion Model for Imaging Applications
Photon Migration, Diffuse Spectroscopy, and Optical Coherence Tomography: Imaging and Functional Assessment, 4160, 153-163, 2000
Abstract: Research into the near-infrared biomedical optical imaging has produced a multitude of inverse imaging algorithms. Recent experience has shown that when these algorithms are tested with experimental data, they falter due to a mismatch between observed and simulated measurements. When considering measurements for imaging, one must consider both measurement and model error. If data is recorded properly, then measurement error tends to be normally distributed with a mean of zero. Model error can be biased and spatially correlated due to inaccuracies in the diffusion approximation, inaccurate parameter estimates, numerical error, and other factors. This contribution discusses trends in the measurement and model error observed from measurements on a single-pixel, frequency domain photon migration system developed for biomedical optical imaging. In order to reduce the model error bias, an empirical approach was applied to find experimental variables that significantly affect it. This approach reduced the mean of the model error on a test data set and produced a slight smoothing effect on its distribution. Image reconstruction attempts show that the modified data set produces an improved image over the image reconstructed from the raw data set. To our knowledge, this is the first time that model and measurement error information have been incorporated into a three dimensional image reconstruction algorithm.
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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).