Stochastic Systems Group
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The research mission of the stochastic systems group is to conduct basic research in the analysis of complex systems and phenomena subject to uncertainty and statistical variability and to develop advanced algorithms for the statistical analysis of signals and imagery. The research within the group spans the very broad spectrum from theoretical development and analysis of new models and algorithms to the in-depth application of these theoretical results to challenging applications. In particular, virtually every student or post-graduate researcher working in the group engages in activities across this entire range, since a key goal in our work is to define new models and theoretical frameworks that lead both to deep insights about complex applications and to enabling technologies which can have a significant impact within these application domains.

At present and for the next few years, a first major theoretical thrust of the group's work involves the development of methods for multiresolution modeling and analysis of complex phenomena and processing of signals and spatial data. The major objective of this work is to develop models that allow us both to capture a wide range of physical and statistical phenomena at multiple scales and to exploit the structure of these models in order to develop algorithms capable of solving problems that had heretofore been considered prohibitively complex. In addition, our group also engages actively in basic research in (i) nonlinear algorithms for robust image analysis; (ii) image reconstruction algorithms and more generally statistical methods for inverse problems in mathematical physics; and (iii) the statistical modeling of the geometry of spatial phenomena and the exploitation of these models in image analysis and computer vision. Applications which are currently driving our work and in which we are also actively engaged include the fusion and assimilation of multisensor data for remote sensing problems in oceanography and hydrology, biomedical image analysis, and the statistical modeling of complex sensing systems for image reconstruction and automatic target recognition. In recent years our research has led to significant new methods and results in each of these fields, providing a foundation on which we plan to build in the years to come.

The research activities within our group are performed in a highly interactive manner, providing a rich and supportive environment for the students and post-graduate researchers involved. Indeed, in addition to the research mission outlined in the preceding paragraph, our group also has an equally important educational mission, namely to foster the professional development of the exceptionally talented young people with whom we have the privilege to work. Both the interactive nature of the environment within the group as well as the mixture of theory and applications play important roles in this process. By blending theory and applications, students learn about and engage in the difficult creative process of defining research problems that satisfy three important criteria, namely that they are interesting, tractable, and of real significance. Also, by working in an interactive environment, students not only learn about the intellectual give-and-take that is such an important part of that creative process, but they also gain valuable experience in working with others and with a team. Our field is changing rapidly, and its interactions with other disciplines and with a dizzying array of applications will, with certainty, continue to grow and change in the future. As a consequence, future leaders in the field will need to have the intellectual and technical agility to adapt to new challenges and the curiosity and enthusiasm to welcome them. We have tried to create an environment and an intellectual agenda that allows students to succeed and thrive in such an arena.

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