Interdisciplinary Study in Image and Signal Processing

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This is a research proposal with an educational emphasis under the Interdisciplinary Grants in theMathematical Sciences program. The principle investigator proposes to obtain a broad back groundin the engineering science specific to image and signal processing, to build an interdisciplinary research program on image processing via morphological neural networks and PDE-based methods, and to prepare materials for a graduate special topics course on mathematical methods in image processing. She plans to study and develop mathematical theories and methods for modeling and analyzing neural networks, especially to investigate the partial differential equations governing phase transition phenomenon related to neural networks. She also proposes to improve existing PDE models and to develop new PDE models for image processing, as well as to study the theories and methods for nonlinear degenerate parabolic equationsarising from image processing.The PI will spend the 1999-2000 academic year in the Department of Computer and Information Science and Engineering (CISE) at the University of Florida. She plans to take several courses from CISE and to interact closely with computer scientists and their graduate students by paricipating in seminars and projects. She plans to work on two projects, one is focused on applying morphologicalneural networks to automated target recognition, and the other one is concerned with the application of image analysis via PDE-based methods to computer assisted radiation therapy.The PI expects to be involved in the creation of new mathematical ideas to meet the needs of emerging technology. She plans to share her findings with her colleagues through seminars, colloquia, conferences and publications. She proposes to involve graduate students in her finding through the special topics course, individual works, projects and research problems, and to involve undergraduate students through an Undergraduate Research Program. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).