Interdisciplinary Study in Image and Signal Processing

这是一个在数学科学跨学科赠款计划下的教育重点的研究建议。 主要研究者建议获得广泛的背景在工程科学具体到图像和信号处理，建立一个跨学科的研究计划，通过形态神经网络和基于PDE的方法图像处理，并准备材料的研究生专题课程的数学方法在图像处理。 她计划研究和发展神经网络建模和分析的数学理论和方法，特别是研究与神经网络相关的控制相变现象的偏微分方程。 她还建议改进现有的偏微分方程模型，发展新的偏微分方程模型，以及研究由图像处理引起的非线性退化抛物方程的理论和方法。1999-2000学年，该项目负责人将在佛罗里达大学计算机与信息科学与工程系（CISE）工作。 她计划参加CISE的几门课程，并通过参加研讨会和项目与计算机科学家及其研究生密切互动。 她计划从事两个项目，一个是将形态神经网络应用于自动目标识别，另一个是通过基于偏微分方程的方法将图像分析应用于计算机辅助放射治疗。PI希望参与创造新的数学思想，以满足新兴技术的需求。她计划通过研讨会、座谈会、会议和出版物与同事分享她的发现。她建议通过专题课程，个人作品，项目和研究问题，让研究生参与她的发现，并通过本科生研究计划让本科生参与。 该IGMS项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。

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).