PDE-based Image Restoration: Efficient Numerical Algorithms and Software Engineering

基于偏微分方程的图像恢复：高效的数值算法和软件工程

• 批准号: 0312223
• 负责人: Seongjai Kim
• 金额: $ 11.05万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0312223&HistoricalAwards=false
• 关键词: PDE; based; Image; Restoration; Efficient

Proposal: DMS-0312223PI: Seongjai Kim [[e-mail]]Institution: University of KentuckyTitle: ITR: PDE-based Image Restoration: Efficient Numerical Algorithms and Software EngineeringABSTRACTAs the field of image processing (IP) requires higher levels of reliability and efficiency, mathematical IP has become an important component. In particular, mathematical frameworks employing recent powerful tools of partial differential equations (PDEs) have been extensively studied to answer fundamental questions in IP. Such PDE-based methods turn out to allow researchers not only to introduce innovative mathematical models but also to analyze and improve traditional algorithms most of which have been developed heuristically. Developing appropriate numerical techniques for the PDE models is another important component for the PDE-based approaches. The proposal is concerned with the development of numerical algorithms for PDE-based image restoration and their applications to challenging problems. The models to be solved include nonlinear PDEs representing motion by mean curvature and Laplacian mean curvature flows, p-harmonic maps, and curvature-based total-variation minimization. The main goals are (a) to develop reliable and efficient numerical algorithms for image restoration, (b) to apply those algorithms for noise removal, image enhancement, and inpainting for real-life images such as medical imagery and satellite images, and (c) to construct related software packages. The newly developed numerical algorithms are expected to deliver large impact on mathematical image analysis; the resulting software packages must be applicable to various interesting problems dealing with images.Many applications in the modern digital age are based on images and therefore the resulting achievements must rely on their quality. Since images are not always in a good quality due to various types of noise, e.g., natural noise, defects in the sensors, and transmission problems, it is important to eliminate the noise automatically. Such image restoration is historically one of the oldest concerns and still a necessary processing step. As the field requires higher levels of reliability and efficiency for the last two decades, mathematical (PDE-based) image restoration has become an important component; it has been extensively studied to answer fundamental questions in image processing and to analyze/improve traditional methods. The proposal is concerned with the development of reliable and efficient computational algorithms for mathematical image restoration, their applications to real-life images, and the construction of software packages. The research emphasis will be on the computational aspects, trying to achieve truly practical algorithms based on the PDE models. Such reliable, efficient, practical algorithms will be implemented for software packages, which will be applicable for critically important problems including medical imaging, security control, crime scene investigation, and environmental watch. The proposed approaches and results can surely deliver benefits not only to research and education in academia but also to practitioners' image processing in industry. In particular, the software packages will provide convenient sources that are easy to maintain and modify for various applications. The investigators propose to explore mathematical frameworks and software engineering techniques to produce reliable and efficient numerical algorithms and related software packages which can support not only research-and-development but also classroom situations.

提案：DMS-0312223 PI：Seongjai Kim [[e-mail]]机构：University of Bucky标题：ITR：基于PDE的图像恢复：高效数值算法与软件工程摘要随着图像处理领域对可靠性和效率的要求越来越高，数学图像处理已经成为一个重要的组成部分。 特别是，数学框架采用最近的强大工具的偏微分方程（PDE）已被广泛研究，以回答IP的基本问题。 这种基于偏微分方程的方法不仅允许研究人员引入创新的数学模型，而且还可以分析和改进传统的算法，其中大多数算法都是在实践中开发的。 为偏微分方程模型开发适当的数值技术是偏微分方程方法的另一个重要组成部分。 该建议是关注的发展基于偏微分方程的图像恢复的数值算法和它们的应用具有挑战性的问题。 要解决的模型包括非线性偏微分方程表示运动的平均曲率和拉普拉斯平均曲率流，p-调和映射，和基于曲率的总变分最小化。 主要目标是（a）开发可靠和有效的图像恢复数值算法，（B）将这些算法应用于去除噪声、图像增强和修复医学图像和卫星图像等真实图像，以及（c）构建相关软件包。 新开发的数值算法有望对数学图像分析产生重大影响;由此产生的软件包必须适用于处理图像的各种有趣问题。现代数字时代的许多应用都基于图像，因此所产生的成就必须依赖于图像的质量。 由于图像由于各种类型的噪声（例如，自然噪声、传感器中的缺陷和传输问题，重要的是自动消除噪声。 这样的图像恢复是历史上最古老的问题之一，并且仍然是必要的处理步骤。 在过去的二十年里，由于该领域需要更高水平的可靠性和效率，数学（基于偏微分方程）图像恢复已成为一个重要组成部分;人们对它进行了广泛的研究，以回答图像处理中的基本问题并分析/改进传统方法。 该提案涉及的发展可靠和有效的计算算法的数学图像恢复，其应用到现实生活中的图像，和软件包的建设。 研究重点将放在计算方面，试图实现真正实用的算法的基础上的偏微分方程模型。 这种可靠、高效、实用的算法将用于软件包，这些软件包将适用于包括医学成像、安全控制、犯罪现场调查和环境监测在内的至关重要的问题。 所提出的方法和结果不仅对学术界的研究和教育，而且对工业界的图像处理从业者也有一定的帮助。 特别是，软件包将提供方便的来源，易于为各种应用程序维护和修改。研究人员建议探索数学框架和软件工程技术，以产生可靠和有效的数值算法和相关的软件包，不仅可以支持研究和开发，而且还可以支持课堂情况。