RUI: New Applications of Curvature in Image Processing

研究人员，学生和合作者将开发和建立图像处理新模型的数学基础，实施，测试和比较这些新模型与现有模型，并直接将这些模型应用于图像融合，医学成像和视频处理中的问题。拟议中的工作有几个目标。第一个是一个新的图像去噪框架的发展和数学分析，该框架以一种新的有效的方式利用图像曲率的丰富信息。第二个是更好地理解如何在学习的，结构化的和过完备的字典中建模几何特征，以处理和融合退化数据。在这项工作中提出的新模型将制定在变分和补丁为基础的框架，并将主要解决数据已受到噪声和线性degradation.Digital图像现在几乎在每一个领域的科学和技术。在这个项目中开发的模型将用于解决真实的世界问题，包括图像融合，视频处理和医学成像的问题。然而，这些模型将以足够的一般性来制定，以潜在地应用于科学中的广泛应用。在此资助下开发的软件将公开提供。该项目还将支持本科研究人员，他们将实施，测试和比较新的和现有的图像处理模型，确定适当的数值方案，直接与科学家合作，将这些模型应用于真实的世界问题，并在地方和国家会议上展示他们的结果。调查员定期讲授图像处理课程，并为中学生和高中女生及少数民族举办图像处理讲习班。因此，这项工作将适用于科学问题，可供直接和间接相关领域的其他工作人员使用，促进青年科学家的培训，并为代表性不足的群体提供教育机会。

The investigator, students, and collaborators will develop and establish the mathematical foundations of new models for image processing, implement, test and compare these new models with existing ones, and directly apply these models to problems in image fusion, medical imaging, and video processing. The proposed work has several over-arching goals. The first is the development and mathematical analyses of a new framework for image denoising that exploits the rich information of the curvature of an image in a new and effective way. The second is a better understanding of how to model geometric features in learned, structured, and overcomplete dictionaries for processing and fusing degraded data. The new models proposed in this work will be formulated in both the variational and patch-based frameworks, and will mainly address data that have been compromised by noise and linear degradations.Digital images are now used in almost every area of science and technology. The models developed in this project will be used to solve real world problems, including problems in image fusion, video processing, and medical imaging. However, the models will be formulated in enough generality to potentially be applied to a wide array of applications in the sciences. Software developed under the auspices of this grant will be made publicly available. This project will also support undergraduate researchers who will implement, test and compare new and existing image processing models, determine appropriate numerical schemes, work directly with scientists to apply these models to real world problems, and present their results at local and national meetings. The investigator regularly teaches courses on image processing, and leads workshops on image processing for middle school students and high school women and minorities. Thus this work will be applied to problems in the sciences, be accessible for others working in directly and indirectly related fields, promote the training of young scientists, and provide educational opportunities for underrepresented groups.