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.
