New variational computational methods for modeling dual spaces of distributions, decomposition of functions, oscillations, and inverse problems in image analysis

研究人员将研究新的计算技术，并将其应用于反问题和图像分析。他们将寻求将变分论证与计算调和分析和偏微分方程的思想相结合的新方法，以克服现有方法的局限性。这项研究将有三个目标：通过处理分布空间，提出图像中卡通和纹理分离的新模型；提出全新的图像分级分解技术；提出解决逆问题的有效算法。从所提出的研究和教育计划中，计算数学、图像处理以及更广泛的科学和工程领域将受益。应用包括图像分析、医学成像、卫星成像、材料科学、地形数据分析、监视和反问题。

The investigators will study new computational techniques withapplications to inverse problems and image analysis. They will seek newmethods that combine variational arguments with ideas from computationalharmonic analysis and partial differential equations in order to overcomelimitations of existing methods. The research will have three objectives:propose new models for cartoon and texture separation in images by workingwith spaces of distributions; propose completely new techniques formultiscale hierarchical decomposition of images; propose efficientalgorithms for solving inverse problems.From the proposed research and educational program, computational mathematics, image processing, as well as more general areas of science andengineering will benefit. Applications include image analysis, medicalimaging, satellite imaging, material science, and terrain data analysis,surveillance and inverse problems.