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与应用反问题和图像分析。他们将寻求新的方法，结合联合收割机变分参数与计算调和分析和偏微分方程的思想，以克服现有方法的局限性。这项研究将有三个目标：提出新的模型，卡通和纹理分离图像的工作空间的分布;提出全新的技术formulscalehierarchicaldecomposition的图像;提出有效的算法来解决逆问题。从拟议的研究和教育计划，计算数学，图像处理，以及更广泛的领域的科学和工程将受益。应用包括图像分析、医学成像、卫星成像、材料科学和地形数据分析、监视和逆问题。

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.