Computational Methods for Applications in Imaging and Remote Sensing

研究人员将与他们的学生和合作者一起开发新的数学公式和计算技术，用于数据科学、遥感、大气科学和医学成像。这项多学科研究包括对许多自然现象的发现和理解的进步，以及医学领域新成像科学方法的发展。飓风图像的超分辨率对科学和社会都很有价值，因为飓风形成和强度预测的许多方面仍然未知，而对社会来说，更准确的信息可以用于预测风暴的强度和发展。提高被大气湍流扭曲的图像的质量将在国防方面有应用，而改进图像配准算法将极大地帮助医学领域的研究、诊断和治疗决策。该项目每年将为一名研究生提供支持。该项目的活动将在有效的数学公式、成像方法和遥感、大气科学和医学成像方面的应用之间建立联系，在这些领域尚未尝试过类似的方法。新的变分方法，迭代和数值分析技术将发展解决这些和相关的逆问题。特别是，本研究将研究新的鲁棒变分方法及其数值近似，包括：用于恢复大气畸变图像的新的联合反褶积和几何校正变分模型；低分辨率序列时空反卷积的局部和非局部全变分正则化超分辨方法及高效计算算法多尺度分层分解在盲反卷积和图像配准中的新应用。研究人员将促进多学科教学、培训和学习。数学专业的学生将接触到广泛的主题和技术：(i)应用和计算数学，图像处理和分析，以及（ii）数学以外的主题，包括遥感，大气科学和医学成像。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The investigators, along wit their students and collaborators, will develop novel mathematical formulations and computational techniques for applications in data science, remote sensing, atmospheric sciences, and medical imaging. This multidisciplinary research includes advancement of discovery and understanding of many natural phenomena and the development of new imaging sciences methods for the medical field. Super-resolution of hurricane imagery will be of value to science, where many aspects of hurricane formation and strength prediction are still unknown, and to society, which could benefit from more accurate information being used in forecasts of storm strength and development. Improving the quality of images distorted by atmospheric turbulence will have applications in defense, while improving image registration algorithms will tremendously help research, diagnosis, and treatment decisions in the medical field. This project will provide support for one graduate student per year.The project's activities will provide links between efficient mathematical formulations, imaging approaches and applications in remote sensing, atmospheric sciences, and medical imaging, where similar approaches have not yet been attempted. Novel variational approaches, iterative and numerical analysis techniques will be developed for solving these and related inverse problems. In particular, this investigation will study novel robust variational approaches and their numerical approximations, including: a new combined deconvolution and geometric correction variational model for restoration of atmospherically-distorted images; local and nonlocal total variation regularized super-resolution method and an efficient computational algorithm for space-time deconvolution of low-resolution sequences; novel applications of multiscale hierarchical decompositions to blind deconvolution and image registration. The investigators will promote multidisciplinary teaching, training and learning. Mathematics students will be exposed to a broad range of topics and techniques: (i) in applied and computational mathematics, image processing and analysis, and (ii) topics outside mathematics, including remote sensing, atmospheric sciences, and medical imaging.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.