Computational Methods for Applications in Imaging and Remote Sensing

研究人员，沿着他们的学生和合作者，将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。 这种多学科的研究包括许多自然现象的发现和理解的进步，以及医学领域新的成像科学方法的发展。飓风图像的超分辨率将对科学和社会都有价值，因为在科学领域，飓风形成和强度预测的许多方面仍然是未知的，而社会则可以从用于风暴强度和发展预测的更准确信息中受益。提高大气湍流导致的图像失真的质量将在国防中得到应用，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。该项目每年将资助一名研究生，其活动将在遥感、大气科学和医学成像等尚未尝试过类似方法的领域提供有效数学公式、成像方法和应用之间的联系。新的变分方法，迭代和数值分析技术将开发解决这些和相关的反问题。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：一种新的用于恢复大气畸变图像的反卷积和几何校正组合变分模型，局部和非局部全变分正则化超分辨率方法和一种有效的低分辨率序列时空反卷积计算算法;多尺度分层分解在盲解卷积和图像配准中的新应用。调查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，（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NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.