CAREER: Signal Processing Through the Lens of Geometry

该项目处理与数据收集和信息处理的下列趋势有关的许多挑战。首先，最近的技术进步正在推动我们的社会产生大量的数据。其次，这种大规模数据的生成和收集正在产生意想不到的后果：这些数据集中定义为不完整，严重错误或错误标记的数据的脏数据比例正在增加。第三，越来越多的人转向依赖相互关联的地理分布数据集进行推理和决策。总的来说，这三个趋势预示着一个不可避免的过渡到数据驱动的世界，充满了大的，肮脏的和分布式的数据。在这个庞大、肮脏、分布式数据的新时代，信息处理需要新的数学数据模型和强大的计算和统计工具。该项目的智力价值在于它解决了庞大、肮脏、分布式数据信息处理的挑战。首先，它通过开发一种新的几何信号/数据模型的理论和算法基础来处理大的脏数据的挑战，该模型可以改善从大数据的推断，即使在脏数据的存在下，由于模型？的能力，忠实地捕捉？环境几何体？of big大data数据.其次，它开发和分析了新的协作处理算法，这些算法建立在所开发的模型之上，以改进对分布在世界各地的大而脏的数据的推断。该项目的研究议程影响了几乎所有依赖于信息处理进步以改进推理和决策的学科。此外，它还通过应用于早期癌症检测、混乱创伤室中的活动识别和协作数字病理学来影响社会和美国医疗保健系统。该项目的教育议程通过新泽西的K-12和大学水平的外展活动，罗格斯大学信号处理课程的现代化，以及对本科生和研究生进行数据科学职业培训，对社会和美国经济产生影响。

This project addresses many of the challenges that pertain to the following trends in data gathering and information processing. First, recent technological advances are pushing our society toward generation of massive quantities of data. Second, this massive data generation and collection is having an unintended consequence: the fraction of dirty data, defined as incomplete, grossly erroneous or mislabeled data, within these data sets is increasing. Third, there is an increasing shift toward relying on interconnected sets of geographically-distributed data for inference and decision making. Collectively, these three trends portend an inevitable transition to a data-driven world rife with big, dirty, and distributed data. Information processing in this new age of big, dirty, distributed data demands novel mathematical data models and robust computational and statistical tools.The intellectual merit of this project lies in the ways it addresses the challenges of information processing for big, dirty, distributed data. First, it deals with the challenge of processing for big, dirty data by developing theoretical and algorithmic foundations of a novel geometric signal/data model that results in improved inference from big data, even in the presence of dirty data, because of the model?s ability to faithfully capture the ?ambient geometry? of big data. Second, it develops and analyzes novel collaborative processing algorithms that build on top of the developed model for improved inference from big, dirty data distributed across the world. The research agenda of this project impacts nearly every discipline that relies on advances in information processing for improved inference and decision making. In addition, it impacts the society and the US healthcare system through its applications to early cancer detection, activity recognition in chaotic trauma bays, and collaborative digital pathology. The education agenda of this project impacts the society and the US economy through K-12 and college level outreach activities within New Jersey, modernization of the Rutgers signal processing curriculum, and training of undergraduate and graduate students for careers in data science.