CAREER: Signal Processing Through the Lens of Geometry

该项目解决了与以下数据收集和信息处理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数据。其次，这种海量数据的生成和收集正在产生意想不到的后果：脏数据在这些数据集中的比例正在增加。脏数据被定义为不完整、严重错误或标签错误的数据。第三，越来越多的人转向依赖地理上分布的相互关联的数据集进行推理和决策。总而言之，这三个趋势预示着不可避免地过渡到数据驱动的世界，这个世界充斥着大数据、肮脏数据和分布式数据。在这个大数据、脏数据、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。该项目的智力优势在于它解决了大数据、脏数据、分布式数据的信息处理挑战。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应对处理大数据的挑战，该模型能够改进对大数据的推断，即使在存在脏数据的情况下也是如此，因为该模型？S能够忠实地捕捉环境几何？大数据。其次，它开发和分析了新的协作处理算法，这些算法建立在开发的模型之上，以改进对分布在世界各地的大数据的推理。这个项目的研究议程影响到几乎所有依赖信息处理进步来改进推理和决策的学科。此外，它还通过其在癌症早期检测、混乱创伤间隔区的活动识别和协作数字病理学方面的应用，影响了社会和美国医疗体系。该项目的教育议程通过在新泽西州的K-12和大学层面的推广活动、罗格斯大学信号处理课程的现代化以及为数据科学的职业生涯培训本科生和研究生来影响社会和美国经济。

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.