Signal and Data Processing Based on Statistical and Graphical Models

这项拟议的研究计划的目标是系统地发展新的信号和数据处理理论，基于统计建模、图表和网络方面的最先进的数学理论。新的图形/网络信号模型也将在来自多媒体、经济大数据和传感器/社交网络的各种应用约束下开发。*随着所有领域(包括视频/图像/音频、商业和生物医学应用)以及来自所有类型的来源(例如传感器网络和在线社交媒体网络)的数字数字数据(无论大小)的增长，在这些新兴应用中分析、处理、组织和检索数字信息存在巨大的需求和技术挑战。探索隐藏在数据中的统计结构和关系，可以通过发现和融合数据的领域知识和内在信号特征，为我们有效地处理和理解大量数据提供强大的工具。因此，它在理论和应用上都是一个特别丰富和及时的研究领域。*基于图和网络上的统计信号分析和概率图形建模的新技术和算法有望有效地阐述从各种形式、多个传感器和各种网络中获取的大量数字数据的复杂结构，从而有助于新兴的新一代数据处理、信息挖掘、检索和内容分析应用。*我之前基于多尺度分析和图形统计建模的研究已经在多媒体、传感器网络、电信和经济中的信号和数据应用方面建立了初步的理论框架。研究还表明，图形模型，如隐马尔可夫模型(HMM)和条件随机场(CRF)模型，结合多尺度分析和传统统计方法，很有可能捕捉复杂的数据结构，如视频事件结构和图像对象结构等。在本研究中，我提出：(I)在现有图形信号处理框架的基础上，发展新的通用网络/图形信号处理理论和算法；(Ii)通过整合图形概率模型和确定性图形信号处理，构建最优的图形信号模型和图基，并开发相关的学习方法；以及(Iii)为多媒体和经济数据中新出现的数据应用问题开发基于图形信号处理和统计模型的算法和解决方案。**

The objective of this proposed research program is to systematically develop new signal and data processing theories based on the state-of-the-art mathematical theory in statistical modeling, graph and network. New graph/network signal models will also be developed under various application constraints coming from multimedia, economic big data, and sensor/social networks.******With growing digital numerical data (big or small) in all areas including multimedia, e.g., video/image/audio, business and biomedical applications, and from all type of sources, such as sensor networks and online social media networks, there are tremendous demands and technical challenges in analyzing, processing, organizing and retrieving digital information in these emerging applications. Exploring statistical structure and relationships hidden in data can provide us powerful tools to process and understand a large amount of data in an efficient way by discovering and incorporating domain knowledge and intrinsic signal characteristics of the data. Therefore it is a particularly fertile and timely area of research in both theory and applications. ******The new technology and algorithms based on statistical signal analysis on graphs and networks, and probabilistic graphical modeling are promising to be effective in elaborating the sophisticated structure of large amount digital data acquired from various modalities, multiple sensors, and various networks, and therefore contribute to the emerging new generation data processing, information mining, retrieval and content analysis applications.******My previous research based on multiscale analysis and graphical statistical modeling has established preliminary theoretical framework in signal and data applications in multimedia, sensor networks, telecommunications and economics. My research also shows that graphical models, such as hidden Markov models (HMM) and conditional random field (CRF) models, combined with multiscale analysis and traditional statistical methods, are promising to capture the complex structure of data such as video event structure and image object structure, among others.******In this research, I propose to (i) develop new general network/graph signal processing theory and algorithms based on the existing state-of-the-art graph signal processing framework; (ii) to construct optimal graph signal models and graph basis and develop related learning methods by consolidating graphic probabilistic models and deterministic graph signal processing; and (iii) to develop algorithms and solutions based on graph signal processing and statistical models for emerging data application problems in multimedia and economic data. **