Signal and Data Processing Based on Statistical and Graphical Models

本研究计划的目标是在统计建模、图和网络的最新数学理论的基础上，系统地发展新的信号和数据处理理论。新的图形/网络信号模型也将在多媒体、经济大数据和传感器/社交网络等各种应用约束下发展。******随着所有领域的数字数据（或大或小）的增长，包括多媒体，如视频/图像/音频，商业和生物医学应用，以及来自所有类型的来源，如传感器网络和在线社交媒体网络，在分析，处理，组织和检索这些新兴应用中的数字信息方面存在巨大的需求和技术挑战。通过发现和整合数据的领域知识和内在信号特征，探索隐藏在数据中的统计结构和关系，可以为我们有效地处理和理解大量数据提供强大的工具。因此，它在理论和应用方面都是一个特别丰富和及时的研究领域。******基于图形和网络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模式、多传感器和各种网络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建立了多媒体、传感器网络、电信和经济学中信号和数据应用的初步理论框架。我的研究还表明，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的统计方法，有望捕获数据的复杂结构，如视频事件结构和图像对象结构等。******在本研究中，我建议(I)基于现有的最先进的图信号处理框架，开发新的通用网络/图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信号处理，构建最优的图信号模型和图基，开发相关的学习方法；（iii）开发基于图形信号处理和统计模型的算法和解决方案，以解决多媒体和经济数据中出现的数据应用问题。**

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. **