Signal and Data Processing Based on Statistical and Graphical Models

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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. **