Sparse Signal Processing and Modeling of High Dimensional Spatio-Temporal Data

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Big high-dimensional spatio-temporal datasets, where the number of measured variables is larger than the sample size, are widely seen in real-world applications (e.g., functional magnetic resonance imaging (fMRI) signals and microarray gene expression time series data). Statistical estimation and inference in high-dimensional situations is fundamentally different from that in the classical setting (with large sample size and smaller number of variables) and many problems are largely open, requiring new statistical signal processing theory and methods involved in regression, clustering, prediction, classification and other statistical problems of high-dimensional data. Generally speaking, estimation and inference in high-dimensional data is not possible without assuming special low-rank (e.g., sparse) structures in the data. With this vision, the current research program will focus on sparse signal processing and modeling of high-dimensional data by both establishing theoretical foundations and developing application-specific novel algorithms.