My research group develops models and algorithms for large-scale inverse problems, especially image reconstruction for X-ray CT and MRI. The models include those based on sparsity using dictionaries learned from large-scale data sets. Developing efficient and accurate methods for dictionary learning is a recent focus.
In the “Big Data” era, data sets are often very large yet incomplete, high dimensional, and complex in nature. Analyzing and deriving critically useful information from such data poses a great challenge to today’s researchers and practitioners. The overall goal of the research agenda of my group is to develop new theoretical frameworks and algorithms for analyzing such large, complex and spatio-temporal data despite the overwhelming presence of missing values and large additive errors. We propose to develop parametric and nonparametric models and methods for (i) handling challenging situations with additive and multiplicative errors, including missing values, in observed variables; (ii) estimating dynamic time varying correlation and graphical structures; (iii) addressing fundamental challenges in “Big Data” such as data reduction, aggregation, interpretation and scale. We expect to uncover the complex structures and the associated conditional independence relationships from observation data with an ensemble of newly designed estimators. Our methods are applicable to many application domains such as neuroscience, geoscience and spatio-temporal modeling, genomics, and network data analysis.