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My research focuses on using convex and non-convex optimization methods to model and solve problems in signal and information processing, physical sciences, and machine learning. I am especially interested in designing optimization procedures that come with theoretical performance guarantees and that are scalable to large data sets. A common theme of my work is leveraging prior structures and domain knowledge in a computationally effective way; these structures could be sparsity, manifold, smoothness, dynamics, graphs, and so on. One of the most interesting parts of this work is to explore the trade-offs between computational time, statistical performance, and sampling complexity. A few current projects include tensor decomposition and completion in machine learning, super-resolution and phase retrieval in imaging, spectral estimation in sensor array and radar problems, and causality inference in graphical modeling.

News

  • Mar. 2016: Dr. Yuejie Chi and I presented a tutorial on “Convex Optimization Techniques for Super-resolution Parameter Estimation” at ICASSP 2016. The slides are here.

  • Feb. 2016: Paper on “Overcomplete Tensor Decomposition via Convex Optimization” with my student Qiuwei Li, Dr. Ashley Prater, and Dr. Lixin Shen was posted on arXiv. In this paper, we constructed a dual certificate to certify tensor decompositions that achieve the tensor nuclear norm under incoherence conditions.

  • Jan. 2016: Paper on “Super-Resolution of Complex Exponentials from Modulations with Unknown Waveforms” with Dehui Yang and Dr. Michael Wakin was posted on arXiv. Poster for ICASSP is here. In this paper, we considered parameter estimation of complex exponentials from their modulations with unknown waveforms, allowing for non-stationary blind super-resolution. The atomic norm minimization achieves information theoretic limit.

  • Sep. 2015: Paper on “Sparse and Low-Rank Tensor Decomposition” with Parikshit Shah and Nikhil Rao has been accepted to NIPS 2015.

  • Dec. 2015: I organized a special session on “Super-resolution and Atomic Norms” at CAMSAP 2015.

  • May 2015: I participated the Air Force Summer Faculty Fellowship Program.