Areas of Interest:

My main research interest is in finding the most pertinent mathematical principles for analyzing and understanding high-dimensional sensorial data such as images, so that machines and human can make more intelligent decisions. The research endeavor has led me into the following specific areas.

A recent essay by me reflecting on the methodology for research: Warning Signs of Bogus Research Progresses.

Powerpoint slides from a recent talk by me on How to do Research.

Project Websites:

• Low-Rank Matrix Recovery and Completion via Convex Optimization (with Wright, Ganesh, Lin, and Candes et. al.).
• Face Recognition via Sparse Representation (with Wright, Ganesh, Yang, Zhou, and Wagner et. al.).
• Clustering and Classification via Lossy Compression (with Wright, Yang, Mobahi, and Rao, et. al.).
• Generalized Principal Component Analysis (with Huang and Vidal).
• Multiple-View Geometry and 3D Reconstruction (with Kosecka, Soatto, and Sastry).

Funded Projects:

• Federal:
• Advances in the Theory and Practice of Low-Rank Matrix Recovery and Modeling (with Emmanuel Candes, sponsored by NSF).
• Harnessing Sparse and Low-Dimensional Structures for Robust Clustering of Visual Data (sponsored by ONR).
• SGER: Explorations of Robust Image Classification (sponsored by NSF-IIS).
• PHYSNET: Physical Interaction Using the Internet (with Ruzena Bajcsy et. al., sponsored by NSF-HCC).
• Control and Sensing under Limited Information (with Daniel Liberzon, sponsored by NSF-ECS).
• Estimation of Hybrid Models as Algebraic Sets (with Robert Fossum, sponsored by NSF-CCF).
• Estimation of Hybrid Models in Computer Vision (sponsored by ONR).
• Identification of Hybrid Dynamical Systems (with Rene Vidal, sponsored by NSF-EHS).
• Identifying Spatial and Dynamical Patterns from Images (sponsored by NSF-IIS).

University:

• DARPA Urban Challenge (sponsored by the University of Illinois and others).
• Geometry and Algebra in Computer Vision, RAP Program (sponsored by Math Department, the University of Illinois).
• Vision-Based Control (sponsored by the University of Illinois Research Board).

Industry:

• Microsoft Research Fellowship (sponsored by the Microsoft Live Lab.).