John Wright

ASSOCIATE PROFESSOR OF APPLIED MATHEMATICS

1300 S.W. Mudd
Mail Code 4712

Tel(212) 854 3105
Fax(212) 932 9421

We are currently in the midst of a data revolution. Massive and ever-growing datasets, arising in science, health, or even everyday life, are poised to impact many areas of society. Many of these datasets are not only large – they are high-dimensional, in the sense that each data point may consist of millions or even billions of numbers. To take an example from imaging, a single image can contain millions of pixels or more; a video may easily contain a billion “voxels”. There are fundamental reasons (“curses of dimensionality”) why learning in high-dimensional spaces is challenging. A basic challenge spanning signal processing, statistics, and optimization is to leverage lower-dimensional structure in high-dimensional datasets. Low-dimensional signal modeling has driven developments both in theory and in applications to a vast array of areas, from medical and scientific imaging, to low-power sensors, to the modeling and interpretation of bioinformatic data sets, just to name a few. However, massive modern datasets pose an additional challenge: as datasets grow, and data collection techniques become increasingly uncontrolled, it is common to encounter noise, missing data, and even gross errors or malicious corruptions. Classical techniques break down completely in this setting, and new theory and algorithms are needed.  Wright’s group develops efficient computational tools for recovering low-complexity models from noisy, incomplete, or corrupted observations, proves their correctness, and collaborates with a wide range of colleagues to apply them to problems in data science, imaging, vision, health, and communications. 

Research Interests

High-dimensional data analysis, signal processing, optimization, computer vision

Research Areas

Wright has made fundamental contributions to the theory and practice of estimation from noisy, incomplete and corrupted observations. Key contributions include the development of theory and algorithms for robust sparse vector and low-rank matrix recovery from grossly corrupted observations [with Candes, Li and Ma], the development of the first provable algorithms for (complete) sparse dictionary learning problems [with Spielman and Wang], global geometric analyses of nonconvex optimization problems in signal processing and machine learning [with Ju Sun, Qing Qu, Yuqian Zhang and Han-Wen Kuo]. His work also played an important role in popularizing modern (low-dimensional) signal models and their associated optimization tools in computer vision [with Ma, Yang, Ganesh, Zhang, others].

Wright received a BS in Computer Engineering in 2004, an MS in Electrical Engineering in 2007, and a PhD in Electrical Engineering in 2009, all from the University of Illinois at Urbana-Champaign. From 2009-2011, he was with Microsoft Research Asia. 

HONORS & AWARDS

  • COLT 2012 Best Paper Award (with Spielman, Wang)
  • SPARS 2015 Student Paper Award (for PhD Advisees Ju Sun, Qing Qu)
  • Information and Inference Best Paper Competition, Second Prize (with Ganesh, Min, Ma)
  • 2015 PAMI TC Young Researcher Award

SELECTED PUBLICATIONS

  • Ju Sun, Qing Qu, John Wright, “Complete Dictionary Recovery over the Sphere I: Overview and Geometric Picture”, IEEE Transactions on Information Theory, 2017
  • Ju Sun, Qing Qu, John Wright, “A Geometric Analysis of Phase Retrieval”, International Symposium on Information Theory, 2016
  • Qing Qu, Ju Sun, John Wright, “Finding a Sparse Vector in a Subspace: Linear Sparsity using Alternating Directions”, IEEE Transactions on Information Theory, 2016
  • Yuqian Zhang, Cun Mu, Han-Wen Kuo, John Wright, “Towards Guaranteed Illumination Models for Nonconvex Objects”, International Conference on Computer Vision (ICCV), 2013 
  • John Wright, Arvind Ganesh, Kerui Min, Yi Ma, “Compressive Principal Component Pursuit”, Information and Inference, 2013
  • Daniel Spielman, Huan Wang, John Wright, “Exact Recovery of Sparsely-Used Dictionaries”, Conference on Learning Theory (COLT), 2012
  • Emmanuel Candès, Xiaodong Li, John Wright, “Robust Principal Component Analysis?” Journal of the Association of Computing Machinery (JACM), 2011
  • John Wright, Yi Ma, Julien Mairal, Guillermo Sapiro, Thomas Huang, Shuicheng Yan, “Sparse Representation for Computer Vision and Pattern Recognition”, Proceedings of the IEEE 2010
  • Jianchao Yang, John Wright, Thomas Huang, Yi Ma, “Image Super-Resolution via Sparse Representation”, IEEE Transactions on Image Processing (TIP), 2010
  • John Wright, Allen Yang, Arvind Ganesh, Shankar Sastry, Yi Ma, “Robust Face Recognition via Sparse Representation”, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2009