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From Symmetry to Geometry: Tractable Nonconvex Problems

Jul 18, 2020
Yuqian Zhang, Qing Qu, John Wright

* review paper, 34 pages, 10 figures 

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Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization

Jun 16, 2020
Chong You, Zhihui Zhu, Qing Qu, Yi Ma


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Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications

Jan 20, 2020
Qing Qu, Zhihui Zhu, Xiao Li, Manolis C. Tsakiris, John Wright, René Vidal

* QQ and ZZ contributed equally to the work. Invited review paper for IEEE Signal Processing Magazine Special Issue on non-convex optimization for signal processing and machine learning. This article contains 26 pages with 11 figures 

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Analysis of the Optimization Landscapes for Overcomplete Representation Learning

Dec 10, 2019
Qing Qu, Yuexiang Zhai, Xiao Li, Yuqian Zhang, Zhihui Zhu

* 68 pages, 5 figures 

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Nonsmooth Optimization over Stiefel Manifold: Riemannian Subgradient Methods

Dec 05, 2019
Xiao Li, Shixiang Chen, Zengde Deng, Qing Qu, Zhihui Zhu, Anthony Man Cho So


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Short-and-Sparse Deconvolution -- A Geometric Approach

Oct 01, 2019
Yenson Lau, Qing Qu, Han-Wen Kuo, Pengcheng Zhou, Yuqian Zhang, John Wright

* *YL and QQ contributed equally to this work; 30 figures, 45 pages; This version: added an experiment comparing with other methods, corrected typos and added references 

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A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution

Sep 05, 2019
Qing Qu, Xiao Li, Zhihui Zhu

* 61 pages, 6 figures; short version accepted as a spotlight paper at NeurIPS'19; long version submitted to FoCM 

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Convolutional Phase Retrieval via Gradient Descent

Dec 03, 2017
Qing Qu, Yuqian Zhang, Yonina C. Eldar, John Wright

* 56 pages , 9 figures, appeared in NIPS 2017 

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A Geometric Analysis of Phase Retrieval

Jan 01, 2017
Ju Sun, Qing Qu, John Wright

* Foundations of Computational Mathematics, 18(5):1131--1198, 2018 
* 61 pages, 5 figures. A short version can be found here http://sunju.org/docs/PR_G4_16.pdf . Revised according to reviewers' feedback 

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Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method

Sep 01, 2016
Ju Sun, Qing Qu, John Wright

* IEEE Trans. Information Theory, 63(2): 885 - 914 (2017) 
* The second of two papers based on the report arXiv:1504.06785. Accepted by IEEE Transaction on Information Theory; revised according to the reviewers' comments 

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Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picture

Sep 01, 2016
Ju Sun, Qing Qu, John Wright

* IEEE Trans. Information Theory, 63(2): 853 - 884 (2017) 
* Accepted by IEEE Transaction on Information Theory; revised according to the reviewers' comments 

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Finding a sparse vector in a subspace: Linear sparsity using alternating directions

Jul 20, 2016
Qing Qu, Ju Sun, John Wright

* IEEE Transaction on Information Theory, 62(10):5855 - 5880, 2016 
* Accepted by IEEE Trans. Information Theory. The paper has been revised by the reviewers' comments. The proofs have been streamlined 

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When Are Nonconvex Problems Not Scary?

Apr 23, 2016
Ju Sun, Qing Qu, John Wright

* 6 pages, 3 figures. New examples on phase synchronization and community detection added; emphasis on all local minimizers being global added; exposition is polished. This is a concise expository article that avoids much technical rigor. We will make a separate submission with full technical details in future 

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Complete Dictionary Recovery over the Sphere

Nov 17, 2015
Ju Sun, Qing Qu, John Wright

* 104 pages, 5 figures. Due to length constraint of publication, this long paper are subsequently divided into two papers (arXiv:1511.03607 and arXiv:1511.04777). Further updates will be made only to the two papers 

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Structured Priors for Sparse-Representation-Based Hyperspectral Image Classification

Jan 16, 2014
Xiaoxia Sun, Qing Qu, Nasser M. Nasrabadi, Trac D. Tran

* IEEE Geoscience and Remote Sensing Letter 

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