(Photo by SL, on the way to Albuquerque for SIAM IS16, May 2016)
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Preprints (* indicates equal contribution)

• J. Sulam, C. You, and Z. Zhu, ‘‘Recovery and Generalization in Over-Realized Dictionary Learning," preprint, 2020.

• Q. Qu*, Z. Zhu*, X. Li, M. C. Tsakiris, J. Wright, and R. Vidal, ‘‘Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications," preprint, 2020.

• Q. Qu, Y. Zhai, X. Li, Y. Zhang, and Z. Zhu, ‘‘Analysis of the Optimization Landscapes for Overcomplete Representation Learning,’’ preprint, 2019.

• X. Li, Z. Zhu, A. M. So, and J. Lee, ‘‘Incremental Methods for Weakly Convex Optimization,’’ preprint, 2019.

• Q. Li*, Z. Zhu*, G. Tang, and M. B. Wakin, ‘‘Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems,’’ preprint, 2019.

• Z. Zhu, Y. Wang, D. P. Robinson, D. Naiman, R. Vidal, and M. C. Tsakiris, ‘‘Dual Principal Component Pursuit: Improved Analysis and Efficient Algorithms,’’ preprint, 2018.

• Z. Zhu and X. Li, ‘‘Convergence Analysis of Alternating Nonconvex Projections,’’ preprint, 2018.

Book chapters

• R. Vidal, Z. Zhu, and B. Haeffele, ‘‘Optimization Landscape of Neural Networks,” in G. Kutyniok and P. Grohs (Eds.), Mathematics of Deep Learning, Cambridge University Press, 2021.

Journal Papers

• Z. Zhu and M. B. Wakin, ‘‘Time-Limited Toeplitz Operators on Abelian Groups: Applications in Information Theory and Subspace Approximation,’’ to appear in Pure and Applied Functional Analysis.

• Z. Zhu*, Q. Li*, G. Tang, and M. B. Wakin, ‘‘The Global Optimization Geometry of Low-Rank Matrix Optimization,’’ IEEE Transactions on Information Theory, vol. 67, no. 2, pp. 1308-1331, 2021.

• X. Li*, S. Chen*, Z. Deng, Q. Qu, Z. Zhu, and A.M.-C. So, ‘‘Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods,’’ SIAM Journal on Optimization, vol. 31, no. 3, pp. 1605–1634, 2021.

• X. Li, Z. Zhu, Q. Li, and K. Liu, ‘‘A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization," IEEE Transactions on Knowledge and Data Engineering, 2021.

• K. Liu, X. Li, Z. Zhu, L. Brand, and H. Wang, ‘‘Factor-Bounded Nonnegative Matrix Factorization,’’ ACM Transactions on Knowledge Discovery from Data, vol. 15, pp. 1-18, 2021.

• Q. Qu, X. Li, and Z. Zhu, ‘‘Exact Recovery of Multichannel Sparse Blind Deconvolution via Gradient Descent", SIAM Journal on Imaging Sciences, vol. 13, no. 3, pp. 1630-1652, 2020.

• Y. Li, Y. Zhang, and Z. Zhu, ‘‘Error-Tolerant Deep Learning for Remote Sensing Image Scene Clas-sification", IEEE Transactions on Cybernetics, vol. 51, no. 4, pp. 1756-1768, 2020.

• S. Li, Q. Li, Z. Zhu, G. Tang, and M. B. Wakin, ‘‘The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery without Regularization," IEEE Signal Processing Letters, vol. 27, pp. 1400-1404, 2020.

• X. Li*, Z. Zhu*, A.M.-C. So, and R. Vidal, ‘‘Nonconvex Robust Low-rank Matrix Recovery,’’ SIAM Journal on Optimization, vol. 30, no. 1, pp. 660-686, 2020. (authors’ copy)

• Z. Zhu, D. Soudry, Y. C. Eldar, and M. B. Wakin, ‘‘The Global Optimization Geometry of Shallow Linear Neural Networks,’’ Mathematical Foundations of Deep Learning in Imaging Science, special issue of Journal of Mathematical Imaging and Vision, vol. 62, pp. 279-292, 2020. (authors’ copy)

• S. Karnik, Z. Zhu, M. B. Wakin, J. Romberg, and M. A. Davenport, ‘‘The Fast Slepian Transform,’’ Applied and Computational Harmonic Analysis, vol 46, no. 3, pp. 624-652, May 2019. (authors’ copy)

• Q. Li, Z. Zhu, and G. Tang, ‘‘The Non-convex Geometry of Low-rank Matrix Optimization,’’Information and Inference: A Journal of the IMA, vol 8, no. 1, pp. 51-96, March 2019. (authors’ copy)

• T. Hong, X. Li, Z. Zhu, and Q. Li, ‘‘Optimized Structured Sparse Sensing Matrices for Compressive Sensing,’’ Signal Processing, vol. 159, pp. 119-129, June 2019.(authors’ copy)

• C. Wang, Z. Zhu, H. Gu, X. Wu, and S. Liu, ‘‘Hankel Low-rank Approximation for Seismic Noise Attenuation,’’ IEEE Transactions on Geoscience and Remote Sensing, vol 57, no. 1, pp. 561-573, January 2019.

• Z. Zhu, S. Karnik, M. B. Wakin, M. A. Davenport, and J. Romberg, ‘‘ROAST: Rapid Orthogonal Approximate Slepian Transform,’’ IEEE Transactions on Signal Processing, vol 66, no. 22, pp. 5887-5901, November 2018. (authors’ copy)

• Z. Zhu, Q. Li, G. Tang, and M. B. Wakin, ‘‘Global Optimality in Low-rank Matrix Optimization,’’ IEEE Transactions on Signal Processing, vol 66, no. 13, pp. 3614–3628, July 2018. (authors’ copy)

• Z. Zhu, G. Li, J. Ding. Q. Li, and X. He, ‘‘On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm,’’ SIAM Journal on Imaging Sciences, vol 11, no. 2, pp. 1717-1758, 2018. (authors’ copy)

• Z. Zhu, S. Karnik, M. A. Davenport, J. K. Romberg, and M. B. Wakin ‘‘The Eigenvalue Distribution of Discrete Periodic Time-Frequency Limiting Operators,’’ IEEE Signal Processing Letters, vol. 25, no. 1, pp.95–99, January 2018. (authors’ copy)

• Z. Zhu and M. B. Wakin, ‘‘Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries,’’ Journal of Fourier Analysis and Applications, vol. 23, no. 6, pp. 1263-1310, December 2017. (authors’ copy)

• X. Wu, and Z. Zhu, ‘‘Methods to Enhance Seismic Faults and Construct Fault Surfaces,’’ Computers & Geosciences, vol. 107, pp. 37-48, October 2017.

• T. Hong and Z. Zhu, ‘‘An Efficient Method for Robust Projection Matrix Design,’’ Signal Processing, vol. 143, pp. 200-210, February 2018.(authors’ copy)

• Z. Zhu and M. B. Wakin, ‘‘On the Asymptotic Equivalence of Circulant and Toeplitz Matrices,’’ IEEE Transactions on Information Theory, vol. 63, no. 5, pp. 2975-2992, May, 2017. (author's copy)

• G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, ‘‘On Projection Matrix Optimization for Compressive Sensing Systems,’’ IEEE Transactions on Signal Processing, vol. 61, no. 11, pp. 2887-2898, June 2013.

Conference Papers–Machine Learning

• Z. Zhu*, T. Ding*, J. Zhou, X. Li, C. You, J. Sulam, and Q. Qu, ‘‘A Geometric Analysis of Neural Collapse with Unconstrained Features," Neural Information Processing Systems (NeurIPS), December 2021. (spotlight, top 3% ; acceptance rate = 26%)

• L. Ding, L. Jiang, Y. Chen, Q. Qu, and Z. Zhu, ‘‘Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery", Neural Information Processing Systems (NeurIPS), December 2021. (acceptance rate = 26%)

• S. Liu*, X. Li*, Y. Zhai, C. You, Z. Zhu, C. Fernandez-Granda, and Q. Qu, ‘‘Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training,’’ Neural Information Processing Systems (NeurIPS), December 2021. (acceptance rate = 26%)

• T. Chen, B. Ji, T. DING, B. Fang, G. Wang, Z. Zhu, L. Liang, Y. Shi, S. Yi, and X. Tu, ‘‘Only Train Once: A One-Shot Neural Network Training And Pruning Framework", Neural Information Processing Systems (NeurIPS), December 2021. (acceptance rate = 26%)

• T. Ding, Z. Zhu, R. Vidal, and D. P. Robinson, ‘‘Dual Principal Component Pursuit for Robust Subspace Learning: Theory and Algorithms for a Holistic Approach", International Conference on Machine Learning (ICML), 2021. (acceptance rate = 21%)

• T. Ding, L. Liang, Z. Zhu, and I. Zharkov, ‘‘CDFI: Compression-driven Network Design for Frame Interpolation," Computer Vision and Pattern Recognition (CVPR), 2021. (acceptance rate = 23%)

• T. Ding, Z. Zhu, M. C. Tsakiris, R. Vidal, and D. P. Robinson, ‘‘Dual Principal Component Pursuit for Learning a Union of Hyperplanes: Theory and Algorithms," Artificial Intelligence and Statistics (AISTATS), 2021. (acceptance rate = 29%)

• C. You*, Z. Zhu*, Q. Qu, and Y. Ma, ‘‘Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization," Neural Information Processing Systems (NeurIPS), December 2020. (spotlight, top 4% ; acceptance rate = 20%)

• X. Li, Z. Zhu, A. M. So, and J. Lee, ‘‘Incremental Methods for Weakly Convex Optimization," NeurIPS 2020 Workshop on Optimization for Machine Learning (OPT 2020), December 2020.

• T. Chen, T. Ding, B. Ji, G. Wang, Y. Shi, S. Yi, X.Tu, Z. Zhu, ‘‘Orthant Based Proximal Stochastic Gradient Method for L-1 Regularized Optimization", to appear in European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), Ghent, Belgium, September 2020. (acceptance rate = 19%)

• T. Ding, Y. Yang, Z. Zhu, D. Robinson, R. Vidal, L. Kneip, M. C. Tsakiris, ‘‘Robust Homography Estimation via Dual Principal Component Pursuit,’’ IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, Washington, June 2020. (acceptance rate = 22%)

• Q. Qu, Y. Zhai, X. Li, Y. Zhang, and Z. Zhu, ‘‘Analysis of the Optimization Landscapes for Overcomplete Representation Learning,’’ International Conference on Learning Representations (ICLR), Addis Ababa, Ethiopia, April 2020. (authors’ copy) (oral, top 1.8% ; acceptance rate = 26%)

• Z. Zhu, T. Ding, M.C. Tsakiris, D. Robinson, and R. Vidal, ‘‘A Linearly Convergent Method for Non-smooth Non-convex Optimization on Grassmannian with Applications to Robust Subspace and Dictionary Learning,’’ Neural Information Processing Systems (NeurIPS), Vancouver, Canada, December 2019. (poster) (code) (acceptance rate = 21%)

• Z. Zhu*, Q. Li*, X. Yang, G. Tang, and M. B. Wakin, ‘‘Global Optimality in Distributed Low-rank Matrix Factorization,’’ Neural Information Processing Systems (NeurIPS), Vancouver, Canada, December 2019. (acceptance rate = 21%)

• Q. Qu, X. Li, and Z. Zhu, ‘‘A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution,’’ Neural Information Processing Systems (NeurIPS), Vancouver, Canada, December 2019. (spotlight , top 4% ; acceptance rate = 21%)

• Q. Li*, Z Zhu*, and G. Tang, ‘‘Alternating Minimizations Converge to Second-Order Optimal Solutions,’’ International Conference on Machine Learning (ICML), Long Beach, CA, USA, June 2019. (acceptance rate = 22%)

• T. Ding*, Z Zhu*, T. Ding, Y. Yang, D. Robinson, M. Tsakiris, and R. Vidal, ‘‘Noisy Dual Principal Component Pursuit,’’ International Conference on Machine Learning (ICML), Long Beach, CA, USA, June 2019. (acceptance rate = 22%)

• Z. Zhu, Y. Wang, D. P. Robinson, D. Naiman, R. Vidal, and M. C. Tsakiris, ‘‘Dual Principal Component Pursuit: Improved Analysis and Efficient Algorithms,’’ Neural Information Processing Systems (NeurIPS), Montreal, Quebec, Canada, December 2018. (author's copy) (acceptance rate = 21%)

• Z. Zhu*, X. Li*, K. Liu, and Q. Li, ‘‘Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization,’’ Neural Information Processing Systems (NeurIPS), Montreal, Quebec, Canada, December 2018. (author's copy) (poster) (acceptance rate = 21%)

Conference Papers–Signal Processing

• Q. Li, X. Yang, Z. Zhu, G. Tang, and M. B. Wakin, ‘‘The Geometric Effects of Distributing Constrained Nonconvex Optimization Problems,’’ IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2019. (candidates for the Best Student Paper Award)

• Y. Li, Y. Zhang, and Zhihui Zhu, ‘‘Learning Deep Networks under Noisy Labels for Remote Sensing Image Scene Classification,’’ IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Yokohama, Japan, July 2019.

• Q. Li, Z. Zhu, G. Tang, and M. B. Wakin, ‘‘The Geometry Of Equality-Constrained Global Consensus Problems,’’ IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK, May 2019.

• Z. Zhu, M. Lopez-Santillana, and M. B. Wakin,‘‘Super-Resolution of Complex Exponentials from Modulations with Known Waveforms,’’ IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Curacao, Dutch Antilles, December 2017.

• Z. Zhu, Q. Li, G. Tang, and M. B. Wakin, ‘‘Global Optimality in Low-rank Matrix Optimization,’’ IEEE Global Conference on Signal and Information Processing (GlobalSIP), Montreal, Quebec, Canada, November 2017.

• Z. Zhu, D. Yang, M. B. Wakin, and G. Tang, ‘‘A Super-resolution Algorithm for Multiband Signal Identification,’’ 51st Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, October 2017.

• Z. Zhu, S. Karnik, M. B. Wakin, M. A. Davenport, and J. K. Romberg, ‘‘Fast Orthogonal Approximations of Sampled Sinusoids and Bandlimited Signals,’’ IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, March 2017.

• G. Li, Z. Zhu, H. Bai, and A. Yu, ‘‘A New Framework for Designing Incoherent Sparsifying Dictionaries,’’ IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, March 2017.

• Q. Li, S. Li, H. Mansour, M. Wakin, D. Yang, and Z. Zhu, ‘‘JAZZ: A Companion to MUSIC for Frequency Estimation with Missing Data,’’ IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, March 2017.

• S. Karnik, Z. Zhu, M. B. Wakin, J. K. Romberg, M. A. Davenport, ‘‘Fast Computations for Approximation and Compression in Slepian Spaces,’’ IEEE Global Conference on Signal and Information Processing (GlobalSIP), Greater Washington, D.C., December 2016.

• Z. Zhu and M. B. Wakin, ‘‘On the Dimensionality of Wall and Target Return Subspaces in Through-theWall Radar Imaging,’’ 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), Aachen, Germany, September 2016.

• Z. Zhu, G. Tang, P. Setlur, S. Gogineni, M. Wakin, and M. Rangaswamy, ‘‘Super-Resolution in SAR Imaging: Analysis With the Atomic Norm,’’ IEEE Sensor Array and Multichannel Signal Processing (SAM) Workshop, Rio de Janeiro, Brazil, July 2016.

• Z. Zhu and M. B. Wakin, ‘‘New Analysis of Multiband Modulated DPSS Dictionaries,’’ Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS’15), Cambridge, England, July 2015.

• Z. Zhu and M. B. Wakin, ‘‘Wall Clutter Mitigation and Target Detection Using Discrete Prolate Spheroidal Sequences,’’ 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), Pisa, Italy, June 2015.

• Z. Zhu and M. B. Wakin, ‘‘Detection of Stationary Targets Using Discrete Prolate Spheroidal Sequences,’’ International Review of Progress in Applied Computational Electromagnetics (ACES), Williamsburg, Virginia, March 2015.

• H. Bai, Z. Zhu, G. Li, and S. Li, ‘‘Design of Optimal Measurement Matrix for Compressive Detection,’’ Proc. of the 10th International Symposium on Wireless Communication Systems (ISWCS 2013), Ilmenau, Germany, August 2013.

• S. Li, Z. Zhu, G. Li, L. Chang, and Q. Li, ‘‘Projection Matrix Optimization for Block-sparse Compressive Sensing,’’ IEEE International Conference on Signal Processing, Communication and Computing (ICSPCC 2014), Kunming, August 2013.

• Q. Li, Z. Zhu, S. Tang, L. Chang, and Gang Li, ‘‘Projection Matrix Optimization Based on SVD for Compressive Sensing Systems," 32nd Chinese Control Conference (CCC), Xi'an, July 2013.

• Z. Zhu, D. Yang, G. Li, and C. Huang, ‘‘Stable 2nd Order Adaptive IIR Filter Structure for Blind Deconvolution," Proc. 4th Int. Conf. on Image and Signal Processing (CISP), Shanghai, October 2011.

Ph.D. thesis

• Z. Zhu, ‘‘Subspace Approximation on the Continuum,’’ Ph.D. thesis, Colorado School of Mines, 2017.

Technical reports

• Q. Li, Z. Zhu, and G. Tang, ‘‘Geometry of Factored Nuclear Norm Regularization,’’ preprint, 2017.