Home Page
Research topics Publications Teaching Curriculum Vitae

## 81. Stability of Least Square
Approximation under Random Sampling, with Xinyue Zhang.
## 80. Stability in Phase Retrieval:
Characterizing Condition Numbers and the Optimal Vector Set, with Yu Xia
and Zili Xu
## 79. Interlacing Polynomial Method for
Matrix Approximation via Generalized Column and Row Selection, with J.-F.
Cai and Zili Xu.
## 78. Asymptotically Sharp Upper Bound for the Column Subset Selection Problem, with J.-F. Cai and Zili Xu, International Mathematics Research Notices, 2024.## 77. Affine phase retrieval for sparse
signals via L1 minimization, with S. Sun, M. Huang, J
Fourier Anal Appl, 2023
## 76. No existence of linear algorithm for Fourier phase retrieval, with Meng Huang, Journal of Complexity, 86 (2025) 101886.## 75. Strong convexity of affine phase
retrieval, with Meng Huang, IEEE Transactions on Signal
Processing, 2024
## 74. The performance of quadratic models for complex phase retrieval, with Yu Xia, Information and Inference: A Journal of the IMA, 2024## 73. 相位恢复：理论、模型与算法，计算数学，2022年2月，第44 卷第1期，1-18.
## 72. Improved bounds in
Weaver's KS_r conjecture for high rank positive semidefinite
matrices, with Zili Xu, Ziheng Zhu, Journal of Functional
Analysis, 29, 2023
## 71. Uniqueness and stability for the
solution of a nonlinear least squares problem, with Meng Huang, Math. Comp., 2024
70. Sparse phase retrieval via
Phaseliftoff, with Yu Xia, IEEE Transactions on Signal Processing,
Page(s): 2129 – 2143, Vol.69, 2021. ## 69.
Bounds on antipodal spherical
designs with few angles, with Z.L. Xu , W.-H. Yu, The Electronic
Journal of Combinatorics,
## 68. Graph Sparsification by Universal Greedy Algorithms, with Ming-jun Lai, Jiaxin Xie, J. Comp. Math., 41 (2023), pp. 741-770.## 67.
Upper and lower bounds for matrix
discrepancy, with
Jiaxin Xie and Ziheng Zhu, J Fourier Anal Appl, (2022) 28:81
## 66.
Performance bound of the
intensity-based model for noisy phase retrieval, with Meng Huang, Applied and
Computational Harmonic Analysis, Volume 68, January 2024, 101584
## 65. The
recovery of complex sparse signals from few phaseless measurements, with Yu Xia, Applied
and Computational Harmonic Analysis, Volume 50,2021.
## 64. Almost Everywhere Generalized Phase Retrieval, with Meng Huang, Yi
Rong and Yang Wang, Applied
and Computational Harmonic Analysis, Vol. 50, January 2021, Pages 16-33
## 63. The minimizers of the $p$-frame
potential,
with Zili Xu, Applied and Computational Harmonic Analysis, Volume
52, May 2021, Pages 366-379
## 62. Subset Selection for Matrices with
Fixed Blocks, with Jiaxin Xie, Israel
Journal of Mathematics, 2021
## 61. Perturbed Amplitude Flow for Phase
Retrieval, with B. Gao, Sun, Yang Wang,
IEEE Transactions on Signal Processing, Vol.68, 5427-5440, 2020.
## 60.The
estimation performance of nonlinear least squares for phase retrieval, with M. Huang, IEEE Transactions
on Information Theory, Volume: 66, Issue: 12, Dec. 7967 -7977, 2020.
## 59. On DC based method for phase
retrieval, with Meng Huang, Ming-jun
Lai and Abraham Varghese,
Approximation
Theory XVI, Nashville, 2019
## 58. Improved bounds for the RIP of
Subsampled Circulant matrices, with Meng Huang, Yuxuan Pang,
Sampling Theory in Signal and Image Processing, (2019), 1–8.
57. Solving Systems of Quadratic
Equations via Exponential-type Gradient Descent Algorithm, with Meng Huang, Journal
of Computational Mathematics, 2019. ## 56. Phase retrieval from the
norms of affine transformations, with Meng Huang, Advance
in Applied Mathematics, Volume 130,2021
55. Data
Recovery on a Manifold from Linear Samples: Theory and Computation, with
J.-F. Cai, Y. Rong, Y. Wang, Annals of Mathematical
Sciences and Applications Volume 3 (2018) Number 1, pp. 337-365 ## 54. Almost everywhere injectivity
conditions for the matrix recovery problem, with Yi Rong, Yang
Wang, Applied
and Computational Harmonic Analysis, Vol.50 January 2021, Pages 386-400
## 53. On generalizations of p-sets and
their applications, with Heng Zhou, Numerical
Mathematics: Theory, Methods and Applications, 12 (2019), pp. 453-466..
## 52. The minimal measurement number problem in
phase retrieval: a review of recent developments, Journal of Mathematical Research with
Applications, Jan, 2017, Vol 37, No.1, pp.40-46.
## 51. Phase retrieval by hyperplanes, with Sara
Botelho-Andrade, Peter G. Casazza, Desai Cheng, John Haas, Tin T. Tran, Janet
C. Tremain Contemporary Mathematics Volume
"Frames and Harmonic Analysis", 2017
50.
A gradient-enhanced L1 approach for
the recovery of sparse trigonometric polynomials, with Tao Zhou.
Commun. Comput. Phys. Vol. 24, No. 1, pp. 286-308, July 2018 ## 49. Improvement of the lower bound of the PCM quantization
error for vectors in R^2, with Heng Zhou, Journal of
approximation theory. Vol. 215, 2017, 1-12.
## 48. Phase Retrieval From the Magnitudes of
Affine Linear Measurements with Bing Gao, Qiyu Sun and Yang
Wang, Advance in Applied Mathematics, 93 (2018), 121–141.
## 47. Phaseless recovery using the
Gauss-Newton method with
B. Gao,
IEEE Trans. Signal Processing. VOL. 65, NO. 22, NOVEMBER 15, 2017
## 46. Generalized phase retrieval :
measurement number, matrix recovery and beyond with Yang Wang. Applied
and Computational Harmonic Analysis, 2019, No.2, 423-446
## 45. The minimal measurement number for
low-rank matrices recovery, Applied
and Computational Harmonic Analysis, 2018
44. Stable Signal Recovery from Phaseless
Measurements with Bing Gao, Yang
Wang. J Fourier Anal Appl (2016) 22: 787. 43. Robustness Properties of
Dimensionality Reduction with Gaussian Random Matrices, with Bin Han, SCIENCE CHINA Mathematics, 2017, 60:
1753-1778 42. A
strong restricted isometry property, with an application to phaseless
compressed sensing, with
V. Voroninski, Applied
and Computational Harmonic Analysis, Volume 40, Issue 2,
March 2016, Pages 386–395. 41. One-Bit Compressed Sensing by Greedy
Algorithms, with W. Liu and D.
Gong,
Numerical Mathematics: Theory , Methods and Applications, Vol. 9, No. 2, pp.
169-184, 2016. 40. Compressed Sensing Matrices from
Fourier Matrices, with
G. Xu,
IEEE Transactions on Information Theory，61(2015),
469-478. 39.
The lower bound of the PCM
quantization error in high dimension, with H. Zhou, Applied
Computational Harmonic Analysis, 2015 38. The performance of orthogonal multi-matching pursuit under RIP , J. Comp. Math 33 (2015), 495-516. 37.
Multivariate discrete least-squares
approximations with a new type of collocation grid, with T. Zhou, A.
Narayan,
SIAM J. Sci. Comput., 36(5), A2401–A2422., 2014. 36.
On sparse interpolation and the
design of deterministic interpolation points, with T. Zhou, SIAM J
Sci. Comp.,Vol.36, 1752-1769, 2014. 35. Phase Retrieval for Sparse Signals, with Yang Wang, Applied
and Computational Harmonic Analysis, Vol 37, 531-544, 2014. 34. On the $\ell_1$-Norm Invariant Convex
k-Sparse Decomposition of Signals, with G. Xu,
Journal of the Operations Research Society of China, December 2013, Volume 1, Issue 4, pp 537-541 33. On B-spline framelets derived from the
unitary extension principle, with Zuowei Shen, SIAM
Journal on Mathematical Analysis, 45(11) 2013, 127-151. 32. The regularity of refinable functions,
with
Yang Wang, Applied Computational Harmonic Analysis，Volume
34, Issue 1, January 2013 31.
Compressed sensing, A survey, Sci Sin Math, 2012, 42(9). 30. The Performance of PCM Quantization
Under Tight Frame Representations, with Yang Wang, SIAM J. MATH.
ANAL, Vol. 44, No. 4, pp. 2802–2823, 2012 29．A remark about orthogonal matching
pursuit algorithm, Advances Adaptive Data Analysis, 2012. 28. Hierarchical zonotopal spaces, with O. Holtz and A.
Ron, Trans.
Amer. Math. Soc., Volume 364, Number 2, 2012. 27．Deterministic Sampling of Sparse
Trigonometric Polynomials, Journal of
Complexity, Volume 27, Issue
2, April 2011, Pages 133-140. 26． Multivariate splines and polytopes, Journal of Approximation Theory, Vol. 163, Issue
3, March 2011.. 25 23．Sagbi bases of Cox-Nagata rings, with Bernd Sturmfels,
Journal
of the European Mathematical Society, Volume 12, Issue 2, 2010. 22．Eulerian
numbers: a spline interpretation , with R. Wang, Y. Xu, Journal of Mathematical Analysis and
Applications, 370 (2010) 486-490. 21．Refinement equations and spline functions, with A.
Dubickas, Adv. Comp. Math. 32: 1-23, 2010. 20．Marginal
Likelihood Integrals for Mixtures of Independence Models, with Shaowei Lin and Bernd
Sturmfels, Journal of Machine Learning Research,
10(Jul):1611--1631, 2009. 18. Discrete Schemes for Gaussian Curvature
and Their Convergence, with G. Xu,
Computers and Mathematics with Applications, 2009 17．Application
of multivariate splines to discrete mathematics, preprint. 16．An explicit formulation for two dimensional vector
partition functions, Contemporary Math : Integer points
in polyhedra--Geometry, Number Theory, Representation Theory, Algebra,
Optimization, Statistics, 2008 PDF 15．Let me tell you my favorite lattice-point
problem, with MATTHIAS BECK, BENJAMIN NILL, BRUCE REZNICK, CARLA SAVAGE
and IVAN SOPRUNOV, Contemporary
Math: Integer points in polyhedra--Geometry, Number Theory, Representation
Theory, Algebra, Optimization, Statistics, 2008. 11．Convergence analysis of discrete differential
geometry operators over surfaces, Lecture Notes in Computer Science,
Mathematics of Surfaces XI, 2005.PDF 6．The
instability degree in the dimension of spaces of bivariate spline, with
Ren-hong Wang, Approx. Theory & its Appl., 18:1,2002,68-80. PS 5．Multivariate
weak spline function space, with Ren-hong Wang, Journal of
Computational and Applied Mathematics, Vol.144, No.1-2, 2002. 2．Application
of uniform design to computer experiments, with Wai-Man Ho, Journal of
the Chinese Statistical Association,2000,No.4. |