PhD in Mathematics
Harvard University, 1990
A new binary representation method for shape convexity and application to image segmentation
Article
A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
Article
Adversarial domain translation networks for integrating large-scale atlas-level single-cell datasets
Article
An Error Analysis of Generative Adversarial Networks for Learning Distributions
Article
Approximation in shift-invariant spaces with deep ReLU neural networks
Article
BiGCN: A bi-directional low-pass filtering graph neural network
Article
Hyper-Gaussian regularized Whittaker–Kotel’nikov–Shannon sampling series
Article
Article
On the Capacity of Deep Generative Networks for Approximating Distributions
Article
Retinex-based variational framework for low-light image enhancement and denoising
Article
Solving phase retrieval with random initial guess is nearly as good as by spectral initialization
Article
The Global Landscape of Phase Retrieval II: Quotient Intensity Models
Article
Almost everywhere generalized phase retrieval
Article
Multiscale high-dimensional sparse Fourier algorithms for noisy data
Article
Overlapping domain decomposition methods for ptychographic imaging
Article
Phase retrieval for sub-Gaussian measurements
Article
The Global Landscape of Phase Retrieval I: Perturbed Amplitude Models
Article
Optimal ℓ ^{1} Rank One Matrix Decomposition
Book chapter
Deep Generative Learning via Schrödinger Bridge
Conference paper
Explore Mindfulness Without Deflection: A Data Art Based on the Book of Songs
Conference paper
Generalized Linear Bandits with Local Differential Privacy
Conference paper
Non-asymptotic Error Bounds for Bidirectional GANs
Conference paper
Dissecting a square into congruent polygons
Article
High-dimensional sparse Fourier algorithms
Article
Perturbed Amplitude Flow for Phase Retrieval
Article
Variational Single Image Dehazing for Enhanced Visualization
Article
Learning Hybrid Representations for Automatic 3D Vessel Centerline Extraction
Conference paper
Almost everywhere injectivity conditions for the matrix recovery problem
Article
Fast Rank-One Alternating Minimization Algorithm for Phase Retrieval
Article
Generalized Phase Retrieval: Measurement Number, Matrix Recovery and Beyond
Article
An Iteration Method for X-Ray CT Reconstruction from Variable-Truncation Projection Data
Conference paper
Convex Shape Prior for Multi-Object Segmentation Using a Single Level Set Function
Conference paper
Data-driven method for 3D axis-symmetric object reconstruction from single cone-beam projection data
Conference paper
Data-driven tight frame for Cryo-EM image denoising and conformational classification
Conference paper
Deep Generative Learning via Variational Gradient Flow
Conference paper
Deep Generative Learning via Variational Gradient Flow
Conference paper
Low-dose X-ray computed tomography image reconstruction using edge sparsity regularization
Conference paper
Data recovery on a manifold from linear samples: theory and computation
Article
Newman Cyclotomic Polynomials, Refinable Splines and the Euler Binary Partition Function
Article
Phase Retrieval from the Magnitudes of Affine Linear Measurements
Article
Random Matrices and Erasure Robust Frames
Article
Scattering Transform and Sparse Linear Classifiers for Art Authentication
Article
Synchronized Recovery Method for Multi-Rank Symmetric Tensor Decomposition
Conference paper
Efficient Estimation of Regularization Parameters via Downsampling and the Singular Value Expansion
Article
Robust Sparse Phase Retrieval Made Easy
Article
Subspace clustering by (k,k)-sparse matrix factorization
Article
Topological Invariants and Lipschitz Equivalence of Fractal Squares
Article
A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging
Book chapter
Fourier bases and Fourier frames on self-affine measures
Conference paper
A multiscale sub-linear time Fourier algorithm for noisy data
Article
Fast Phase Retrieval from Local Correlation Measurements
Article
On the decay of the smallest singular value of submatrices of rectangular matrices
Article
Stable Signal Recovery from Phaseless Measurements
Article
Stylometry and mathematical study of authorship
Book chapter
Gabor orthonormal bases generated by the unit cubes
Article
Self-similar subsets of the Cantor set
Article
Tiling Z^{2} by a Set of Four Elements
Conference paper
Lipschitz equivalence of self-similar sets with touching structures
Article
Phase retrieval for sparse signals
Article
Phase retrieval from very few measurements
Article
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
Conference paper
Adaptive sub-linear time Fourier algorithms
Article
Bayesian learning of sparse multiscale image representations
Article
Edge detection from truncated Fourier data using spectral mollifiers
Article
Invertibility and robustness of phaseless reconstruction
Article
Necessary and sufficient conditions to perform Spectral Tetris
Article
Phase aliasing correction for robust blind source separation using DUET
Article
Source extraction in audio via background learning
Article
The regularity of refinable functions
Article
Vakman's problem and the extension of Hilbert transform
Article
On the convergence of iterative filtering empirical mode decomposition
Book chapter
Speeding up scientific imaging workflows: Design of automated image annotation tool
Conference paper
A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows
Article
Coarse quantization for random interleaved sampling of bandlimited signals
Article
Empirical mode decomposition analysis for visual stylometry
Article
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel
Article
Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios
Article
Mathematical methods for images and surfaces 2011
Article
Mode Decomposition Evolution Equations
Article
Selective extraction of entangled textures via adaptive PDE transform
Article
Sparse PCA by iterative elimination algorithm
Article
Spectral Tetris Fusion Frame Constructions
Article
The performance of PCM quantization under tight frame representations
Article
Constructing tight fusion frames
Article
Partial differential equation transform: Variational formulation and Fourier analysis
Article
Reconstruction from irregular Fourier samples and Gaussian spectral mollifiers
Article
Spectral tetris fusion frame constructions
Conference paper
Classification of Refinable Splines in ℝd
Article
Mathematical methods for images and surfaces
Article
Article
Article
Convergence of a convolution-filtering-based algorithm for empirical mode decomposition
Article
Iterative filtering as an alternative algorithm for empirical mode decomposition
Article
Lattice quantization error for redundant representations
Article
On the structures of generating iterated function systems of Cantor sets
Article
The β α-Encoders for robust A/D conversion
Article
Constructions and existence of tight fusion frames
Conference paper
Lattice quantization error for redundant representations
Conference paper
Sigma-delta quantization errors and the traveling salesman problem
Article
Asymptotic white noise hypothesis for PCM quantization
Conference paper
Multifractal analysis and authentication of Jackson Pollock paintings
Conference paper
Article
Refinable functions with non-integer dilations
Article
Structure of refinable splines
Article
White noise hypothesis for uniform quantization errors
Article
βα-Encoders for A/D conversion
Conference paper
Classification of refinable splines
Article
Generation of finite tight frames by Householder transformations
Article
Simultaneous translational and multiplicative tiling and wavelet sets in ℝ2
Article
Some properties of spectral measures
Article
Total variation wavelet-based medical image denoising
Article
A class of self-affine sets and self-affine measures
Article
Absolute continuity of self-similar measures and Bernoulli convolutions
Article
Self-similar measures associated to IFS with non-uniform contraction ratios
Article
Bernoulli convolutions associated with certain non-Pisot numbers
Article
Quantum integers and cyclotomy
Article
Sparse complete Gabor systems on a lattice
Article
The existence of Gabor bases and frames
Article
Article
Self-affine Tiling via Substitution Dynamical Systems and Rauzy Fractals
Article
Wavelets, tiling, and spectral sets
Article
Disk-like self-affine tiles in ℝ2
Article
Hausdorff dimension of self-similar sets with overlaps
Article
Lattice tiling and the Weyl-Heisenberg frames
Article
On the number of Daubechies scaling functions and a conjecture of Chyzak et al.
Article
Subdivision schemes and refinement equations with nonnegative masks
Article
Universal spectra, universal tiling sets and the spectral set conjecture
Article
Article
Orthogonality criteria for compactly supported refinable functions and refinable function vectors
Article
Orthonormal bases of exponentials for the n-cube
Article
Arbitrarily smooth orthogonal nonseparable wavelets in ℝ2
Article
Compactly supported orthogonal symmetric scaling functions
Article
Geometry of Self-Affine Tiles I
Article
Geometry of Self-Affine Tiles II
Article
Haar bases for L^{2}(ℝ^{n}) and algebraic number theory
Article
Haar-type multiwavelet bases and self-affine multi-tiles
Article
Book chapter
On the use of high-order ambiguity function for multi-component polynomial phase signals
Article
Exploring lag diversity in the high-order ambiguity function for polynomial phase signals
Article
Integral self-affine tiles in ℝ^{n} part II: Lattice tilings
Article
Spectral sets and factorizations of finite Abelian groups
Article
On the use of high order ambiguity function for multicomponent polynomial phase signals
Conference paper
Haar bases for L^{2}(ℝ^{n}) and algebraic number theory
Article
Integral Self-Affine Tiles in ℝ^{n} I. Standard and Nonstandard Digit Sets
Article
Nonnegative radix representations for the orthant R_{+}^{n}
Article
Article
Tiling the line with translates of one tile
Article
Two-scale dilation equations and the mean spectral radius
Article
Article
Haar Type Orthonormal Wavelet Bases in R^{2}
Article
The finiteness conjecture for the generalized spectral radius of a set of matrices
Article
Two-scale dilation equations and the cascade algorithm
Article
Bounded semigroups of matrices
Article
Multidimensional two-scale dilation equations
Book chapter
On the order and number of zero divisors of a finite ring
Article
A new binary representation method for shape convexity and application to image segmentation
A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
Adversarial domain translation networks for integrating large-scale atlas-level single-cell datasets
An Error Analysis of Generative Adversarial Networks for Learning Distributions
Approximation in shift-invariant spaces with deep ReLU neural networks
BiGCN: A bi-directional low-pass filtering graph neural network
Hyper-Gaussian regularized Whittaker–Kotel’nikov–Shannon sampling series
On the Capacity of Deep Generative Networks for Approximating Distributions
Retinex-based variational framework for low-light image enhancement and denoising
Solving phase retrieval with random initial guess is nearly as good as by spectral initialization
The Global Landscape of Phase Retrieval II: Quotient Intensity Models
Multiscale high-dimensional sparse Fourier algorithms for noisy data
Overlapping domain decomposition methods for ptychographic imaging
The Global Landscape of Phase Retrieval I: Perturbed Amplitude Models
Almost everywhere injectivity conditions for the matrix recovery problem
Fast Rank-One Alternating Minimization Algorithm for Phase Retrieval
Generalized Phase Retrieval: Measurement Number, Matrix Recovery and Beyond
An Iteration Method for X-Ray CT Reconstruction from Variable-Truncation Projection Data
Convex Shape Prior for Multi-Object Segmentation Using a Single Level Set Function
Data-driven method for 3D axis-symmetric object reconstruction from single cone-beam projection data
Data-driven tight frame for Cryo-EM image denoising and conformational classification
Low-dose X-ray computed tomography image reconstruction using edge sparsity regularization
Data recovery on a manifold from linear samples: theory and computation
Newman Cyclotomic Polynomials, Refinable Splines and the Euler Binary Partition Function
Phase Retrieval from the Magnitudes of Affine Linear Measurements
Scattering Transform and Sparse Linear Classifiers for Art Authentication
Synchronized Recovery Method for Multi-Rank Symmetric Tensor Decomposition
Efficient Estimation of Regularization Parameters via Downsampling and the Singular Value Expansion
Topological Invariants and Lipschitz Equivalence of Fractal Squares
A multiscale sub-linear time Fourier algorithm for noisy data
On the decay of the smallest singular value of submatrices of rectangular matrices
A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows
Coarse quantization for random interleaved sampling of bandlimited signals
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel
Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios
Selective extraction of entangled textures via adaptive PDE transform
The performance of PCM quantization under tight frame representations
Partial differential equation transform: Variational formulation and Fourier analysis
Reconstruction from irregular Fourier samples and Gaussian spectral mollifiers
A multiscale sub-linear time Fourier algorithm for noisy data
Article
Fast Phase Retrieval from Local Correlation Measurements
Article
On the decay of the smallest singular value of submatrices of rectangular matrices
Article
Stable Signal Recovery from Phaseless Measurements
Article
Stylometry and mathematical study of authorship
Book chapter
Gabor orthonormal bases generated by the unit cubes
Article
Self-similar subsets of the Cantor set
Article
Tiling Z^{2} by a Set of Four Elements
Conference paper
Lipschitz equivalence of self-similar sets with touching structures
Article
Phase retrieval for sparse signals
Article
Phase retrieval from very few measurements
Article
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
Conference paper
Adaptive sub-linear time Fourier algorithms
Article
Bayesian learning of sparse multiscale image representations
Article
Edge detection from truncated Fourier data using spectral mollifiers
Article
Invertibility and robustness of phaseless reconstruction
Article
Necessary and sufficient conditions to perform Spectral Tetris
Article
Phase aliasing correction for robust blind source separation using DUET
Article
Source extraction in audio via background learning
Article
The regularity of refinable functions
Article
Vakman's problem and the extension of Hilbert transform
Article
On the convergence of iterative filtering empirical mode decomposition
Book chapter
Speeding up scientific imaging workflows: Design of automated image annotation tool
Conference paper
A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows
Article
Coarse quantization for random interleaved sampling of bandlimited signals
Article
Empirical mode decomposition analysis for visual stylometry
Article
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel
Article
Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios
Article
Mathematical methods for images and surfaces 2011
Article
Mode Decomposition Evolution Equations
Article
Selective extraction of entangled textures via adaptive PDE transform
Article
Sparse PCA by iterative elimination algorithm
Article
Spectral Tetris Fusion Frame Constructions
Article
The performance of PCM quantization under tight frame representations
Article
Constructing tight fusion frames
Article
Partial differential equation transform: Variational formulation and Fourier analysis
Article
Reconstruction from irregular Fourier samples and Gaussian spectral mollifiers
Article
Spectral tetris fusion frame constructions
Conference paper
Classification of Refinable Splines in ℝd
Article
Mathematical methods for images and surfaces
Article
Article
Article
Convergence of a convolution-filtering-based algorithm for empirical mode decomposition
Article
Iterative filtering as an alternative algorithm for empirical mode decomposition
Article
Lattice quantization error for redundant representations
Article
On the structures of generating iterated function systems of Cantor sets
Article
The β α-Encoders for robust A/D conversion
Article
Constructions and existence of tight fusion frames
Conference paper
Lattice quantization error for redundant representations
Conference paper
Sigma-delta quantization errors and the traveling salesman problem
Article
Asymptotic white noise hypothesis for PCM quantization
Conference paper
Multifractal analysis and authentication of Jackson Pollock paintings
Conference paper
Article
Refinable functions with non-integer dilations
Article
Structure of refinable splines
Article
White noise hypothesis for uniform quantization errors
Article
βα-Encoders for A/D conversion
Conference paper
Classification of refinable splines
Article
Generation of finite tight frames by Householder transformations
Article
Simultaneous translational and multiplicative tiling and wavelet sets in ℝ2
Article
Some properties of spectral measures
Article
Total variation wavelet-based medical image denoising
Article
A class of self-affine sets and self-affine measures
Article
Absolute continuity of self-similar measures and Bernoulli convolutions
Article
Self-similar measures associated to IFS with non-uniform contraction ratios
Article
Bernoulli convolutions associated with certain non-Pisot numbers
Article
Quantum integers and cyclotomy
Article
Sparse complete Gabor systems on a lattice
Article
The existence of Gabor bases and frames
Article
Article
Self-affine Tiling via Substitution Dynamical Systems and Rauzy Fractals
Article
Wavelets, tiling, and spectral sets
Article
Disk-like self-affine tiles in ℝ2
Article
Hausdorff dimension of self-similar sets with overlaps
Article
Lattice tiling and the Weyl-Heisenberg frames
Article
On the number of Daubechies scaling functions and a conjecture of Chyzak et al.
Article
Subdivision schemes and refinement equations with nonnegative masks
Article
Universal spectra, universal tiling sets and the spectral set conjecture
Article
Article
Orthogonality criteria for compactly supported refinable functions and refinable function vectors
Article
Orthonormal bases of exponentials for the n-cube
Article
Arbitrarily smooth orthogonal nonseparable wavelets in ℝ2
Article
Compactly supported orthogonal symmetric scaling functions
Article
Geometry of Self-Affine Tiles I
Article
Geometry of Self-Affine Tiles II
Article
Haar bases for L^{2}(ℝ^{n}) and algebraic number theory
Article
Haar-type multiwavelet bases and self-affine multi-tiles
Article
Book chapter
On the use of high-order ambiguity function for multi-component polynomial phase signals
Article
Exploring lag diversity in the high-order ambiguity function for polynomial phase signals
Article
Integral self-affine tiles in ℝ^{n} part II: Lattice tilings
Article
Spectral sets and factorizations of finite Abelian groups
Article
On the use of high order ambiguity function for multicomponent polynomial phase signals
Conference paper
Haar bases for L^{2}(ℝ^{n}) and algebraic number theory
Article
Integral Self-Affine Tiles in ℝ^{n} I. Standard and Nonstandard Digit Sets
Article
Nonnegative radix representations for the orthant R_{+}^{n}
Article
Article
Tiling the line with translates of one tile
Article
Two-scale dilation equations and the mean spectral radius
Article
Article
Haar Type Orthonormal Wavelet Bases in R^{2}
Article
The finiteness conjecture for the generalized spectral radius of a set of matrices
Article
Two-scale dilation equations and the cascade algorithm
Article
Bounded semigroups of matrices
Article
Multidimensional two-scale dilation equations
Book chapter
On the order and number of zero divisors of a finite ring
Article
MSBD5004 | Mathematical Methods for Data Analysis |
No Teaching Assignments |
No Teaching Assignments |
No Teaching Assignments |
No Teaching Assignments |
No Teaching Assignments |
CAO, Yifan
(co-supervision)
Individualized Interdisciplinary Program (Computational Media and Arts)
CHEN, Lizhong
(co-supervision)
Mathematics
LAI, Yanming
Mathematics
LI, Yang
(co-supervision)
Individualized Interdisciplinary Program (Artificial Intelligence)
LU, Xiaoyue
(co-supervision)
Individualized Interdisciplinary Program
WANG, Hongrui
(co-supervision)
Mathematics
WU, Tong
Mathematics
YAN, Bokai
Mathematics
YANG, Xingxing
Individualized Interdisciplinary Program
CHOW, Marcos Gee Liang
(co-supervision)
Public Policy
LI, Jiayi
(co-supervision)
Mathematics
CHENG, Lan
Individualized Interdisciplinary Program
HAN, Yuxuan
Mathematics
QUAN, Xueyang
Mathematics
CHEN, Zhixian
Mathematics
HAN, Yuzi
(co-supervision)
Mechanical Engineering
WANG, Gefei
(co-supervision)
Mathematics
ZHENG, Candi
Mathematics
DO, Van Thuat
Mathematics
LO, Yi-su
Mathematics
YANG, Yunfei
Mathematics( Completed in 2022 )
MIAO, Lizhang
Mathematics( Completed in 2020 )
RONG, Yi
Mathematics( Completed in 2020 )
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