87 citations · 91 across the 14 of their papers we have counts for
14 papers
Tensor Completion using Subspace Information
Jingyang Li, Michael K. Ng
Tensor completion has attracted significant attention in both applications and theoretical research. Under standard uniform sampling, existing polynomial-time guarantees generally…
Tensor Orthogonal Subspace Split: Theory and Applications
Jifei Miao, Juan Han, Michael K. Ng +1
Tensor representations have emerged as a fundamental paradigm for modeling multidimensional data by preserving intrinsic correlations across multiple modes. This paper proposes a n…
Block Diagonalization of Quaternion Circulant Matrices with Applications
Junjun Pan, Michael K. Ng
It is well-known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit . The main aim of this paper is to demonstrate tha…
Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery
Yisi Luo, Xile Zhao, Zhemin Li +2
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become on…
Stochastic Variance Reduced Gradient for affine rank minimization problem
Ningning Han, Juan Nie, Jian Lu +1
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linea…
A Momentum Accelerated Adaptive Cubic Regularization Method for Nonconvex Optimization
Yihang Gao, Michael K. Ng
The cubic regularization method (CR) and its adaptive version (ARC) are popular Newton-type methods in solving unconstrained non-convex optimization problems, due to its global con…
Approximate Secular Equations for the Cubic Regularization Subproblem
Yihang Gao, Man-Chung Yue, Michael K. Ng
The cubic regularization method (CR) is a popular algorithm for unconstrained non-convex optimization. At each iteration, CR solves a cubically regularized quadratic problem, calle…
Separable Quaternion Matrix Factorization for Polarization Images
Junjun Pan, Michael K. Ng
Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the source…
Deep neural networks for solving large linear systems arising from high-dimensional problems
Yiqi Gu, Michael K. Ng
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to…
Deep adaptive basis Galerkin method for high-dimensional evolution equations with oscillatory solutions
Yiqi Gu, Micheal K. Ng
In this paper, we study deep neural networks (DNNs) for solving high-dimensional evolution equations with oscillatory solutions. Different from deep least-squares methods that deal…
Signal Reconstruction from Phase-only Measurements: Uniqueness Condition, Minimal Measurement Number and Beyond
Junren Chen, Michael K. Ng
This paper studies the phase-only reconstruction problem of recovering a complex-valued signal in from the phase of where is…
Deep Ritz method for the spectral fractional Laplacian equation using the Caffarelli-Silvestre extension
Yiqi Gu, Micheal K. Ng
In this paper, we propose a novel method for solving high-dimensional spectral fractional Laplacian equations. Using the Caffarelli-Silvestre extension, the -dimensional spectra…
Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery
Yi-Si Luo, Xi-Le Zhao, Tai-Xiang Jiang +3
In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to…
Tensor Completion by Multi-Rank via Unitary Transformation
Guang-Jing Song, Michael K. Ng, Xiongjun Zhang
One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study $n_1 \times n_…