Search Results for author: Michael K. Ng

Found 41 papers, 2 papers with code

Multispectral Image Restoration by Generalized Opponent Transformation Total Variation

no code implementations19 Mar 2024 Zhantao Ma, Michael K. Ng

Here opponent transformations for multispectral images are generalized from a well-known opponent transformation for color images.

Image Restoration

On the Expressive Power of a Variant of the Looped Transformer

no code implementations21 Feb 2024 Yihang Gao, Chuanyang Zheng, Enze Xie, Han Shi, Tianyang Hu, Yu Li, Michael K. Ng, Zhenguo Li, Zhaoqiang Liu

Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms.

Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors

no code implementations16 Sep 2023 Junren Chen, Shuai Huang, Michael K. Ng, Zhaoqiang Liu

The problem of recovering a signal $\boldsymbol{x} \in \mathbb{R}^n$ from a quadratic system $\{y_i=\boldsymbol{x}^\top\boldsymbol{A}_i\boldsymbol{x},\ i=1,\ldots, m\}$ with full-rank matrices $\boldsymbol{A}_i$ frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging.

A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate

no code implementations30 Aug 2023 Junren Chen, Michael K. Ng

By employing dithering scales varying across entries, our estimator enjoys an improved operator norm error rate that depends on the effective rank of the underlying covariance matrix rather than the ambient dimension, thus closing the theoretical gap.

Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery

no code implementations30 Dec 2022 Junren Chen, Michael K. Ng, Di Wang

Our major standpoint is that (near) minimax rates of estimation error are achievable merely from the quantized data produced by the proposed scheme.

Matrix Completion Quantization

Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery

no code implementations1 Dec 2022 YiSi Luo, XiLe Zhao, Zhemin Li, Michael K. Ng, Deyu Meng

To break this barrier, we propose a low-rank tensor function representation (LRTFR), which can continuously represent data beyond meshgrid with infinite resolution.

Denoising Hyperparameter Optimization +2

SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition

no code implementations16 Nov 2022 Yihang Gao, Ka Chun Cheung, Michael K. Ng

Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods.

Transfer Learning

Phase Retrieval of Quaternion Signal via Wirtinger Flow

no code implementations25 Oct 2022 Junren Chen, Michael K. Ng

Moreover, we develop a variant of QWF that can effectively utilize a pure quaternion priori (e. g., for color images) by incorporating a quaternion phase factor estimate into QWF iterations.


A Momentum Accelerated Adaptive Cubic Regularization Method for Nonconvex Optimization

no code implementations12 Oct 2022 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 convergence to local minima under mild conditions.


Approximate Secular Equations for the Cubic Regularization Subproblem

no code implementations27 Sep 2022 Yihang Gao, Man-Chung Yue, Michael K. Ng

In this paper, we propose and analyze a novel CRS solver based on an approximate secular equation, which requires only some of the Hessian eigenvalues and is therefore much more efficient.

Sparse Nonnegative Tucker Decomposition and Completion under Noisy Observations

no code implementations17 Aug 2022 Xiongjun Zhang, Michael K. Ng

In this paper, we propose a sparse nonnegative Tucker decomposition and completion method for the recovery of underlying nonnegative data under noisy observations.

Tensor Decomposition

Separable Quaternion Matrix Factorization for Polarization Images

no code implementations28 Jul 2022 Junjun Pan, Michael K. Ng

To determine the source factor matrix in quaternion space, we propose a heuristic algorithm called quaternion successive projection algorithm (QSPA) inspired by the successive projection algorithm.

HessianFR: An Efficient Hessian-based Follow-the-Ridge Algorithm for Minimax Optimization

no code implementations23 May 2022 Yihang Gao, Huafeng Liu, Michael K. Ng, Mingjie Zhou

Wide applications of differentiable two-player sequential games (e. g., image generation by GANs) have raised much interest and attention of researchers to study efficient and fast algorithms.

Image Generation

High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization

no code implementations26 Feb 2022 Junren Chen, Cheng-Long Wang, Michael K. Ng, Di Wang

In heavy-tailed regime, while the rates of our estimators become essentially slower, these results are either the first ones in an 1-bit quantized and heavy-tailed setting, or already improve on existing comparable results from some respect.

Low-Rank Matrix Completion Quantization +1

Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss

no code implementations4 Feb 2022 Junren Chen, Michael K. Ng

To fill the theoretical vacancy, we obtain the error bound in both clean and corrupted regimes, which relies on some new results of quaternion matrices.

Image Inpainting Matrix Completion

Morphological feature visualization of Alzheimer's disease via Multidirectional Perception GAN

no code implementations25 Nov 2021 Wen Yu, Baiying Lei, Yanyan Shen, Shuqiang Wang, Yong liu, Zhiguang Feng, Yong Hu, Michael K. Ng

In this work, a novel Multidirectional Perception Generative Adversarial Network (MP-GAN) is proposed to visualize the morphological features indicating the severity of AD for patients of different stages.

Generative Adversarial Network

FastHyMix: Fast and Parameter-free Hyperspectral Image Mixed Noise Removal

no code implementations18 Sep 2021 Lina Zhuang, Michael K. Ng

This paper introduces a fast and parameter-free hyperspectral image mixed noise removal method (termed FastHyMix), which characterizes the complex distribution of mixed noise by using a Gaussian mixture model and exploits two main characteristics of hyperspectral data, namely low-rankness in the spectral domain and high correlation in the spatial domain.


Signal Reconstruction from Phase-only Measurements: Uniqueness Condition, Minimal Measurement Number and Beyond

no code implementations8 Sep 2021 Junren Chen, Michael K. Ng

This paper studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$.

Co-Separable Nonnegative Matrix Factorization

no code implementations2 Sep 2021 Junjun Pan, Michael K. Ng

It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix are equal to columns of the input matrix.

Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks

1 code implementation30 Aug 2021 Yihang Gao, Michael K. Ng

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations.

Uncertainty Quantification

Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery

no code implementations29 May 2021 Yi-Si Luo, Xi-Le Zhao, Tai-Xiang Jiang, Yi Chang, Michael K. Ng, Chao Li

Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image processing applications.

Approximating Probability Distributions by using Wasserstein Generative Adversarial Networks

no code implementations18 Mar 2021 Yihang Gao, Michael K. Ng, Mingjie Zhou

Studied here are Wasserstein generative adversarial networks (WGANs) with GroupSort neural networks as their discriminators.

Tensor Completion by Multi-Rank via Unitary Transformation

no code implementations16 Dec 2020 Guang-Jing Song, Michael K. Ng, Xiongjun Zhang

The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries.


Non-Local Robust Quaternion Matrix Completion for Color Images and Videos Inpainting

no code implementations17 Nov 2020 Zhigang Jia, Qiyu Jin, Michael K. Ng, XiLe Zhao

A new patch group based NSS prior scheme is proposed to learn explicit NSS models of natural color images.

Matrix Completion SSIM +1

Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion

no code implementations26 Sep 2020 Tai-Xiang Jiang, Xi-Le Zhao, Hao Zhang, Michael K. Ng

In this paper, we propose a novel tensor learning and coding model for third-order data completion.

Dictionary Learning

Tangent Space Based Alternating Projections for Nonnegative Low Rank Matrix Approximation

no code implementations2 Sep 2020 Guangjing Song, Michael K. Ng, Tai-Xiang Jiang

In this paper, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices.


Tensorizing GAN with High-Order Pooling for Alzheimer's Disease Assessment

no code implementations3 Aug 2020 Wen Yu, Baiying Lei, Michael K. Ng, Albert C. Cheung, Yanyan Shen, Shuqiang Wang

To the best of our knowledge, the proposed Tensor-train, High-pooling and Semi-supervised learning based GAN (THS-GAN) is the first work to deal with classification on MRI images for AD diagnosis.

Vocal Bursts Intensity Prediction

Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images

no code implementations28 Jul 2020 Tai-Xiang Jiang, Michael K. Ng, Junjun Pan, Guangjing Song

The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications.

Sparse Nonnegative Tensor Factorization and Completion with Noisy Observations

no code implementations21 Jul 2020 Xiongjun Zhang, Michael K. Ng

We propose to minimize the sum of the maximum likelihood estimation for the observations with nonnegativity constraints and the tensor $\ell_0$ norm for the sparse factor.


Tensor train rank minimization with nonlocal self-similarity for tensor completion

no code implementations29 Apr 2020 Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma

The TT rank minimization accompany with \emph{ket augmentation}, which transforms a lower-order tensor (e. g., visual data) into a higher-order tensor, suffers from serious block-artifacts.

Orthogonal Nonnegative Tucker Decomposition

no code implementations21 Oct 2019 Junjun Pan, Michael K. Ng, Ye Liu, Xiongjun Zhang, Hong Yan

In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD).

Face Recognition Hyperspectral Unmixing

Bilinear Constraint based ADMM for Mixed Poisson-Gaussian Noise Removal

no code implementations18 Oct 2019 Jie Zhang, Yuping Duan, Yue Lu, Michael K. Ng, Huibin Chang

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] in order to remove mixed Poisson-Gaussian(MPG) noise.

Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion

no code implementations16 Sep 2019 Tai-Xiang Jiang, Michael K. Ng, Xi-Le Zhao, Ting-Zhu Huang

In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices.

Robust Tensor Completion Using Transformed Tensor SVD

no code implementations2 Jul 2019 Guangjing Song, Michael K. Ng, Xiongjun Zhang

In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD.

Parallel Active Subspace Decomposition for Scalable and Efficient Tensor Robust Principal Component Analysis

no code implementations28 Dec 2017 Jonathan Q. Jiang, Michael K. Ng

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields.

Exact Tensor Completion from Sparsely Corrupted Observations via Convex Optimization

no code implementations2 Aug 2017 Jonathan Q. Jiang, Michael K. Ng

This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries.

Sparse Kernel Canonical Correlation Analysis via $\ell_1$-regularization

no code implementations16 Jan 2017 Xiaowei Zhang, Delin Chu, Li-Zhi Liao, Michael K. Ng

Our algorithm is based on a relationship between kernel CCA and least squares.

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