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The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color artifacts in…

Computer Vision and Pattern Recognition · Computer Science 2025-01-28 Zhigang Jia , Yuelian Xiang , Meixiang Zhao , Tingting Wu , Michael K. Ng

The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm…

Computer Vision and Pattern Recognition · Computer Science 2025-07-25 Jiangjun Peng , Yisi Luo , Xiangyong Cao , Shuang Xu , Deyu Meng

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

Machine Learning · Statistics 2020-05-27 Daqian Sun , Martin T. Wells

Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…

Machine Learning · Computer Science 2022-02-15 Qianqian Song

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao

In this report, we discuss a simple model for RGB color and polarization images under a unified framework of quaternion nonnegative matrix factorization (QNMF) and present a hierarchical nonnegative least squares method to solve the factor…

Numerical Analysis · Mathematics 2024-07-23 Junjun Pan

A novel tag completion algorithm is proposed in this paper, which is designed with the following features: 1) Low-rank and error s-parsity: the incomplete initial tagging matrix D is decomposed into the complete tagging matrix A and a…

Computer Vision and Pattern Recognition · Computer Science 2014-06-10 Xue Li , Yu-Jin Zhang , Bin Shen , Bao-Di Liu

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

Information Theory · Computer Science 2018-09-11 Shashanka Ubaru , Arya Mazumdar , Yousef Saad

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the…

Computer Vision and Pattern Recognition · Computer Science 2022-11-08 Tatiana Gelvez-Barrera , Jorge Bacca , Henry Arguello

Remote sensing image restoration aims to reconstruct missing or corrupted areas within images. To date, low-rank based models have garnered significant interest in this field. This paper proposes a novel low-rank regularization term, named…

Image and Video Processing · Electrical Eng. & Systems 2024-12-17 Shuang Xu , Chang Yu , Jiangjun Peng , Xiangyong Cao , Deyu Meng

Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle…

Computer Vision and Pattern Recognition · Computer Science 2018-02-22 Haijuan Hu , Jacques Froment , Quansheng Liu

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…

Optimization and Control · Mathematics 2010-08-09 Benjamin Recht , Maryam Fazel , Pablo A. Parrilo

Almost every single image restoration problem has a closely related parameter, such as the scale factor in super-resolution, the noise level in image denoising, and the quality factor in JPEG deblocking. Although recent studies on image…

Image and Video Processing · Electrical Eng. & Systems 2021-11-02 Fangzhou Luo , Xiaolin Wu , Yanhui Guo

Low-rank tensor completion (LRTC) aims to recover a complete low-rank tensor from incomplete observed tensor, attracting extensive attention in various practical applications such as image processing and computer vision. However, current…

Computer Vision and Pattern Recognition · Computer Science 2024-04-19 Hongbing Zhang

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Statistics Theory · Mathematics 2021-05-06 Yunhua Xiang , Tianyu Zhang , Xu Wang , Ali Shojaie , Noah Simon

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

Machine Learning · Computer Science 2017-07-27 Wenqi Wang , Vaneet Aggarwal , Shuchin Aeron

The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…

Optimization and Control · Mathematics 2018-11-26 Angang Cui , Jigen Peng , Haiyang Li , Junxiong Jia , Meng Wen

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

Optimization and Control · Mathematics 2019-05-14 Angang Cui , Meng Wen , Haiyang Li , Jigen Peng

Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase…

Computer Vision and Pattern Recognition · Computer Science 2025-05-09 Ren Hu , Pan Lian

Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…

Optimization and Control · Mathematics 2024-11-11 Chen Ling , Chenjian Pan , Liqun Qi