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The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…

Numerical Analysis · Mathematics 2024-03-01 Peng-Ling Wu , Kit Ian Kou , Hongmin Cai , Zhaoyuan Yu

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

Information Theory · Computer Science 2009-03-19 Emmanuel J. Candes , Yaniv Plan

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

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Numerical Analysis · Mathematics 2024-08-07 Xuan Liu , Zhigang Jia , Xiaoqing Jin

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

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Computer Vision and Pattern Recognition · Computer Science 2016-11-16 Ping Li , Jun Yu , Meng Wang , Luming Zhang , Deng Cai , Xuelong Li

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…

Computer Vision and Pattern Recognition · Computer Science 2014-06-12 Yilun Wang , Xinhua Su

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function…

Optimization and Control · Mathematics 2018-06-21 Angang Cui , Jigen Peng , Haiyang Li

In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…

Numerical Analysis · Computer Science 2013-12-25 Anupriya Gogna , Ankita Shukla , Angshul Majumdar

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

Computer Vision and Pattern Recognition · Computer Science 2018-05-29 Shengke Xue , Wenyuan Qiu , Fan Liu , Xinyu Jin

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix…

Computer Vision and Pattern Recognition · Computer Science 2023-08-08 Liang Liao , Zhuang Guo , Qi Gao , Yan Wang , Fajun Yu , Qifeng Zhao , Stephen Johh Maybank

Optimization models involving quaternion matrices are widely used in color image process and other engineering areas. These models optimize real functions of quaternion matrix variables. In particular, $\ell_0$-norms and rank functions of…

Optimization and Control · Mathematics 2020-11-10 Liqun Qi , Ziyan Luo , Qingwen Wang , Xinzhen Zhang

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Optimization and Control · Mathematics 2012-09-19 Bart Vandereycken

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…

Optimization and Control · Mathematics 2025-07-29 Lijun Ding , Zhen Qin , Liwei Jiang , Jinxin Zhou , Zhihui Zhu

It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…

Machine Learning · Computer Science 2022-06-28 Zhemin Li , Zhi-Qin John Xu , Tao Luo , Hongxia Wang

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

Numerical Analysis · Mathematics 2025-09-01 Mohamed El Guide , Anas El Hachimi , Khalide Jbilou , Lothar Reichel

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

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Numerical Analysis · Mathematics 2010-06-29 Rick Ma , Samuel Cheng

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…

Image and Video Processing · Electrical Eng. & Systems 2020-05-26 Yunyi Li , Guan Gui , Xiefeng Cheng

In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…

Signal Processing · Electrical Eng. & Systems 2024-06-25 Hamideh. Sadat Fazael Ardakani , Sajad Daei , Arash Amini , Mikael Skoglund , Gabor Fodor