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Low-rank matrix completion (LRMC) has demonstrated remarkable success in a wide range of applications. To address the NP-hard nature of the rank minimization problem, the nuclear norm is commonly used as a convex and computationally…

Computer Vision and Pattern Recognition · Computer Science 2025-12-25 Zhijie Wang , Liangtian He , Qinghua Zhang , Jifei Miao , Liang-Jian Deng , Jun Liu

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

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model…

Computer Vision and Pattern Recognition · Computer Science 2025-05-01 Yu Guo , Guoqing Chen , Tieyong Zeng , Qiyu Jin , Michael Kwok-Po Ng

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 low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Hongbing Zhang , Bing Zheng

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix…

Signal Processing · Electrical Eng. & Systems 2021-09-21 Yongwei Huang , Sergiy A. Vorobyov , Zhi-Quan Luo

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…

Numerical Analysis · Mathematics 2021-01-01 Guangjing Song , Weiyang Ding , Michael K. Ng

Moving target detection is a challenging computer vision task aimed at generating accurate segmentation maps in diverse in-the-wild color videos captured by static cameras. If backgrounds and targets can be simultaneously extracted and…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Liyang Wang , Shiqian Wu , Shun Fang , Qile Zhu , Jiaxin Wu , Sos Again

Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a…

Numerical Analysis · Mathematics 2020-01-30 Jifei Miao , Kit Ian Kou , Wankai Liu

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

Optimization and Control · Mathematics 2026-03-31 Muge Dedeoglu , Buket Ozen , Burak Kocuk

Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the…

Computer Vision and Pattern Recognition · Computer Science 2017-06-28 Zhiyuan Zha , Xinggan Zhang , Yu Wu , Qiong Wang , Lan Tang

Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case…

Machine Learning · Computer Science 2019-04-09 Chunsheng Liu

In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank…

Machine Learning · Computer Science 2024-09-23 Cho-Ying Wu , Jian-Jiun Ding

Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…

Numerical Analysis · Mathematics 2023-08-09 Chao Wang , Jean-Francois Aujol , Guy Gilboa , Yifei Lou

In this letter, we propose a novel low-rank quaternion approximation (LRQA) model by directly constraining the quaternion rank prior for effectively removing the noise in color images. The LRQA model treats the color image holistically…

Image and Video Processing · Electrical Eng. & Systems 2020-06-02 Jifei Miao , Kit Ian Kou

In this paper, we study color image inpainting as a pure quaternion matrix completion problem. In the literature, the theoretical guarantee for quaternion matrix completion is not well-established. Our main aim is to propose a new…

Computer Vision and Pattern Recognition · Computer Science 2022-10-27 Junren Chen , Michael K. Ng

Robust Principal Component Analysis (RPCA) and its associated non-convex relaxation methods constitute a significant component of matrix completion problems, wherein matrix factorization strategies effectively reduce dimensionality and…

Optimization and Control · Mathematics 2024-03-28 Zhenzhi Qin , Liping Zhang

In this paper, we propose a depth-aided color image inpainting method in the quaternion domain, called depth-aided low-rank quaternion matrix completion (D-LRQMC). In conventional quaternion-based inpainting techniques, the color image is…

Image and Video Processing · Electrical Eng. & Systems 2025-03-24 Shunki Tatsumi , Ryo Hayakawa , Youji Iiguni

In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…

Machine Learning · Computer Science 2016-12-09 Yeshwanth Cherapanamjeri , Kartik Gupta , Prateek Jain

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…

Numerical Analysis · Computer Science 2017-12-01 Damiana Lazzaro , Elena Loli Piccolomini , Fabiana Zama