Related papers: Low Rank Support Quaternion Matrix Machine

Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm…

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and…

The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven to be a very…

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…

To address the non-negativity dropout problem of quaternion models, a novel quasi non-negative quaternion matrix factorization (QNQMF) model is presented for color image processing. To implement QNQMF, the quaternion projected gradient…

For many years, channels of a color image have been processed individually, or the image has been converted to grayscale one with respect to color image processing. Pure quaternion representation of color images solves this issue as it…

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…

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…

Recently, a quaternion tensor product named Qt-product was proposed, and then the singular value decomposition and the rank of a third-order quaternion tensor were given. From a more applicable perspective, we extend the Qt-product and…

Reduced biquaternion (RB), as a four-dimensional algebra highly suitable for representing color pixels, has recently garnered significant attention from numerous scholars. In this paper, for color image processing problems, we introduce a…

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…

The advancements of hardware technology in recent years has brought many possibilities for low-precision applications. However, the use of low precision can introduce significant computational errors, posing a considerable challenge to…

Neural networks in the real domain have been studied for a long time and achieved promising results in many vision tasks for recent years. However, the extensions of the neural network models in other number fields and their potential…

In this paper, we propose a new approaches for low rank approximation of quaternion tensors \cite{chen2019low,zhang1997quaternions,hamilton1866elements}. The first method uses quasi-norms to approximate the tensor by a low-rank tensor using…

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…

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…

Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion…

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…

Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on…