Related papers: Quaternion tensor left ring decomposition and appl…
The use of quaternions as a novel tool for color image representation has yielded impressive results in color image processing. By considering the color image as a unified entity rather than separate color space components, quaternions can…
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…
Color image completion is a challenging problem in computer vision, but recent research has shown that quaternion representations of color images perform well in many areas. These representations consider the entire color image and…
The color video inpainting problem is one of the most challenging problem in the modern imaging science. It aims to recover a color video from a small part of pixels that may contain noise. However, there are less of robust models that can…
A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail,…
Matrix completion is one of the most challenging problems in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. Because it treats the color image as a whole, the…
Input features are conventionally represented as vectors, matrices, or third order tensors in the real field, for color image classification. Inspired by the success of quaternion data modeling for color images in image recovery and…
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…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
As a new color image representation tool, quaternion has achieved excellent results in the color image processing, because it treats the color image as a whole rather than as a separate color space component, thus it can make full use of…
In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of…
Tensor completion has emerged as a powerful framework for recovering missing data in multidimensional signals by exploiting low-rank tensor structures. Among existing approaches, linear transform-based tensor nuclear norm (TNN) methods have…
Color image inpainting is a challenging task in imaging science. The existing method is based on real operation, and the red, green and blue channels of the color image are processed separately, ignoring the correlation between each…
As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color…
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…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the…
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…
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…