Quaternion tensor ring decomposition and application for color image inpainting

In recent years, tensor networks have emerged as powerful tools for solving large-scale optimization problems. One of the most promising tensor networks is the tensor ring (TR) decomposition, which achieves circular dimensional permutation invariance in the model through the utilization of the trace operation and equitable treatment of the latent cores. On the other hand, more recently, quaternions have gained significant attention and have been widely utilized in color image processing tasks due to their effectiveness in encoding color pixels. Therefore, in this paper, we propose the quaternion tensor ring (QTR) decomposition, which inherits the powerful and generalized representation abilities of the TR decomposition while leveraging the advantages of quaternions for color pixel representation. In addition to providing the definition of QTR decomposition and an algorithm for learning the QTR format, this paper also proposes a low-rank quaternion tensor completion (LRQTC) model and its algorithm for color image inpainting based on the QTR decomposition. Finally, extensive experiments on color image inpainting demonstrate that the proposed QTLRC method is highly competitive

A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling

We propose a new image watermarking scheme based on the real SVD and Arnold scrambling to embed a color watermarking image into a color host image. Before embedding watermark, the color watermark image W with size of M×M is scrambled by Arnold transformation to obtain a meaningless image W~. Then, the color host image A with size of N×N is divided into nonoverlapping N/M×N/M pixel blocks. In each (i,j) pixel block Ai,j, we form a real matrix Ci,j with the red, green, and blue components of Ai,j and perform the SVD of Ci,j. We then replace the three smallest singular values of Ci,j by the red, green, and blue values of W~ij with scaling factor, to form a new watermarked host image A~ij. With the reserve procedure, we can extract the watermark from the watermarked host image. In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image

The Color Clifford Hardy Signal: Application to Color Edge Detection and Optical Flow

This paper introduces the idea of the color Clifford Hardy signal, which can be used to process color images. As a complex analytic function's high-dimensional analogue, the color Clifford Hardy signal inherits many desirable qualities of analyticity. A crucial tool for getting the color and structural data is the local feature representation of a color image in the color Clifford Hardy signal. By looking at the extended Cauchy-Riemann equations in the high-dimensional space, it is possible to see the connection between the different parts of the color Clifford Hardy signal. Based on the distinctive and important local amplitude and local phase generated by the color Clifford Hardy signal, we propose five methods to identify the edges of color images with relation to a certain color. To prove the superiority of the offered methodologies, numerous comparative studies employing image quality assessment criteria are used. Specifically by using the multi-scale structure of the color Clifford Hardy signal, the proposed approaches are resistant to a variety of noises. In addition, a color optical flow detection method with anti-noise ability is provided as an example of application.Comment: 13 page