Quaternion Generative Adversarial Neural Networks and Applications to Color Image Inpainting

In 1843, the concept of quaternions was first introduced by Sir William Rowan Hamilton. Nowadays, quaternions have emerged as a crucial mathematical concept in various fields such as Mechanics [1, 36, 41], Optics [4, 16], Modern Computer Graphics [25, 34], Color Image Processing [30, 39, 44], and more. As a new tool for color image representation, quaternions have obtained remarkable results in color image processing. The three imaginary parts of the quaternion correspond to the three channels of the color image, and each color image corresponds to a quaternion matrix, and the quaternion can achieve the fusion of color information by processing the color information of different color channels simultaneously. Therefore, quaternion is applied to convolutional neural networks. The pioneering work of Zhu et al. introduces the Quaternion Convolutional Neural Networks (QCNN) [45], which incorporates network layers such as convolutional layer and fully connected layer. In a similar vein, Parcollet et al. propose the Quaternion Recurrent Duan Wang was with School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, P. R. China.