Brief Introduction

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 applications are not fully-investigated yet. Focusing on color images, which can be naturally represented as quaternion matrices, we propose a quaternion convolutional neural network (QCNN) model to obtain more representative features. In particular, we re-design the basic modules like convolution layer and fully-connected layer in the quaternion domain, which can be used to establish fully-quaternion convolutional neural networks. Moreover, these modules are compatible with almost all deep learning techniques and can be plugged into traditional CNNs easily.

Focusing on the problems mentioned above, we propose a novel quaternion convolutional neural network (QCNN) model, which represents color image in the quaternion domain. In particular, each color pixel in a color image is represented as a quaternion, and accordingly, the image is represented as a quaternion matrix rather than three independent real-valued matrices. Taking the quaternion matrix as the input of our network, we design a series of basic modules, e.g., quaternion convolution layer, quaternion fully-connected layer. While the traditional real-valued convolution is only capable to enforce scaling transformation on the input, specifically, the quaternion convolution achieves the scaling and the rotation of input in the color space, which provides us with more structural representation of color information.

We test our QCNN models in both color image classification and denoising tasks. Experimental results show that they outperform the real-valued CNNs with same structures, especially for colorful images.