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 redesign 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. 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.

通过使用四元数矩阵表示，我们提出了一个四元数卷积神经网络（QCNN）模型来在彩色图像分类和去噪任务中得到更具代表性的特征，并测试结果表明该模型优于具有相同结构的实值卷积神经网络。