Quaternion-based sparse representation of color image

In this paper, we propose a quaternion-based sparse representation model for color images and its corresponding dictionary learning algorithm. Differing from traditional sparse image models, which represent RGB channels separately or process RGB channels as a concatenated real vector, the proposed model describes the color image as a quaternion vector matrix, where each color pixel is encoded as a quaternion unit and thus the inter-relationship among RGB channels is well preserved. Correspondingly, we propose a quaternion-based dictionary learning algorithm using a socalled K-QSVD method. It conducts the sparse basis selection in quaternion vector space, providing a kind of vectorial representation for the inherent color structures rather than a scalar representation via current sparse image models. The proposed sparse model is validated in the applications of color image denoising and inpainting. The experimental results demonstrate that our sparse image model avoids the hue bias phenomenon successfully and shows its potential as a powerful tool in color image analysis and processing domain.