Sparse representation based on vector extension of reduced quaternion matrix for multiscale image denoising

Sparse representations of multi-channel signals have drawn considerable interest in recent years. In this study, a new vector-valued sparse representation model is proposed for colour images using reduced quaternion matrix (RQM). The colour image is described as a RQM by the proposed model. In the dictionary training state, k-means clustering RQM value decomposition is proposed which makes sparse basis selection in quaternion space. Then, a reduced quaternion-based orthogonal matching pursuit algorithm is presented in the sparse coding stage. To demonstrate the effectiveness of the proposed sparse representation model, the authors apply the model to common colour image processing problem-colour image denoising. The proposed model is compared with other sparse models for colour image denoising in terms of visual quality and peak signal-to-noise ratio. The experimental results indicate that the proposed image sparse model is competitive with other sparse models.