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Reduced quaternion matrix-based sparse representation and its application to colour image processing

The traditional colour image sparse models ignore the relationship among the three separate colour channels. The authors propose a novel colour image sparse model by employing reduced quaternion matrix, which can treat independent colour channels as a whole. In addition, reduced quaternion matrix singular value decomposition is employed to design the corresponding dictionary learning algorithm. To make the proposed model robust and tractable, a reduced quaternion split Bregman iteration is developed to solve the minimisation problem. The proposed model cannot only preserve inherent colour structures but also avoid hue bias issue efficiently. Extensive experiments on colour image de-noising, in-painting, and super-resolution manifest that the proposed sparse representation model outperforms the state-of-the-art schemes.