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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. 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