The document proposes a vector sparse representation model for color images using quaternion matrix analysis. It represents color images as quaternion matrices, where a quaternion dictionary learning algorithm uses K-quaternion SVD to select sparse bases in quaternion space. This preserves inherent color structures during reconstruction while being more efficient than current sparse models. Experimental results show it avoids hue bias issues and has potential in color image analysis and processing. Future work may explore using the real part of quaternions for four-channel color spaces and improving algorithm convergence.