<p>Quaternion CUR decomposition (QCUR) is a powerful tool for low-rank approximation to large-scale quaternion matrices, with critical applications in color image processing tasks, such as color image reconstruction, color image inpainting, color image denoising, and so on. This decomposition offers significant advantages such as high interpretability, reduced storage, and explicit preservation of the sparsity inherent in the original quaternion matrix. Existing QCUR methods either rely on quaternion operations directly, or rewrite the low-rank approximation problem into real-valued computations via structure-preserving techniques. However, the former incurs cumbersome quaternion arithmetic, and the latter leads to an expansion of dimensions. Consequently, these methods may suffer from heavy computational overhead when dealing with large-scale quaternion matrices. To overcome these difficulties, we introduce a novel QCUR decomposition method integrated with the discrete empirical interpolation method (DEIM) and real projection technique. To the best of our knowledge, this is the first application of such a framework to QCUR decomposition, with a key distinction lying in the adoption of real projection for both sampling and constructing approximation. More precisely, we first employ the real projection technique to efficiently determine the row and column selection indices, and sample some real matrices associated with the original quaternion matrix. Then, we construct a low-rank approximation to large-scale quaternion matrix with the help of real projectors. Theoretical analysis is given to show the rationality of our strategies. Extensive experiments demonstrate that the proposed method achieves significant speedups over the state-of-the-art QCUR methods, while maintaining comparable approximation accuracy.</p>