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Strict ‘0-1’ block-diagonal structure has been widely used for learning structured representation in face recognition problems. However, it is questionable and unreasonable to assume the within-class representations are the same. To circumvent this problem, in this paper, we propose a slack block-diagonal (SBD) structure for representation where the target structure matrix is dynamically updated, yet its blockdiagonal nature is preserved. Furthermore, in order to depict the noise in face images more precisely, we propose a robust dictionary learning algorithm based on mixed-noise model by utilizing the above SBD structure (SBD²L). SBD²L considers that there exists two forms of noise in data which are drawn from Laplacian and Gaussion distribution, respectively. Moreover, SBD2L introduces a low-rank constraint on the representation matrix to enhance the dictionary’s robustness to noise. Extensive experiments …