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In this talk, I will present two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as lp-norm fidelity plus lq-norm regularization. The fidelity term is used to fit image patches and the regularization term is employed for sparse coding. Particularly, we utilize proximal (and proximal linearized) alternating minimization methods as the main solvers to deal with these two models. We remove the Gaussian noise under the assumption that the uncorrupted image can be approximated with a linear representation under an appropriate orthogonal basis. We use different ways to remove impulse noise for these two models.

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