Structured Dictionary Learning for Image Denoising Under Mixed Gaussian and Impulse Noise

Although image denoising as a basic task of image restoration has been widely studied in the past decades, there are not many studies on mixed noise denoising. In this paper, we propose two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as <inline-formula> <tex-math notation="LaTeX">$\ell _{p}$ </tex-math></inline-formula>-norm fidelity plus <inline-formula> <tex-math notation="LaTeX">$\ell _{q}$ </tex-math></inline-formula>-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. The experimental results are reported to compare the existing methods and demonstrate the performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics.