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 $\ell _{p}$ -norm fidelity plus $\ell _{q}$ -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.

中文翻译：

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混合高斯和脉冲噪声下图像去噪的结构化字典学习。


尽管图像去噪作为图像恢复的基本任务在过去几十年中得到了广泛的研究，但对于混合噪声去噪的研究并不多。在本文中，我们提出了两种结构化字典学习模型来恢复被混合高斯和脉冲噪声损坏的图像。这两个模型可以合并为$\ell_{p}$ - 标准保真度加$\ell_{q}$ -范数正则化。保真度项用于拟合图像块，正则化项用于稀疏编码。特别是，我们利用近端（和近端线性化）交替最小化方法作为主要求解器来处理这两个模型。我们在假设未损坏的图像可以在适当的正交基础下用线性表示来近似的情况下去除高斯噪声。我们使用不同的方法来消除这两个模型的脉冲噪声。实验结果用于比较现有方法，并证明所提出的去噪模型在某些质量评估指标方面的性能优于其他现有方法。