The nonlocal self-similarity of images means that groups of similar patches have low-dimensional property. The property has been previously used for image denoising, with particularly notable success via sparse coding. However, only a few studies have focused on the varying statistics of noise in different similar patches during the iterative denoising process. This has motivated us to introduce an improved weighted sparse coding for gray-level image denoising in this paper. On the basis of traditional sparse coding, we introduce a weight matrix to account for the noise variation characteristics of different similar patches, while introduce another weight matrix to make full use of the sparsity priors of natural images. The Maximum A-Posterior estimation (MAP) is used to obtain the closed-form solution of the proposed method. Experimental results demonstrate the competitiveness of the proposed method compared with that of state-of-the-art methods in both the objective and perceptual quality.

图像的非局部自相似性意味着相似补丁的组具有低维属性。该属性先前已用于图像去噪，通过稀疏编码获得了显着的成功。然而，只有很少的研究集中在迭代去噪过程中不同相似补丁中噪声的变化统计。这促使我们引入一种改进的加权稀疏编码，用于灰度图像去噪。在传统的稀疏编码的基础上，我们引入了一个权重矩阵来考虑不同相似补丁的噪声变化特征，同时引入了另一个权重矩阵来充分利用自然图像的稀疏先验。使用最大后验估计（MAP）来获得所提出方法的闭合形式解。