Abstract: Recovering clean images from noisy images is one of the important premises for effective image processing and analysis. However, preserving the image features is a challenging problem of image denoising. In order to remove the noise and maintain the local geometry structures of the image as much as possible, an image denoising algorithm based on graph Laplacian regularized sparse transform learning is proposed in this paper. By introducing graph Laplacian regulari-zation to constrain the neighborhood pixels, the correlation between adjacent pixels can be better protected and the local smoothness of the image can be enhanced. Moreover, in order to make better use of the non-local information of the image, the optimized sparse coding is introduced into the similarity measurement of the image blocks to find more accurate similar image blocks. Experimental results show that the proposed algorithm can achieve good denoising performance both in quantitative indicators and visual quality.

Key words: image denoising, sparse transform learning, graph Laplacian regularization, local geometry structures, block matching

摘要： 从噪声图像中恢复干净的图像是对图像进行有效处理与分析的首要前提之一，而去除噪声的同时保持图像的特征则是图像去噪的一个具有挑战性的问题。为了在去除噪声的同时尽量保持图像的局部结构特征，提出了一种基于图拉普拉斯正则化稀疏变换学习的图像去噪算法。通过引入图拉普拉斯正则化对邻域像素进行约束，可以较好地保护相邻像素之间的相关性，从而增强图像的局部平滑性。并且，为了更好地利用图像的非局部信息，在相似图像块度量中引入优化后的稀疏编码，从而寻找到更准确的相似图像块。实验结果表明，无论是在量化指标还是视觉质量上，所提算法均能取得较好的去噪性能。

关键词: 图像去噪, 稀疏变换学习, 图拉普拉斯正则化, 局部几何结构, 图像块匹配