Abstract: Overcomplete dictionary was used to represent an image sparsely in order to improve image denoising performance. The sparse representation may represent efficiently the singular geometry of the images with the redundancy of over-complete dictionary. Global image prior model based on the sparse representation of image patches was presented in Bayesian framework. Then maximum a posteriori probability estimator for denoising image was constructed. The dictionary was composed of two orthonormal bases. A method based on singular value decomposition was used for dictionary learning. The orthonormal property was used to update the one chosen basis effectively. The method can improve the performance of image denoising. The experimental results verify the validity of the method.

Key words: image denoising, dictionary learning, sparse representation, Singular Value Decomposition (SVD), Bayesian estimation

摘要： 为了提高图像去除白高斯噪声的性能，利用超完备字典作为图像的稀疏表示。超完备字典的冗余性可以有效地表示图像的各种几何奇异特征。在贝叶斯框架下，以图像块的稀疏表示定义了全局图像先验概率模型，给出了最大后验概率模型下的优化图像去噪算法。超完备字典使用两个不同的正交基构成，给出了基于奇异值分解（SVD）的优化字典计算方法。该方法充分利用正交基的特点，采用SVD方法进行高效的字典学习。基于双正交基字典的去噪算法提高了图像去噪性能，实验结果证实了所提方法的有效性。

关键词: 图像去噪, 字典学习, 稀疏表示, 奇异值分解, 贝叶斯估计