Abstract: The sparse representations of signal theory has been extensively and deeply researched in recent years, and been widely applied to image processing. For the huge computation of over-complete dictionary structure and sparse decomposition, a new self-adaptive method for image denoising based on sparse decomposition and clustering was proposed. Firstly, an overcomplete dictionary was designed by training samples with a modified K-means clustering algorithm. In the training process, atoms of the dictionary were updated adaptively in every iterative step to better fit the sparse representation of the samples. Secondly, the sparse representation of the test image was obtained by using the dictionary combined with Orthogonal Matching Pursuit (OMP) algorithm, so as to achieve image denoising. The experimental results show that in terms of image denoising and computational complexity, the performance of the proposed method is better than the traditional dictionary training algorithm.

Key words: K-means clustering, sparse decomposition, image denoising, Orthogonal Matching Pursuit (OMP), overcomplete dictionary

摘要： 随着信号稀疏表示原理的深入研究，稀疏分解越来越广泛地应用于图像处理领域。针对过完备字典构造和稀疏分解运算量巨大的问题，提出一种基于稀疏分解和聚类相结合的自适应图像去噪新方法。该方法首先通过改进的K均值(K-means)聚类算法训练样本，构造过完备字典;其次，通过训练过程中每一次迭代，自适应地更新字典的原子，使字典更适应样本的稀疏表示;然后利用正交匹配追踪(OMP)算法实现图像的稀疏表示，从而达到图像去噪的目的。实验结果表明：与传统的字典训练方法相比，新算法有效地降低了运算复杂度，并取得更好的图像去噪效果。

关键词: K均值聚类, 稀疏分解, 图像去噪, 正交匹配追踪, 过完备字典