利用核模糊聚类和正则化的图像稀疏去噪

吴一全; 李立

doi:doi:10.3788/gzxb20144303.0310001

光子学报, 2014, 43 (3): 0310001, 网络出版: 2014-04-09

利用核模糊聚类和正则化的图像稀疏去噪

Image Denoising Using Kernel Fuzzy Clustering and Regularization on Sparse Model

论文大纲

吴一全 ^*李立

作者单位

南京航空航天大学电子信息工程学院, 南京 210016

摘要

针对目前图像去噪方法噪音抑制不彻底、容易模糊细节等问题，提出了一种利用核模糊C均值聚类和正则化的图像稀疏去噪方法.该方法首先将图像分成大小相同的若干块，并采用核模糊C均值聚类算法对相似的图像块进行聚类，从而保证同一类图像块共享相同的稀疏去噪模型；然后，选择由经典图像库中图像训练而得的全局字典作为初始字典，很好地适应图像的多种特征；接着，对于同一类图像块，通过施加1/2范数正则化约束，实现该类图像块在字典下的稀疏分解，确保分解系数更为稀疏；最后，通过改进的K-奇异值分解算法完成字典的更新，并选择与原稀疏模型差异最大的图像块来替换更新字典的冗余原子，从而有效地去除图像噪音.实验结果表明，与小波扩散去噪法、固定字典去噪法、最优方向去噪法、K-奇异值分解去噪法相比，该方法能更有效地去除图像噪音，保留图像细节，改善图像视觉效果.

Abstract

Aimed at the problems that the existing denoising methods suppress noise incompletely and blur the details of image, an image denoising method using kernel fuzzy C-means clustering and regularization on sparse model was proposed. Firstly, the image was divided into equal pieces and kernel fuzzy C-means clustering algorithm was used for clustering the similar image pieces, thereby ensuring image pieces in the same class share the same sparse denoising model. Then, the global dictionary trained by images from the classical image library was selected as the initial dictionary to adapt to the various characteristics of image very well. Next, a 1/2 norm regularization constraint condition was imposed and sparse decomposition of image pieces in the same class under the dictionary was achieved, which made decomposition coefficients sparser. Finally, the update of dictionary was completed by improved K-singular value decomposition algorithm, and image pieces with the largest difference from the original sparse model were selected to replace the redundancy atoms of the uapdated dictionary. Thus, noise in the image was suppressed effectively. Experimental results show that, compared with denoising method based on wavelet combining with nonlinear diffusion, denoising method based on constant dictionary, denoising method of optimal directions and K-singular value decomposition denoising method, the proposed method can remove noise of the image more effectively and preserve the details of the image and improve the visual effect better.

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吴一全, 李立. 利用核模糊聚类和正则化的图像稀疏去噪[J]. 光子学报, 2014, 43(3): 0310001. WU Yi-quan, LI Li. Image Denoising Using Kernel Fuzzy Clustering and Regularization on Sparse Model[J]. ACTA PHOTONICA SINICA, 2014, 43(3): 0310001.

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