Abstract: This paper proposed an image denoising method using transform-domain sparse representation with the characteristic that fewer Discrete Cosine Transformation (DCT) nonzero coefficients exist in image smoothing-domain. This method overcame the shortcoming of traditional denoising method, i.e. losing information of edge and texture. Firstly, similar image block was grouped by computing l2 norm; secondly, according to transform-domain coefficient sparsity, denoising was performed by threshold. To improve it, Principal Component Analysis (PCA) was used on these groups, processing groups with PC components. Lastly, the image with processed groups was reconstructed using Kaiser windows method. Compared to traditional method, this method preserves image edge and texture information, so that the noise could be preferably removed and the effect of image visual could be improved.

Key words: image denoising, Discrete Cosine Transform (DCT), grouping, PC component, Kaiser window

摘要： 为解决传统图像去噪算法存在边缘纹理信息损失的问题，根据图像平滑区域离散余弦变换(DCT)非零系数个数较少的特点，提出了基于图像变换域稀疏表示的去噪算法：首先依据l2范式将图像的相似区域块构成块群；然后对块群中的各块进行DCT。由变换域系数的稀疏性，利用阈值进行首次去噪。为进一步去除噪声，对块群进行主成分分析（PCA），提取块群PC分量，运用PC分量对块群进行分析处理；最后把处理后的图块结合Kaiser窗口返回到原图像中，得到去噪后的图像。与传统去噪相比，该方法在去噪过程中保留了边缘纹理信息，抑制了该信息对去噪的影响，提高了图像的视觉效果。

关键词: 图像去噪, 离散余弦变换, 组群, PC分量, Kaiser窗口