IEEE Trans Image Process. 2015 May;24(5):1536-48. doi: 10.1109/TIP.2014.2383316. Epub 2014 Dec 18.
Many patch-based image denoising methods can be viewed as data-dependent smoothing filters that carry out a weighted averaging of similar pixels. It has recently been argued that these averaging filters can be improved using their doubly stochastic approximation, which are symmetric and stable smoothing operators. In this paper, we introduce a simple principle of consistency that argues that the relative similarities between pixels as imputed by the averaging matrix should be preserved in the filtered output. The resultant consistency filter has the theoretically desirable properties of being symmetric and stable, and is a generalized doubly stochastic matrix. In addition, we can also interpret our consistency filter as a specific form of Laplacian regularization. Thus, our approach unifies two strands of image denoising methods, i.e., symmetric smoothing filters and spectral graph theory. Our consistency filter provides high-quality image denoising and significantly outperforms the doubly stochastic version. We present a thorough analysis of the properties of our proposed consistency filter and compare its performance with that of other significant methods for image denoising in the literature.
许多基于补丁的图像去噪方法可以看作是依赖数据的平滑滤波器，它对相似的像素进行加权平均。最近有人认为，这些平均滤波器可以通过其双重随机逼近得到改进，双重随机逼近是对称且稳定的平滑算子。在本文中，我们引入了一个简单的一致性原则，即平均矩阵推断出的像素之间的相对相似性应该在滤波输出中保持不变。所得的一致性滤波器具有对称和稳定的理论理想特性，并且是广义的双重随机矩阵。此外，我们还可以将我们的一致性滤波器解释为拉普拉斯正则化的一种特殊形式。因此，我们的方法统一了图像去噪方法的两个方面，即对称平滑滤波器和谱图理论。我们的一致性滤波器提供了高质量的图像去噪，并且明显优于双重随机版本。我们对所提出的一致性滤波器的性质进行了彻底的分析，并将其性能与文献中其他重要的图像去噪方法进行了比较。
