On the origin of the bilateral filter and ways to improve it
On the origin of the bilateral filter and ways to improve it
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DOI：
10.1109/tip.2002.801126
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发表时间：
2002-10-01
影响因子：
10.6
通讯作者：
Elad, M
中科院分区：
文献类型：
--
作者：
Elad, M
从给定信号中去除加性噪声是信号处理中的一个重要问题。该领域最吸引人的方面是能够将其引用到完善的理论，以及该领域提出的算法高效且实用。提出了基于各向异性扩散（AD）、加权最小二乘法（WLS）和鲁棒估计（RE）的自适应方法作为用于噪声去除的迭代局部自适应机器。最近，Tomasi 和 Manduchi 提出了一种替代的非迭代双边滤波器，用于去除图像中的噪声。该过滤器被证明可以提供与通过迭代方法获得的结果相似且可能更好的结果。然而，双边滤波器被提出作为一种直观的工具，与经典方法没有理论联系。在本文中，我们提出了这样一个桥梁，并表明双边滤波器也是从贝叶斯方法中出现的，作为一些众所周知的迭代算法的单次迭代。基于这一观察，我们还展示了如何改进和扩展双边滤波器以处理更一般的重建问题。
Additive noise removal from a given signal is an important problem in signal processing. Among the most appealing aspects of this field are the ability to refer it to a well-established theory, and the fact that the proposed algorithms in this field are efficient and practical. Adaptive methods based on anisotropic diffusion (AD), weighted least squares (WLS), and robust estimation (RE) were proposed as iterative locally adaptive machines for noise removal. Recently, Tomasi and Manduchi proposed an alternative noniterative bilateral filter for removing noise from images. This filter was shown to give similar and possibly better results to the ones obtained by iterative approaches. However, the bilateral filter was proposed as an intuitive tool without theoretical connection to the classical approaches. In this paper we propose such a bridge, and show that the bilateral filter also emerges from the Bayesian approach, as a single iteration of some well-known iterative algorithm. Based on this observation, we also show how the bilateral filter can be improved and extended to treat more general reconstruction problems.