Elad Michael
Dept. of Comput. Sci., Stanford Univ., CA 94306-9025, USA.
IEEE Trans Image Process. 2002;11(10):1141-51. doi: 10.1109/TIP.2002.801126.
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. Tomasi and Manduchi (see Proc. 6th Int. Conf. Computer Vision, New Delhi, India, p.839-46, 1998) 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. 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.
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包括能够将其归结为一个成熟的理论，以及该领域中提出的算法高效且实用这一事实。基于各向异性扩散（AD）、加权最小二乘法（WLS）和稳健估计（RE）的自适应方法被提出作为用于噪声去除的迭代局部自适应机制。托马西和曼杜奇（见《第六届国际计算机视觉会议论文集》，印度新德里，第839 - 46页，1998年）提出了一种用于从图像中去除噪声的非迭代双边滤波器。结果表明，该滤波器能给出与迭代方法相似甚至可能更好的结果。然而，双边滤波器最初是作为一种直观工具提出的，与经典方法没有理论联系。我们搭建了这样一座桥梁，并表明双边滤波器也源自贝叶斯方法，是一些著名迭代算法的单次迭代。基于这一观察结果，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。
