数学与统计学院知识库

在图像处理领域，乘性噪声的去除是一个具有挑战性的问题. 这是因为乘性噪声以相乘的方式污染图像，所以在被乘性噪声污染的图像中，原始图像的大部分信息会丢失. 乘性噪声的去除方法大致可以分为两类：一类是贝叶斯最大后验概率估计（MAP）的方法；另一类是在对数域中进行乘性噪声的去除，这时乘性噪声转化为加性噪声，数值实验结果表明这种加性噪声近似服从高斯分布，因此只要在对数域中利用去除高斯加性噪声的方法，就可达到去除乘性噪声的目的. 本文中，我们构造了基于最小加权核范数（WNNM)去除图像乘性噪声的方法，并考虑了该方法中的权重选择问题. 数值实验结果表明本文提出的方法能有效的去除图像中的乘性噪声，与现有的乘性噪声的去除方法相比，无论是在视觉效果还是去噪质量方面都有很大的提高.

In the field of image processing, multiplicative noise removal is a challenging image processing problem. Because a recorded image is the product of the original image and noise, most of the information of the original image is lost.The methods for multi plicative noise removal can be classified into two categories: the methods derived from the classical MAP Bayesian rule , and the ones that convert the multiplicative noise removal problem into additive noise removal problem. The numerical experimental results
have shown that the additive noise is approximately Gaussian noise . Therefore, we can remove multiplicative noise in the logarithmic domain, by applying additive noise removal methods. In this paper, we construct a method for multiplicative noise removal
method based on weighted nuclear norm minimization(WNNM) to remove image multiplicative noise.Taking into account the weighted nuclear of the method in the selection problem.Numerical experiments have shown that the model proposed in this paper is effective in removing multiplicative noise in images. Compared with existing methods of multiplicative noise removal, it has greatly improved both visual effect and denoising quality.