【作者】 黄志强；

【导师】 杜博；

【作者基本信息】 武汉大学 ， 计算机应用技术， 2018， 硕士

【摘要】 近年来,随着成像设备的普及,图像越来越成为我们生活工作的重要组成部分。然而图像在获取过程中常受到各种噪声的干扰,如光照条件差、气象条件不佳、高速摄影、长曝光等外部因素,及散粒噪声、热噪声等内部因素。噪声不仅使得图像质量下降,美感降低,也会导致后续的视觉处理算法精度降低,如图像分类、目标探测等。图像去噪算法试图从获得的噪声图像中恢复其中不含噪声的真实信号。对于这个欠定的问题,我们需要对图像作出各种假设以使问题可解。近年来常见的假设有图像相邻像素的平滑性、图像块用字典表达的表达系数的稀疏性、相似图像块组成的矩阵的低秩性、图像块服从高斯分布等。另外我们还需要对噪声作出各种假设,常见的假设有噪声服从高斯分布或拉普拉斯分布等。在基于高斯先验的图像去噪算法中,从噪声图像训练高斯分布存在相似样本少以及样本含有噪声的问题。在高光谱图像去噪算法中,基于低秩的去噪算法往往在模型中加入核范数作为正则化项,然而核范数作为秩函数的凸松驰形式,往往使得主信号衰减过多。高光谱图像不同波段的高斯噪声强度往往不同,现有的高光谱图像去噪算法的数学模型中往往没有体现这一点。为克服以上问题,本文作出如下改进:(1)对于基于高斯先验的图像去噪,我们对找到的相似样本分配一个权重,表示它们服从相同高斯分布的可能性,然后用加权均值作为分布的均值参数;对协方差参数,我们添加半正定约束,以使优化目标为凸函数。(2)在高光谱图像去噪中,提出结合加权核范数和全变分联合正则化。加权核范数能更好地突出主信号,从而使得在处理过程中减少其衰减。全变分则能保持图像空域的平滑性。(3)在高光谱图像去噪中,提出逐波段噪声模型,并结合低秩假设,使用低秩矩阵分解,得到一个容易求解的目标函数。更多还原

【Abstract】 In recent years,with the popularity of imaging equipment,images are increasingly becoming an important part of our life and work.However,the image is often interfered by various noises in the process of acquisition,such as poor illumination conditions,poor weather conditions,high-speed photography,long exposure and other internal factors,such as shot noise and thermal noise.Noise not only causes the image quality to decline,reduces the aesthetic feeling,also leads to the decrease of precision of the subsequent vision processing algorithms,such as image classification and target detection.The image denoising algorithm attempts to recover the true signal without noise from the obtained noisy image.For this underdetermined problem,we need to make assumptions about the image to make the problem solvable.The common assumption in recent years is the smoothness of neighbor pixels,the sparsity of the representation coefficients expressed by redundant dictionary,the low-rank property of the matrix of similar image blocks and the obeying Gaussian distribution of image blocks.In addition,we also need to make various assumptions about noise.The common assumption is that noise is subject to Gaussian distribution or Laplace distribution.In the image denoising algorithm based on Gaussian priors,when training Gaussian from noisy image,there is a problem that there are less similar samples and the samples contain noise.In the hyperspectral image denoising,the denoising algorithm based on low rank tends to add the nuclear norm as regularization term in the model.However,as the convex relaxation of the rank function,the nuclear norm often makes the principal signal decay too much.The Gaussian noise intensity of different bands in hyperspectral images tends to be different,which is often not found in the mathematical models of hyperspectral image denoising algorithms.In order to overcome the above problems,this paper makes the following improve-ments:(1)For image denoising based on Gaussian priors,we assign a weight to the similar patches,indicating the possibility that they obey the same Gaussian distribu-tion,and then use the weighted mean of these patches as the mean parameter of the distribution;for the covariance parameter,we add the positive semi-definite constraint,so that the objective is a convex function.(2)In the hyperspectral image denois-ing,a joint regularization with weighted nuclear norm and total variation is proposed.Weighted nuclear norm can better highlight the principal signal,so reduce the atten-uation of it in the denoising process.The total variation maintains the smoothness of the hyperspectral image in spatial domain.(3)In the hyperspectral image denoising,a band-by-band noise model is proposed,and combined with the low-rank hypothesis,a low-rank matrix factorization is used to obtain an easily solved objective function.更多还原