【作者】 刘鑫；

【导师】 冯象初；

【作者基本信息】 西安电子科技大学 ， 计算数学， 2018， 硕士

【摘要】 图像作为人类社会活动中最常用的信息载体,是人类认识世界的重要工具。然而由于现有技术以及设备等的不完善,图像在获取和传输的过程中,会发生一定程度的质量退化问题,影响后续图像处理的效果。因此,如何得到高质量的图像一直是研究人员努力的方向。图像恢复的目标是从观测的低质量图像中恢复出原始高质量图像。本文在非局部均值正则化方法的基础上,提出了两种新的正则化方法,并通过实验验证了新方法的有效性。首先,本文通过数值实验分析发现非局部均值去噪算法余项的概率密度函数具有拖尾性质,符合Laplace分布的特点。基于此,使用l₁范数去刻画非局部均值去噪算法余项,提出了基于l₁范数的非局部均值正则模型。然后利用Bregman算子分裂算法对模型进行求解,新算法可看作Plug-and-Play priors算法的推广。实验结果表明,新方法在图像恢复的任务中,保护图像的边缘、细节等信息方面的性能均优于非局部均值正则模型及其改进方法。此外,本文在基于l₁范数的非局部均值正则模型的基础上提出了基于加权l₁范数的方法噪声正则模型。一方面,该模型使用l₁范数作为先验约束能保证原始干净图像方法噪声的稀疏性;另一方面,该模型在方法噪声中加入与梯度相关的权值函数来保护图像的边缘结构信息。并且新模型还可以看成是l2范数的非局部均值正则模型的推广。最后结合全局稀疏梯度算法和Bregman算子分裂算法设计了一个能有效求解新模型的算法。数值实验表明,新方法在数值结果和视觉效果方面均优于l2范数的非局部均值正则方法及l₁范数的非局部均值正则方法。更多还原

【Abstract】 As the most commonly used information carrier in human social activities,image is an important tool for human to understand the world.However,due to the existing technologies and equipments are imperfect,there exists a certain degree of quality degradation,which may affect the subsequent image processing in the process of image acquisition and transmission.Therefore,how to get the high quality image has become the research direction of many scholars.The image restoration technique aims to restore the high-quality image from its degraded image.Based on the nonlocal means regularization method,two new regularization methods are given in this paper.Experiments show that our methods are of better performances than other methods.We empirically found that the distribution of the residual in the nonlocal means denoising algorithm（differences between the noisy image and the denoised result）is heavy-tailed,which fits well the Laplacian distribution.Based on this observation,a new regularization model is proposed by using the l₁-norm to describe the nonlocal means residual.Then it is solved by utilizing the Bregman operator splitting algorithm,which can be regarded as an extension of Plug-and-Play priors algorithm.Experimental results show that the new model achieves better performance than l2-nonlocal means regularization model and other similar models in terms of both preserving the edges and details of the image.In addition,based on above model,a new regularization model is proposed by using the weighted l₁-norm constraint residual as the regularization term.On one hand,this model can ensure the sparseness of the method-noise of a clean image by using the l₁-norm as the prior constraint.On the other hand,a weight function is introduced to the method-noise so that it can protect the edge structure information.Then the corresponding optimization algorithm is designed by utilizing the global sparse gradient algorithm and the Bregman operator splitting algorithm.Numerical experiments show that the proposed method obtain better results than other similar regularization methods,and our resulting images have better visual effects.更多还原