【作者】 李娜；

【导师】 王萍；

【作者基本信息】 天津大学 ， 计算数学， 2016， 硕士

【摘要】 图像修复在医学成像以及监控视频等领域应用广泛,由于现实中图像污染成因的复杂性以及污染途径的多样性,导致目前还没有统一实用的修复模型。图像修复仍然是计算机视觉领域的热点与难点。图像先验知识在图像修复中起到关键性作用,稀疏先验和非局部自相似先验都是是图像修复中最常用的先验信息。在实际应用中,将稀疏先验、非局部自相似先验与其它先验知识相结合能够取得更好的图像修复效果。因此,本文着重研究联合稀疏先验、非局部自相似先验与其它先验知识进行图像修复,主要内容包括两个部分。第一,利用高斯混合模型从自然图像中学习高斯混合先验信息,然后从学习的高斯混合模型中借助奇异值分解得到每一个图像相似块矩阵的字典,再基于稀疏表示技术,设计了一种新的将稀疏先验、非局部自相似先验和自然图像的高斯先验相结合的图像修复模型,该算法在图像修复问题中取得了相当好的修复结果。第二,首先将图像修复问题视作一个低秩矩阵恢复问题,然后将低秩矩阵恢复问题的求解转化为加权核范数极小化问题,此外,为了恢复出更多的图像细节信息,在算法中利用稀疏先验知识,建立了基于稀疏表示和加权核范数极小化的图像去噪模型,并用交替迭代法求解模型,该模型有效地将稀疏先验、非局部自相似先验和低秩先验同时用于图像去噪,并取得了很好的去噪效果。实验结果表明,将稀疏先验、非局部自相似先验与其它合适的先验知识相结合能达到更好的图像修复效果。更多还原

【Abstract】 Recovering a clear image from its degraded version has a wide range of applications in medical imaging,surveillance video,etc.However,due to the complexity and diversity of the causes of image contaminated by noise,there is no practical restoration method.Image restoration remains to be a hot and difficult topic in computer vision.Image prior knowledge plays a key role in image restoration,sparsity prior and nonlocal self-similar prior are the most commonly used prior knowledge in image restoration.In practice,the joint use of sparsity prior,nonlocal self-similar prior and other prior knowledge can achieve better results of image restoration.Therefore,this thesis focuses on combining sparsity prior,nonlocal self-similar prior with other prior knowledge of image restoration,and mainly includes two parts.First,Gaussian mixture models is used to learn image prior knowledge from natural clean images,then,singular value decomposition is exploited to learn dictionary from the learned Gaussian mixture models,and then based on the sparse representation,a new image restoration algorithm is designed by using sparsity prior,nonlocal self-similar prior and Gaussian prior of natural images,which achieves competitive denoising results.Second,image denoising problem is regarded as a low rank matrix completion problem,and then the weighted nuclear norm minimization is used to deal with the low rank matrix completion problem.Additionally,in order to reconstruct more image details,sparsity representation technique is introduced into the algorithm,image denoising model is established by jointly utilizing the sparse representation and low rank matrix approximation,and then the alternate iteration method is utilized to solve the model.The algorithm realizes the goal of image denoising by using sparsity prior,nonlocal self-similar prior and low rank prior,and this method is comparable with the state-of-the-art denoising methods.Experimental results show that combining sparsity prior,nonlocal self-similar prior with other proper prior knowledge can achieve better restoration results.更多还原