【作者】 何艳敏；

【导师】 王厚军；

【作者基本信息】 电子科技大学 ， 测试计量技术及仪器， 2011， 博士

【摘要】 在信号分析中,人们总希望能将信号简洁地表示出来,以便揭示其最本质的特征。稀疏表示提供了这样一种途径,它力求用尽量少的元素来表示信号。作为一种新兴的表示方法,稀疏表示引起了国内外广大学者的普遍关注,并对信号处理和分析产生了极为重要的影响。目前稀疏表示已被广泛地应用到图像处理、模式识别,自动测控等的多个领域。本论文研究了稀疏表示及其在图像处理中的应用,围绕原子库构建和稀疏分解两个关键问题,对基于冗余原子库稀疏表示的图像压缩和图像去噪方法进行了探索性的研究,主要的研究成果表现在:第一,本文提出一个带可变参数的不动点定理,在此基础上提出一种新的迭代可控的分形解码方案。新方案提供了丰富的质量渐进解码模式以满足实际应用的需要,且无需修改分形编码部分即可直接应用到现有的分形压缩系统中。第二,本文提出一种新的基于多尺度追踪的稀疏分解方法。该方法在多个尺度上进行匹配运算,并自适应地完成尺度间的切换;同时利用原子库的几何特性,在原图像分辨率层进行原子的重建和提取,从而在降低分解的计算复杂度的同时保持了逼近精度。第三,本文提出一种基于块划分的匹配追踪图像编码方法。该方法利用匹配追踪分解后原子的能量和位置分布特性,对原子的系数和位置参数进行了有效的组织和编码,在编码效率和伸缩性能方面相对于同类方法有了显著的提高,在低到中码率段获得了与当前先进方法相当的客观率失真性能和更优的主观质量,同时提供了更灵活的质量和分辨率的伸缩性,更适合于异构网络环境下的多媒体应用。第四,本文提出一种新的基于全局原子库的稀疏去噪方法,从原子库学习和稀疏分解去噪两个方面对以往的方法进行了改进。在原子库学习方面,提出一种两阶段学习算法,通过引入相关系数匹配准则和原子库裁剪机制,很好处理了信号提取和噪声抑制之间的矛盾;在稀疏分解去噪方面,提出了一种多级去噪方案,在挖掘图像多尺度特性的同时进一步减少了人为噪声。基于以上特点,该方法的去噪性能较同类方法有了显著的提高,在噪声强度较大的情况下,获得了比当前先进方法更好的主客观图像恢复质量。第五,本文提出一种新的基于空间自适应原子库的稀疏去噪方法。该方法结合“非局部”和“冗余稀疏”两种思想,通过为每一个空间图像块训练一个自适应的子原子库来实现对图块的稀疏表示。在原子库的训练及基原子的选择中,联合使用了全局和局部两种子空间分析方法,有效地克服了以往自适应去噪方法所面临的诸多问题。与使用固定基或原子库来分解图像的方法相比,该方法提供了一种局部自适应的图像表示,因而能更好地捕获图像细节特征。在对图像边缘和纹理的保持上,该方法表现非常出色,获得了比当前先进方法更好的效果。更多还原

【Abstract】 In signal analysis, it is always desirable to represent the signal in a compact way so as to reveal its essential features. Toward this goal, the sparse representation which describes the signal with as few elements as possible has been developed. As a new powerful method, the sparse representation has attracted much attention and had an important impact on signal processing and analysis. At present, it has been widely applied to many fields such as image processing, pattern recognization, and automantic measurement and control, etc.This thesis addresses the issues of sparse representation and its application to image processing. Surrounding the two main problems, dictionary construction and sparse decomposition, the image coding and denoising methods based on sparse representations over redundant dictionaries are deeply studied. The main contributions are as follows:1) A new fixed-point theorem with a variable parameter is presented. Based on this theorem, a novel controllable decoding scheme is developed for fractal image compression. The new scheme provides various progressive modes to meet the needs of different applications. The proposed decoder can be applied directly to the existing fractal compression systems without imposing any constraints on the encoding process.2) A new multiscale matching pursuit method for image approximation is proposed. In this method, the pursuit is performed at various scales and the task of scale transition is done adaptively. By exploiting the geometric properties of the dictionary, the target atom is built and extracted at the original scale. Consequently, the proposed method offers a reduction in computational complexity while maintaining the high performance of approximation.3) A novel matching pursuit (MP) image coding method based on block partitioning is proposed. By exploiting the energy and position distributions of MP atoms, the coefficient and position parameters of atoms are organized and coded effectively. The proposed coder achieves a significant improvement over the existing MP coder in both coding efficiency and scalability. Compared to other state-of-the-art coders, it offers comparable PSNR performance and better visual quality at low to medium rates. At the same time, the new coder has the advantage of producing highly flexible streams in terms of both rate and resolution scalability, which makes it very attractive for various multimedia applications over heterogeneous networks.4) A new denoising method using sparse representations over a global dictionary is proposed. This method improves the previous ones in two aspects: dictionary training and denoising. In the dictionary training, a two-phase dictionary training algorithm is proposed. By introducing a correlation coefficient matching criterion and a dictionary pruning scheme, the conflicting problems of structure extraction and artifact suppression are better tackled. In the denoising, a multi-stage sparse coding scheme is proposed to exploit the multiscale nature of the image and further reduce the artifacts. The proposed method achieves significant improvements over the previous sparse denoising methods and outperforms the state-of-the-art methods in terms of both objective and subjective quality at high noise level.5) A novel denoising method using sparse representations over a spatially adaptive dictionary is proposed. This method combines the ideas of non-local and redundant sparsity, and obtains the sparse image representation by training an adaptive sub-dictionary for each image patch. In the dictionary training as well as the atom selection, the strength of both the global and local subspace analysis is combined to overcome the problems of previous adaptive denoising methods. Compared to the methods using fix basis or dictionary to decompose the image, this method provides a local-adaptive representation and thus has the ability to better capture image details. Not surprisingly, the proposed method outperforms the state-of-the-art methods in preserving image details such as edges and textures.更多还原