基于稀疏表示的超分辨率重建和图像修复研究
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摘要
稀疏表示理论已成为近几年来图像处理和模式识别领域的研究热点,研究基于学习字典的模型构造方法、快速有效的稀疏表示算法及其在图像处理中的应用,具有非常重要的理论研究价值和实际意义。
本论文基于稀疏表示理论,深入分析了其在图像表示方面的应用,并在此基础上以学习字典理论为重点,对基于稀疏表示理论的超分辨率重建、图像修复、图像类推等做了探索性和创新性的研究。主要内容有:
1阐述了稀疏表示理论的基本概念、数学模型、优化算法、稀疏表示的唯一性和边界条件等内容,以及其在模式识别、图像处理等领域的应用。
2提出基于稀疏字典的超分辨率重建方法,在保持稀疏字典自适应性和灵活性的同时,还加强了字典的正则性和有效性,提高了对先验知识的稀疏表示能力;采用形态分量分析法提取图像特征,更有效地利用了图像的几何结构和纹理特征信息,提高了稀疏编码的精度。
3结合非局部自相似和联合稀疏近似的概念,提出一种基于跨尺度自相似的非局部稀疏编码的超分辨率重建框架。通过联合稀疏近似的方法,建立待处理图像的跨尺度高、低分辨率图像块间的稀疏关联,并将这种关联作为先验知识来指导超分辨率重建;在超分辨率重建过程中,既利用了样本图像的先验知识,又充分考虑了待处理图像本身的跨尺度自相似信息,能更有效地估计图像的高频细节,提高了算法的自适应性。
4提出基于联合稀疏近似的彩色图像超分辨率方法,将彩色图像的各通道数据进行联合稀疏编码,并保证它们具有相同的稀疏性模式。该方法同时考虑彩色图像的各通道数据,兼顾了它们之间的相关性,进一步增强了对彩色图像信息的表达能力,更有效地建立高、低分辨率彩色图像间的稀疏关联。
5提出基于稀疏分解的超分辨率方法,利用形态分量分析方法将图像分解为几何结构分量、纹理分量和残差分量,再分别对各图像分量进行超分辨率重建,提高了重建质量。
6研究学习字典在图像修复领域应用的新方法。将非局部自相似图像块统一进行联合稀疏近似,训练高效的学习字典,使自相似图像块保持相同的稀疏性模式,保证自相似图像块投影到稀疏空间后也保留一定的相似性。该方法在字典学习过程中,既利用了样本图像的先验知识,又充分考虑待修复图像本身的相关信息,增强了图像修复算法的自适应性。
7将学习字典应用到图像类推算法中,并将图像类推分为字典学习和类推重建两个阶段。字典学习过程可离线实现,提高了计算效率;在类推重建过程中,使用稀疏先验的线性优化问题代替传统图像类推方法中的匹配、搜索过程,进一步提高算法的计算效率。
In recent years, sparse representation has become a hotspot of research in the fields of image processing and pattern recognition. It’s theoretically and practically important to do research on construction model of learned dictionary and effective, fast sparse representation algorithms in image representation and image processing. The paper takes sparse representation theory as basis, deeply analyzes its applications in image representation; and then focuses on learned dictionary, makes an exploratory and innovative study of sparse representation based image processing techniques, including super-resolution, image inpainting and image analogies. The main contents of the paper include:
1 The paper introduces the basic concepts, mathematical model, optimized algorithm, uniqueness and boundary conditions of sparse representation, as well as its applications in pattern recognition, image processing, etc.
2 A novel super-resolution method based on sparse dictionary is presented. The method keeps the adaptability and flexibility of sparse dictionary, and strengthens its regularity and validity to improve the image sparse representation capability. Morphological component analysis method is applied to improve the accuracy of sparse coding. Moreover, super-resolution reconstruction and denoising are carried out simultaneously.
3 A novel super-resolution method based on non-local simultaneous sparse coding is presented, which combines non-local self-similarity and simultaneous sparse approximation. The method defines the sparse association between high- and low-resolution patches pairs via simultaneous sparse approximation. Then the association is used as a priori knowledge to guide super-resolution reconstruction. This method not only takes advantage of the sparse prior of examples, but also takes into account image cross-scale self-similarity information. The method efficiently estimates the high frequency information of the low resolution image and the adaptability is enhanced.
4 A novel super-resolution method for color images based on simultaneous sparse approximation is presented. The multichannel data of color images are unified for simultaneous sparse coding to make sure the same sparsity patterns. The expression ability of prior information is enhanced because of considering each channel and correlation among them. Furthermore, the sparse association between HR and LR image feature patches is efficiently built.
5 A super-resolution method based on sparse image decomposition is presented. Firstly, the input image is decomposed into cartoon component, texture component and error component using morphological component analysis method. Next, super-resolution reconstruction of each component is performed, and the quality of super-resolved image is improved effectively.
6 Image inpainting method based on learned dictionary is studied. The non-local self-similar patches are unified for simultaneous sparse approximation and learned dictionary, in which each element of the self-similar patches has the same sparsity pattern. The method assures the self-similar patches also possess similarity when projected onto the sparse space. During training learned dictionary, the method not only takes into account the priori knowledge of samples, but also considers the non-local self-similar information of input image, thus the adaptability is enhanced.
7 Learned dictionary is applied to image analogies. The method mainly includes two stages: training learned dictionary and image analogies reconstruction. The dictionary training process can be off-line achieved to improve the computational efficiency. During image analogies process, the method uses the linear optimization problem of sparse prior instead of searching and matching in conventional methods to further improve the computational efficiency.
本论文基于稀疏表示理论,深入分析了其在图像表示方面的应用,并在此基础上以学习字典理论为重点,对基于稀疏表示理论的超分辨率重建、图像修复、图像类推等做了探索性和创新性的研究。主要内容有:
1阐述了稀疏表示理论的基本概念、数学模型、优化算法、稀疏表示的唯一性和边界条件等内容,以及其在模式识别、图像处理等领域的应用。
2提出基于稀疏字典的超分辨率重建方法,在保持稀疏字典自适应性和灵活性的同时,还加强了字典的正则性和有效性,提高了对先验知识的稀疏表示能力;采用形态分量分析法提取图像特征,更有效地利用了图像的几何结构和纹理特征信息,提高了稀疏编码的精度。
3结合非局部自相似和联合稀疏近似的概念,提出一种基于跨尺度自相似的非局部稀疏编码的超分辨率重建框架。通过联合稀疏近似的方法,建立待处理图像的跨尺度高、低分辨率图像块间的稀疏关联,并将这种关联作为先验知识来指导超分辨率重建;在超分辨率重建过程中,既利用了样本图像的先验知识,又充分考虑了待处理图像本身的跨尺度自相似信息,能更有效地估计图像的高频细节,提高了算法的自适应性。
4提出基于联合稀疏近似的彩色图像超分辨率方法,将彩色图像的各通道数据进行联合稀疏编码,并保证它们具有相同的稀疏性模式。该方法同时考虑彩色图像的各通道数据,兼顾了它们之间的相关性,进一步增强了对彩色图像信息的表达能力,更有效地建立高、低分辨率彩色图像间的稀疏关联。
5提出基于稀疏分解的超分辨率方法,利用形态分量分析方法将图像分解为几何结构分量、纹理分量和残差分量,再分别对各图像分量进行超分辨率重建,提高了重建质量。
6研究学习字典在图像修复领域应用的新方法。将非局部自相似图像块统一进行联合稀疏近似,训练高效的学习字典,使自相似图像块保持相同的稀疏性模式,保证自相似图像块投影到稀疏空间后也保留一定的相似性。该方法在字典学习过程中,既利用了样本图像的先验知识,又充分考虑待修复图像本身的相关信息,增强了图像修复算法的自适应性。
7将学习字典应用到图像类推算法中,并将图像类推分为字典学习和类推重建两个阶段。字典学习过程可离线实现,提高了计算效率;在类推重建过程中,使用稀疏先验的线性优化问题代替传统图像类推方法中的匹配、搜索过程,进一步提高算法的计算效率。
In recent years, sparse representation has become a hotspot of research in the fields of image processing and pattern recognition. It’s theoretically and practically important to do research on construction model of learned dictionary and effective, fast sparse representation algorithms in image representation and image processing. The paper takes sparse representation theory as basis, deeply analyzes its applications in image representation; and then focuses on learned dictionary, makes an exploratory and innovative study of sparse representation based image processing techniques, including super-resolution, image inpainting and image analogies. The main contents of the paper include:
1 The paper introduces the basic concepts, mathematical model, optimized algorithm, uniqueness and boundary conditions of sparse representation, as well as its applications in pattern recognition, image processing, etc.
2 A novel super-resolution method based on sparse dictionary is presented. The method keeps the adaptability and flexibility of sparse dictionary, and strengthens its regularity and validity to improve the image sparse representation capability. Morphological component analysis method is applied to improve the accuracy of sparse coding. Moreover, super-resolution reconstruction and denoising are carried out simultaneously.
3 A novel super-resolution method based on non-local simultaneous sparse coding is presented, which combines non-local self-similarity and simultaneous sparse approximation. The method defines the sparse association between high- and low-resolution patches pairs via simultaneous sparse approximation. Then the association is used as a priori knowledge to guide super-resolution reconstruction. This method not only takes advantage of the sparse prior of examples, but also takes into account image cross-scale self-similarity information. The method efficiently estimates the high frequency information of the low resolution image and the adaptability is enhanced.
4 A novel super-resolution method for color images based on simultaneous sparse approximation is presented. The multichannel data of color images are unified for simultaneous sparse coding to make sure the same sparsity patterns. The expression ability of prior information is enhanced because of considering each channel and correlation among them. Furthermore, the sparse association between HR and LR image feature patches is efficiently built.
5 A super-resolution method based on sparse image decomposition is presented. Firstly, the input image is decomposed into cartoon component, texture component and error component using morphological component analysis method. Next, super-resolution reconstruction of each component is performed, and the quality of super-resolved image is improved effectively.
6 Image inpainting method based on learned dictionary is studied. The non-local self-similar patches are unified for simultaneous sparse approximation and learned dictionary, in which each element of the self-similar patches has the same sparsity pattern. The method assures the self-similar patches also possess similarity when projected onto the sparse space. During training learned dictionary, the method not only takes into account the priori knowledge of samples, but also considers the non-local self-similar information of input image, thus the adaptability is enhanced.
7 Learned dictionary is applied to image analogies. The method mainly includes two stages: training learned dictionary and image analogies reconstruction. The dictionary training process can be off-line achieved to improve the computational efficiency. During image analogies process, the method uses the linear optimization problem of sparse prior instead of searching and matching in conventional methods to further improve the computational efficiency.
引文
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