基于稀疏表示的光学遥感影像超分辨率重建算法研究
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摘要
图像超分辨率重建是图像处理、摄影测量与遥感、计算机视觉等领域的一个经久不衰的研究主题。稀疏表示理论起源于视觉神经系统的研究,为图像处理提供了一个崭新的研究视角,近年来,已成为信号和图像处理领域的国际前沿和热点之一,引起学者的广泛关注。
论文在国家科技基础条件平台“地球系统科学数据共享平台——长江三角洲科学数据共享平台”的支持下,以稀疏表示理论为指导,开展了其在光学遥感影像超分辨率重建中的应用方法研究,主要围绕稀疏表示理论中字典学习模型和算法、基于稀疏表示的遥感影像超分辨率重建模型和算法方面进行了深入研究。论文的主要研究内容与结论包括：
(1)深入研究了遥感影像稀疏表示理论基础。阐述了稀疏表示理论的神经生理学背景,人类视觉系统的视觉特性为图像稀疏表示提供了直接生理依据,推动了图像稀疏表示理论的发展。分析了遥感影像的稀疏特性及其与超分辨率重建问题的关系,单幅遥感影像的超分辨率重建问题是典型的反问题,具有“不适定性”,通过引入稀疏先验约束,使得超分辨率重建问题可以稳定、唯一求解。探讨了稀疏先验约束的表达方法,深入研究了遥感影像的稀疏表示模型。分析了稀疏表示理论中字典的类型,分为基于解析式的字典和基于学习的字典。通过解析公式构造的字典,不需要矩阵乘法运算,具有快速的计算速度,而构造的原子较简单,自适应性较差。基于学习的字典,通过机器学习的方法,从训练样本中学习获得,具有较好的自适应性,能对各种特征的图像进行有效表示,但结构性较弱,计算复杂度较高。
(2)深入研究了高、低分辨率字典对的学习方法。给出了一种联合字典对学习模型,通过将高、低分辨率字典进行链接,实现高、低分辨率字典对的同步学习。提出了一种基于MM (Majorization Minimization)方法的联合字典对学习算法,通过构造一个参数互相解耦的易于优化的代理函数,替代原来的参数互相耦合难以优化的目标函数,保证每一次迭代求解的值在局部范围内最优。研究了一种耦合学习字典对学习方法,通过在高、低分辨率特征块空间中分别学习高、低分辨率字典,保证了字典对具有相同的稀疏表示。在此基础上,提出了一种耦合稀疏字典对学习方法,将耦合思想推广到稀疏字典学习中,一方面保证了高、低分辨率稀疏字典对具有相同的稀疏表示,另一方面,使字典同时具有良好的自适应性和紧凑的结构。提出了一种松耦合稀疏字典对学习模型,通过在学习高、低分辨率稀疏字典的同时,学习它们之间的线性关系,将相同的稀疏表示这一严格要求进一步放松,使得高、低分辨率稀疏字典对之间的关系更加灵活。
(3)对单幅光学遥感影像的超分辨率重建算法进行了深入研究。给出了一种基于联合字典对的超分辨率重建算法,将学习的高、低分辨率字典对作为先验知识用以指导其他影像的超分辨率重建。实验验证了稀疏先验约束的有效性,算法可为相同区域相同类型的低分辨率遥感影像的超分辨率重建提供有用的高频信息。研究了一种基于预分类联合字典对的遥感影像超分辨率重建算法。依据字典中原子之间的结构特征,通过改进的K均值聚类方法将原字典进一步分为多个子字典,将影像特征块的稀疏分解过程限制在一个原子数更少的学习字典子集中。实验表明该算法在保证重建质量的前提下,能提高算法50%左右的计算性能。
研究了一种基于耦合学习字典对的遥感影像超分辨率重建算法,使字典学习和超分辨率重建两个过程在相同的特征空间中进行。实验验证了该方法的有效性,与基于联合字典对的超分辨率方法相比,两者重建结果较接近,差异很小,从侧面验证了联合字典对超分辨率方法中的空间差异性对重建结果的影响较小。在此基础上,提出了一种基于耦合稀疏字典对的超分辨率重建算法,保证了稀疏字典学习和超分辨率重建两个过程在相同的特征空间中进行,并使字典同时具有良好的自适应性和紧凑的结构。实验验证了该方法的有效性,与耦合学习字典超分辨率算法相比,重建效果更不理想,究其原因可能与基字典的构建有关。
提出了一种基于松耦合稀疏字典对的遥感影像超分辨率重建算法,将学习的高、低分辨率稀疏字典及它们之间的线性映射关系一起作为先验知识,用以指导其他低分辨率遥感影像的超分辨率重建。通过定性分析和定量试验,与其他超分辨率方法相比,该方法的重建质量均取得一定提高。
Image super-resolution reconstruction is an enduring research topic in the fields of image processing, photogrammetry and remote sensing,and computer vision. Sparse representation theory, originated in the study of the visual nervous system, provides a new perspective for remote sensing image processing and causes widespread concern of scholars. It has become an international frontier and one of the focus in the fields of signal and image processing in recent years.
This paper is supported by the national science and technology infrastructure "Data Sharing Infrastructure of Earth System Science——Data Sharing Infrastructure of Yangtze River Delta". Based on the sparse representation theory, this paper deeply studies on the super-resolution reconstruction methods of optical remote sensing image, and mainly revolves around two aspects of sparse representation theory, which includes dictionary learning model and algorithm, super-resolution reconstruction model and algorithm. The main contents and conclusions of the paper include:
(1) The theoretical basis of remote sensing image sparse representation is studied. The neurophysiological background of sparse representation theory is expounded in this paper. The visual characteristics of human visual system provide a direct physiological basis for sparse representation of image, which promotes the development of image sparse representation theory. The relationship between the sparse characteristics of remote sensing image and its super-resolution reconstruction is analysised. The super-resolution reconstruction of single remote sensing image is a typical ill-posed problem. With sparsity as a prior for regularizing the ill-posed super-resolution problem, the problem can have a stable and unique solution. The expression methods of prior constraint of sparse are discussed and the sparse representation model of remote sensing image is studied. The types of dictionary in sparse representation theory is analyzed, which include analytical-based dictionary and learning-based dictionary. The analytical-based dictionary doesn't need matrix multiplication, which has a fast computing speed but poor adaptability for the atoms are simple. Learning-based dictionary is trained from training samples by the machine learning methods, which has good adaptability and can represent the images with various features. But learning-based dictionary has weak structure and higher computational complexity.
(2) The high-and low-resolution dictionaries learning methods are deeply studied. A joint dictionary learning model is given. By jointly learning the high-and low-resolution dictionaries, the two dictionaries are learned synchronously. A learning algorithm based on majorization minimization method for the joint learning model is presented. In which the original objective function is replaced by a surrogate objective function which is updated in each optimization step and can be easily minimized. The parameters in the surrogate functions are decoupled, so that the surrogate function can be minimized element-wise. And the method can guarantee to find local minima in each optimization step. A coupled dictionary learning method is studied. The high-and low-resolution dictionaries are studied in the high-and low-resolution feature space, respectively. And the two dictionaries have the same sparse representation. Based on this, a coupled sparse dictionary learning method is proposed, which spread the coupled thinking into sparse dictionary learning. As a result, on one hand it can ensure high-and low-resolution dictionaries have the same sparse representation, on the other hand, the dictionaries have good adaptability and compact structure. A loosely-coupled sparse dictionary learning model is proposed, in which the high-and low-resolution sparse dictionaries are learned, and the linear relationship between them is learned synchronously. For the strict requirement of the same sparse representation is further relaxed, the relationship between high-and low-resolution sparse dictionaries is more flexible.
(3) The super-resolution reconstruction algorithms of single optical remote sensing image are deeply studied. A super-resolution reconstruction algorithm based on joint dictionary is given. In which the high-and low-resolution dictionary are used as prior knowledge to tutor super-resolution reconstruction for other images. Experimental results demonstrate the effectiveness of the sparsity as a prior for patch-based super-resolution. The algorithm can supply useful high-frequency information for super-resolution reconstruction of low-resolution remote sensing images under same area with same kind. A super-resolution reconstruction algorithm of remote sensing image based on pre-classified joint dictionary is studied. According to structural feature among atoms, the original dictionary is divided into several sub-dictionaries using improved K-means clustering algorithm, therefore, the sparse decomposition process of image patches is limited in a subset of learned dictionary with fewer number atoms. Experimental results show that the computation performance can be improved by50%, and the reconstruction quality can be assured, too.
A super-resolution reconstruction algorithm of remote sensing image based on two coupled dictionaries is given, in which dictionary learning process and super-resolution reconstruction process are under the same feature space. Experimental results demonstrate the effectiveness of the algorithm. Compared with the super-resolution reconstruction algorithm based on joint dictionary, the reconstruction results of the two algorithms are close to each other, the difference between them is small. Which demonstrates the spatial difference has little influence on reconstruction results of the algorithm based on joint dictionary in another way. Based on this, a super-resolution reconstruction algorithm based on two coupled sparse dictionaries is proposed. On one hand, learning process of sparse dictionary and super-resolution reconstruction are ensured under the same feature space. On the other hand, the learned dictionaries not only has good adaptability but also has compact structure. Experimental results show the effectiveness of the algorithm. But the reconstruction effect is not ideal compared to the previous algorithm. After some analysis, the reason may be in association with construction of basic dictionary.
A super-resolution reconstruction algorithm of remote sensing image based on two loosely-coupled sparse dictionaries is proposed. High-and low-resolution sparse dictionaries and the linear mapping relationship between them are conducted as prior knowledge for regularizing image super-resolution. Experimental results demonstrate that the loosely-coupled sparse dictionary learning method can outperform the joint dictionary learning method and the coupled dictionary learning method both quantitatively and qualitatively.
论文在国家科技基础条件平台“地球系统科学数据共享平台——长江三角洲科学数据共享平台”的支持下,以稀疏表示理论为指导,开展了其在光学遥感影像超分辨率重建中的应用方法研究,主要围绕稀疏表示理论中字典学习模型和算法、基于稀疏表示的遥感影像超分辨率重建模型和算法方面进行了深入研究。论文的主要研究内容与结论包括：
(1)深入研究了遥感影像稀疏表示理论基础。阐述了稀疏表示理论的神经生理学背景,人类视觉系统的视觉特性为图像稀疏表示提供了直接生理依据,推动了图像稀疏表示理论的发展。分析了遥感影像的稀疏特性及其与超分辨率重建问题的关系,单幅遥感影像的超分辨率重建问题是典型的反问题,具有“不适定性”,通过引入稀疏先验约束,使得超分辨率重建问题可以稳定、唯一求解。探讨了稀疏先验约束的表达方法,深入研究了遥感影像的稀疏表示模型。分析了稀疏表示理论中字典的类型,分为基于解析式的字典和基于学习的字典。通过解析公式构造的字典,不需要矩阵乘法运算,具有快速的计算速度,而构造的原子较简单,自适应性较差。基于学习的字典,通过机器学习的方法,从训练样本中学习获得,具有较好的自适应性,能对各种特征的图像进行有效表示,但结构性较弱,计算复杂度较高。
(2)深入研究了高、低分辨率字典对的学习方法。给出了一种联合字典对学习模型,通过将高、低分辨率字典进行链接,实现高、低分辨率字典对的同步学习。提出了一种基于MM (Majorization Minimization)方法的联合字典对学习算法,通过构造一个参数互相解耦的易于优化的代理函数,替代原来的参数互相耦合难以优化的目标函数,保证每一次迭代求解的值在局部范围内最优。研究了一种耦合学习字典对学习方法,通过在高、低分辨率特征块空间中分别学习高、低分辨率字典,保证了字典对具有相同的稀疏表示。在此基础上,提出了一种耦合稀疏字典对学习方法,将耦合思想推广到稀疏字典学习中,一方面保证了高、低分辨率稀疏字典对具有相同的稀疏表示,另一方面,使字典同时具有良好的自适应性和紧凑的结构。提出了一种松耦合稀疏字典对学习模型,通过在学习高、低分辨率稀疏字典的同时,学习它们之间的线性关系,将相同的稀疏表示这一严格要求进一步放松,使得高、低分辨率稀疏字典对之间的关系更加灵活。
(3)对单幅光学遥感影像的超分辨率重建算法进行了深入研究。给出了一种基于联合字典对的超分辨率重建算法,将学习的高、低分辨率字典对作为先验知识用以指导其他影像的超分辨率重建。实验验证了稀疏先验约束的有效性,算法可为相同区域相同类型的低分辨率遥感影像的超分辨率重建提供有用的高频信息。研究了一种基于预分类联合字典对的遥感影像超分辨率重建算法。依据字典中原子之间的结构特征,通过改进的K均值聚类方法将原字典进一步分为多个子字典,将影像特征块的稀疏分解过程限制在一个原子数更少的学习字典子集中。实验表明该算法在保证重建质量的前提下,能提高算法50%左右的计算性能。
研究了一种基于耦合学习字典对的遥感影像超分辨率重建算法,使字典学习和超分辨率重建两个过程在相同的特征空间中进行。实验验证了该方法的有效性,与基于联合字典对的超分辨率方法相比,两者重建结果较接近,差异很小,从侧面验证了联合字典对超分辨率方法中的空间差异性对重建结果的影响较小。在此基础上,提出了一种基于耦合稀疏字典对的超分辨率重建算法,保证了稀疏字典学习和超分辨率重建两个过程在相同的特征空间中进行,并使字典同时具有良好的自适应性和紧凑的结构。实验验证了该方法的有效性,与耦合学习字典超分辨率算法相比,重建效果更不理想,究其原因可能与基字典的构建有关。
提出了一种基于松耦合稀疏字典对的遥感影像超分辨率重建算法,将学习的高、低分辨率稀疏字典及它们之间的线性映射关系一起作为先验知识,用以指导其他低分辨率遥感影像的超分辨率重建。通过定性分析和定量试验,与其他超分辨率方法相比,该方法的重建质量均取得一定提高。
Image super-resolution reconstruction is an enduring research topic in the fields of image processing, photogrammetry and remote sensing,and computer vision. Sparse representation theory, originated in the study of the visual nervous system, provides a new perspective for remote sensing image processing and causes widespread concern of scholars. It has become an international frontier and one of the focus in the fields of signal and image processing in recent years.
This paper is supported by the national science and technology infrastructure "Data Sharing Infrastructure of Earth System Science——Data Sharing Infrastructure of Yangtze River Delta". Based on the sparse representation theory, this paper deeply studies on the super-resolution reconstruction methods of optical remote sensing image, and mainly revolves around two aspects of sparse representation theory, which includes dictionary learning model and algorithm, super-resolution reconstruction model and algorithm. The main contents and conclusions of the paper include:
(1) The theoretical basis of remote sensing image sparse representation is studied. The neurophysiological background of sparse representation theory is expounded in this paper. The visual characteristics of human visual system provide a direct physiological basis for sparse representation of image, which promotes the development of image sparse representation theory. The relationship between the sparse characteristics of remote sensing image and its super-resolution reconstruction is analysised. The super-resolution reconstruction of single remote sensing image is a typical ill-posed problem. With sparsity as a prior for regularizing the ill-posed super-resolution problem, the problem can have a stable and unique solution. The expression methods of prior constraint of sparse are discussed and the sparse representation model of remote sensing image is studied. The types of dictionary in sparse representation theory is analyzed, which include analytical-based dictionary and learning-based dictionary. The analytical-based dictionary doesn't need matrix multiplication, which has a fast computing speed but poor adaptability for the atoms are simple. Learning-based dictionary is trained from training samples by the machine learning methods, which has good adaptability and can represent the images with various features. But learning-based dictionary has weak structure and higher computational complexity.
(2) The high-and low-resolution dictionaries learning methods are deeply studied. A joint dictionary learning model is given. By jointly learning the high-and low-resolution dictionaries, the two dictionaries are learned synchronously. A learning algorithm based on majorization minimization method for the joint learning model is presented. In which the original objective function is replaced by a surrogate objective function which is updated in each optimization step and can be easily minimized. The parameters in the surrogate functions are decoupled, so that the surrogate function can be minimized element-wise. And the method can guarantee to find local minima in each optimization step. A coupled dictionary learning method is studied. The high-and low-resolution dictionaries are studied in the high-and low-resolution feature space, respectively. And the two dictionaries have the same sparse representation. Based on this, a coupled sparse dictionary learning method is proposed, which spread the coupled thinking into sparse dictionary learning. As a result, on one hand it can ensure high-and low-resolution dictionaries have the same sparse representation, on the other hand, the dictionaries have good adaptability and compact structure. A loosely-coupled sparse dictionary learning model is proposed, in which the high-and low-resolution sparse dictionaries are learned, and the linear relationship between them is learned synchronously. For the strict requirement of the same sparse representation is further relaxed, the relationship between high-and low-resolution sparse dictionaries is more flexible.
(3) The super-resolution reconstruction algorithms of single optical remote sensing image are deeply studied. A super-resolution reconstruction algorithm based on joint dictionary is given. In which the high-and low-resolution dictionary are used as prior knowledge to tutor super-resolution reconstruction for other images. Experimental results demonstrate the effectiveness of the sparsity as a prior for patch-based super-resolution. The algorithm can supply useful high-frequency information for super-resolution reconstruction of low-resolution remote sensing images under same area with same kind. A super-resolution reconstruction algorithm of remote sensing image based on pre-classified joint dictionary is studied. According to structural feature among atoms, the original dictionary is divided into several sub-dictionaries using improved K-means clustering algorithm, therefore, the sparse decomposition process of image patches is limited in a subset of learned dictionary with fewer number atoms. Experimental results show that the computation performance can be improved by50%, and the reconstruction quality can be assured, too.
A super-resolution reconstruction algorithm of remote sensing image based on two coupled dictionaries is given, in which dictionary learning process and super-resolution reconstruction process are under the same feature space. Experimental results demonstrate the effectiveness of the algorithm. Compared with the super-resolution reconstruction algorithm based on joint dictionary, the reconstruction results of the two algorithms are close to each other, the difference between them is small. Which demonstrates the spatial difference has little influence on reconstruction results of the algorithm based on joint dictionary in another way. Based on this, a super-resolution reconstruction algorithm based on two coupled sparse dictionaries is proposed. On one hand, learning process of sparse dictionary and super-resolution reconstruction are ensured under the same feature space. On the other hand, the learned dictionaries not only has good adaptability but also has compact structure. Experimental results show the effectiveness of the algorithm. But the reconstruction effect is not ideal compared to the previous algorithm. After some analysis, the reason may be in association with construction of basic dictionary.
A super-resolution reconstruction algorithm of remote sensing image based on two loosely-coupled sparse dictionaries is proposed. High-and low-resolution sparse dictionaries and the linear mapping relationship between them are conducted as prior knowledge for regularizing image super-resolution. Experimental results demonstrate that the loosely-coupled sparse dictionary learning method can outperform the joint dictionary learning method and the coupled dictionary learning method both quantitatively and qualitatively.
引文
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