基于广义稀疏表示的图像超分辨重建方法研究
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摘要
在日常生活与生产实践中，图像是应用最广泛的信息载体之一。然而，在实际成像过程中，受光学模糊、运动模糊、欠采样和噪声等退化因素的影响，人们往往很难获得期望的高分辨率图像或图像序列，这给后续的图像处理、分析与理解带来诸多困难，影响人们正确认识客观世界及其规律。如何提高所获图像的空间分辨率，改善图像质量，是图像处理领域极具挑战性的课题。图像超分辨重建技术是解决上述问题较经济而有效的手段之一。利用图像超分辨重建技术，不仅能获得高于现有成像系统空间分辨率的高质量图像，而且能充分利用大量已有的低分辨图像资源。该技术在模式识别、计算机视觉、视频监控、遥感成像以及生活娱乐等方面具有广泛的应用前景，受到国内外学者的广泛关注。
针对超分辨重建面临的挑战性问题，本文利用广义稀疏表示思想，从邻域样本的选择、映射关系的估计、正则化先验的设计以及自相似冗余信息的学习等方面，对基于实例学习和基于重构的图像超分辨重建方法进行了深入研究，主要研究成果为：
(1)提出了一种基于高斯混合模型聚类和部分监督邻域嵌入的实例学习图像超分辨方法。在学习阶段，使用高斯混合模型聚类方法构造类别预测器，用于估计训练集中低分辨图像块的类别信息；在合成阶段，结合类别信息，使用部分监督邻域选择方案调整输入图像块与训练集样本之间的距离，一定程度上克服了传统邻域嵌入超分辨算法在邻域选择方面存在的不足。
(2)针对邻域嵌入超分辨算法低分辨图像块与高分辨图像块在邻域关系不能保持不一致问题，提出了一种基于对偶约束的联合学习超分辨重建方法。首先，通过对偶约束方法将低分辨图像块与对应高分辨图像块构成成组块对，通过联合学习构造低分辨图像块与高分辨图像块的联合特征子空间；然后，在联合特征子空间中进行邻域的选择和低分辨与高分辨图像块之间的映射关系的估计。最后，结合全局约束和一致性先验，进一步提高初始化估计超分辨重建图像的质量。
(3)为提高已有邻域嵌入算法的重建效率，同时解决邻域选择方法存在的不足，提出了一种基于方向梯度直方图（Histograms of Oriented Gradients，HOG）特征聚类的稀疏邻域嵌入的实例学习超分辨方法。为提高重建效率，引入HOG特征描述低分辨图像块的局部几何结构，通过k-means聚类技术将大规模训练集划分成多个结构相似的子类;针对已有邻域嵌入超分辨算法在邻域选择方面存在的不足，提出了一种结合鲁棒性SL0稀疏表示与k/K最近邻策略的稀疏邻域选择算法，能同时实现邻域的选择与重构权值的计算，有效提高了图像超分辨重建的质量。
(4)考虑到实例学习方法和重构方法在超分辨重建方面的互补性，提出了一种基于多尺度字典学习和自适应正则化相结合的图像超分辨方法。为实现基于实例的重建方法，直接从输入的低分辨图像中提取不同尺度的图像块，通过联合学习多个尺度字典，以构建稀疏幻像正则项；为实现基于重构的方法，使用可控核回归技术构造局部先验正则项，以获取图像的局部结构信息；使用非局部均值滤波技术构造非局部先验正则项，以获取图像中相似性冗余性信息。将全局重构约束项、局部与非局部正则项和稀疏幻像正则项相组合，构成一个统一的超分辨重建框架优化求解。在不需要外部训练图像的情况下，提出的方法在保持清晰的图像边缘和恢复丰富的高频细节两方面均能取得较好的效果。
(5)本质上，基于实例学习方法的重建质量很大程度上依赖于训练图像。鉴于此，提出了一种多尺度自相似冗余学习的图像超分辨方法。该方法首先利用低分辨图像不同尺度的自相似冗余结构构造训练图像块对，然后，使用邻域嵌入算法和逐层重建策略，逐步将输入的低分辨图像放大到所需要的高分辨图像。最后，利用非局部均值滤波技术获取图像中相同尺度的自相似冗余信息，通过构造非局部正则项，以进一步提高超分辨重建的质量。
综上所述，本文以信号处理、模式识别为理论基础，以统计学习方法为主要技术手段，提出了五种新的图像超分辨重建方法，有效克服了现有方法存在的不足，在重建清晰的图像边缘和恢复丰富的纹理方面取得了较好的效果，为解决图像超分辨重建问题提供了新的途径。
In everyday life and actual production, images have become one of most widely usedinformation carrier. However, in the practical imaging process, due to the limitations of thedegraded factors such as optical blurring, motion blurring, down-sampling, and noising, it isnot always easy to capture an image or image sequences at a desired high-resolution (HR)level, which causes many difficulities for image processing, analysis, and understanding,leading to an obstacle in correctly understanding the laws of the objective world. Therefore, itis challenging to increase the spatial resolution of an image and to improve its quality. Withimage super-resolution (SR) technique, it is possible to obtain an HR image with the existingimaging systems and to make full use of a lot of low-resolution (LR) image resource.Accordingly, the SR technique has its wide application in many fields pattern recognition,computer vision, video surveillance, remote imaging, entertainment, and so on, and hasattracted broad attention from the academic world at home and abroad.
For the challenging problems of SR reconstruction, this thesis makes a deep research onexample-and reconstruction-based SR methods, in which the philosophy of generalizedsparse representation is adopted to achieve neighbor selection, mapping relationshipestimation, regularization prior design, and redundancies of self-similarity learning. Themajor contributions are the following:
(1) An example-based SR method is proposed based upon Gaussian mixture model(GMM) clustering and partially supervised neighbor embedding (PSNE). In the training phase,a class predictor is constructed by using the GMM clustering to estimate the class informationof each LR image patch in the training dataset; in the synthesis phase, a partially supervisedneighbor selection scheme is developed to adjust the distances between the test example andthose in the training database. Based on this scheme, the proposed method can reduce theproblem of neighbor selection in the original neighbor embedding (NE) algorithm to a certaindegree.
(2) To target the problem that the neighborhood relationship between LR image patchesand the corresponding HR image patches in NE-based methods cannot be perfectly preserved,an example-based SR method is presented by using joint learning via couple constraint. First,the grouping patch pairs (GPP) is established with the combination of the LR and thecorresponding HR image patches, and then a joint learning is applied to train two projectionmatrices simultaneously and to map the original LR and HR feature spaces onto a unifiedfeature subspace; then the k-nearest neighbor (k-NN) selection of the input LR image patchesis performed in the unified feature subspace to estimate the reconstruction weights forsynthesizing the initial HR images. Finally, the global reconstruction constraint andconsistency prior are applied to further enhance the quality of the initial SR estimate.
(3) To improve the reconstruction efficiency of the existing NE algorithms and toovercome the limitation of neighbor selection method, an example-based SR method that is based on clustering on histograms of oriented gradients (HOG) of LR image patches andsparse neighbor embedding (SpNE) algorithm is proposed. To achieve a high efficiency ofreconstruction, the HOG feature is introduced to represent the local geometrical structure ofLR image patches and to divide the training database in large scale into a set of subsets withsimilar structure; to overcome the limitation of neighbor selection scheme used in theprevious NE-based methods, a sparse neighbor selection (SpNS) scheme is developed byintegrating the robust SL0algorithm and the k/K-nearest neighbor criterion. With theproposed scheme, the neighbor selection and calculation of reconstruction weights cansimultaneously be achieved, leading to better SR recovery.
(4) Considering the complementarity of example-and reconstruction-based SR methods,a novel SR method that combines multi-scale dictionary learning and adaptive regularizationis proposed. To achieve an example-based SR method, a multi-scale dictionary is jointlylearnt from image patches at different scales from the LR input. To obtain areconstruction-based SR method, the steering kernel regression (SKR) is applied to formulatea local regularization to capture the local structure information and the non-local means(NLM) filter is adopted to construct non-local regularization term to capture the similarityredundancy at the same scale. The reconstruction term, the local and non-local priorregularization terms, and sparse hallucination regularization term are integrated into a unifiedSR framework for optimization. Without the help of any external training image, the proposedmethod can obtain a better SR recovery, leading to sharper edges as well as richer highfrequency details.
(5) Essentially, the reconstruction quality of example-based methods heavily depends onthe supporting training images. In view of this, an image SR method is proposed by exploitingthe redundancies of self-similarity at different scales. First, the proposed method directlyexploits the redundancies of self-similarity at different scales in the input LR image itself toconstruct training image patch pairs and the NE-based algorithm is adopted to graduallymagnify the LR input to the desired size. Finally, the NLM filter is introduced to obtain theredundancy of similarity at the same scale and a non-local regularization term is formulated tofurther improve the quality of SR recovery.
In summary, on the basis of the fundamental theory of signal processing and patternrecognition, this thesis takes statistical learning as the main investigative means and proposesfive novel SR methods. The proposed methods can effectively overcome the limitations of theexisting methods and achieve better SR recovery on producing sharper edges and richerdetails, providing a new approach to SR reconstruction.
针对超分辨重建面临的挑战性问题，本文利用广义稀疏表示思想，从邻域样本的选择、映射关系的估计、正则化先验的设计以及自相似冗余信息的学习等方面，对基于实例学习和基于重构的图像超分辨重建方法进行了深入研究，主要研究成果为：
(1)提出了一种基于高斯混合模型聚类和部分监督邻域嵌入的实例学习图像超分辨方法。在学习阶段，使用高斯混合模型聚类方法构造类别预测器，用于估计训练集中低分辨图像块的类别信息；在合成阶段，结合类别信息，使用部分监督邻域选择方案调整输入图像块与训练集样本之间的距离，一定程度上克服了传统邻域嵌入超分辨算法在邻域选择方面存在的不足。
(2)针对邻域嵌入超分辨算法低分辨图像块与高分辨图像块在邻域关系不能保持不一致问题，提出了一种基于对偶约束的联合学习超分辨重建方法。首先，通过对偶约束方法将低分辨图像块与对应高分辨图像块构成成组块对，通过联合学习构造低分辨图像块与高分辨图像块的联合特征子空间；然后，在联合特征子空间中进行邻域的选择和低分辨与高分辨图像块之间的映射关系的估计。最后，结合全局约束和一致性先验，进一步提高初始化估计超分辨重建图像的质量。
(3)为提高已有邻域嵌入算法的重建效率，同时解决邻域选择方法存在的不足，提出了一种基于方向梯度直方图（Histograms of Oriented Gradients，HOG）特征聚类的稀疏邻域嵌入的实例学习超分辨方法。为提高重建效率，引入HOG特征描述低分辨图像块的局部几何结构，通过k-means聚类技术将大规模训练集划分成多个结构相似的子类;针对已有邻域嵌入超分辨算法在邻域选择方面存在的不足，提出了一种结合鲁棒性SL0稀疏表示与k/K最近邻策略的稀疏邻域选择算法，能同时实现邻域的选择与重构权值的计算，有效提高了图像超分辨重建的质量。
(4)考虑到实例学习方法和重构方法在超分辨重建方面的互补性，提出了一种基于多尺度字典学习和自适应正则化相结合的图像超分辨方法。为实现基于实例的重建方法，直接从输入的低分辨图像中提取不同尺度的图像块，通过联合学习多个尺度字典，以构建稀疏幻像正则项；为实现基于重构的方法，使用可控核回归技术构造局部先验正则项，以获取图像的局部结构信息；使用非局部均值滤波技术构造非局部先验正则项，以获取图像中相似性冗余性信息。将全局重构约束项、局部与非局部正则项和稀疏幻像正则项相组合，构成一个统一的超分辨重建框架优化求解。在不需要外部训练图像的情况下，提出的方法在保持清晰的图像边缘和恢复丰富的高频细节两方面均能取得较好的效果。
(5)本质上，基于实例学习方法的重建质量很大程度上依赖于训练图像。鉴于此，提出了一种多尺度自相似冗余学习的图像超分辨方法。该方法首先利用低分辨图像不同尺度的自相似冗余结构构造训练图像块对，然后，使用邻域嵌入算法和逐层重建策略，逐步将输入的低分辨图像放大到所需要的高分辨图像。最后，利用非局部均值滤波技术获取图像中相同尺度的自相似冗余信息，通过构造非局部正则项，以进一步提高超分辨重建的质量。
综上所述，本文以信号处理、模式识别为理论基础，以统计学习方法为主要技术手段，提出了五种新的图像超分辨重建方法，有效克服了现有方法存在的不足，在重建清晰的图像边缘和恢复丰富的纹理方面取得了较好的效果，为解决图像超分辨重建问题提供了新的途径。
In everyday life and actual production, images have become one of most widely usedinformation carrier. However, in the practical imaging process, due to the limitations of thedegraded factors such as optical blurring, motion blurring, down-sampling, and noising, it isnot always easy to capture an image or image sequences at a desired high-resolution (HR)level, which causes many difficulities for image processing, analysis, and understanding,leading to an obstacle in correctly understanding the laws of the objective world. Therefore, itis challenging to increase the spatial resolution of an image and to improve its quality. Withimage super-resolution (SR) technique, it is possible to obtain an HR image with the existingimaging systems and to make full use of a lot of low-resolution (LR) image resource.Accordingly, the SR technique has its wide application in many fields pattern recognition,computer vision, video surveillance, remote imaging, entertainment, and so on, and hasattracted broad attention from the academic world at home and abroad.
For the challenging problems of SR reconstruction, this thesis makes a deep research onexample-and reconstruction-based SR methods, in which the philosophy of generalizedsparse representation is adopted to achieve neighbor selection, mapping relationshipestimation, regularization prior design, and redundancies of self-similarity learning. Themajor contributions are the following:
(1) An example-based SR method is proposed based upon Gaussian mixture model(GMM) clustering and partially supervised neighbor embedding (PSNE). In the training phase,a class predictor is constructed by using the GMM clustering to estimate the class informationof each LR image patch in the training dataset; in the synthesis phase, a partially supervisedneighbor selection scheme is developed to adjust the distances between the test example andthose in the training database. Based on this scheme, the proposed method can reduce theproblem of neighbor selection in the original neighbor embedding (NE) algorithm to a certaindegree.
(2) To target the problem that the neighborhood relationship between LR image patchesand the corresponding HR image patches in NE-based methods cannot be perfectly preserved,an example-based SR method is presented by using joint learning via couple constraint. First,the grouping patch pairs (GPP) is established with the combination of the LR and thecorresponding HR image patches, and then a joint learning is applied to train two projectionmatrices simultaneously and to map the original LR and HR feature spaces onto a unifiedfeature subspace; then the k-nearest neighbor (k-NN) selection of the input LR image patchesis performed in the unified feature subspace to estimate the reconstruction weights forsynthesizing the initial HR images. Finally, the global reconstruction constraint andconsistency prior are applied to further enhance the quality of the initial SR estimate.
(3) To improve the reconstruction efficiency of the existing NE algorithms and toovercome the limitation of neighbor selection method, an example-based SR method that is based on clustering on histograms of oriented gradients (HOG) of LR image patches andsparse neighbor embedding (SpNE) algorithm is proposed. To achieve a high efficiency ofreconstruction, the HOG feature is introduced to represent the local geometrical structure ofLR image patches and to divide the training database in large scale into a set of subsets withsimilar structure; to overcome the limitation of neighbor selection scheme used in theprevious NE-based methods, a sparse neighbor selection (SpNS) scheme is developed byintegrating the robust SL0algorithm and the k/K-nearest neighbor criterion. With theproposed scheme, the neighbor selection and calculation of reconstruction weights cansimultaneously be achieved, leading to better SR recovery.
(4) Considering the complementarity of example-and reconstruction-based SR methods,a novel SR method that combines multi-scale dictionary learning and adaptive regularizationis proposed. To achieve an example-based SR method, a multi-scale dictionary is jointlylearnt from image patches at different scales from the LR input. To obtain areconstruction-based SR method, the steering kernel regression (SKR) is applied to formulatea local regularization to capture the local structure information and the non-local means(NLM) filter is adopted to construct non-local regularization term to capture the similarityredundancy at the same scale. The reconstruction term, the local and non-local priorregularization terms, and sparse hallucination regularization term are integrated into a unifiedSR framework for optimization. Without the help of any external training image, the proposedmethod can obtain a better SR recovery, leading to sharper edges as well as richer highfrequency details.
(5) Essentially, the reconstruction quality of example-based methods heavily depends onthe supporting training images. In view of this, an image SR method is proposed by exploitingthe redundancies of self-similarity at different scales. First, the proposed method directlyexploits the redundancies of self-similarity at different scales in the input LR image itself toconstruct training image patch pairs and the NE-based algorithm is adopted to graduallymagnify the LR input to the desired size. Finally, the NLM filter is introduced to obtain theredundancy of similarity at the same scale and a non-local regularization term is formulated tofurther improve the quality of SR recovery.
In summary, on the basis of the fundamental theory of signal processing and patternrecognition, this thesis takes statistical learning as the main investigative means and proposesfive novel SR methods. The proposed methods can effectively overcome the limitations of theexisting methods and achieve better SR recovery on producing sharper edges and richerdetails, providing a new approach to SR reconstruction.
引文
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