基于空间域正则化方法的图像超分辨率技术研究
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摘要
在图像获取过程中，受成像条件和成像方式的限制，所得到的图像分辨率往往不能满足实际应用的要求。如何提高图像的空间分辨率，改善图像质量，一直以来都是图像处理技术所致力解决的问题。多帧图像超分辨率重建技术利用同一场景的多幅图像之间的互补信息，采用信号处理的方法进行融合得到一幅高分辨率的图像。这一技术能够在不改变硬件设备条件的前提下实现高于系统分辨率的观测，是一种提高图像分辨率的经济有效方法，在众多领域中具有非常广阔的应用前景，近年来受到科技和工程界的广泛重视，因此对该技术的研究具有十分重要的理论和现实意义。
本论文通过对图像超分辨率重建技术的系统分析，以空间域正则化方法的超分辨率重建算法为主线，利用图像的先验信息，充分考虑图像不同区域对人眼的视觉影响，研究发展了边缘保持、图像去噪的图像模型，并在此基础上相应地提出了一系列基于空间域正则化方法的多幅图像超分辨率重建算法。论文取得的主要创新成果包括：
（1）分析了高阶MRF（Markov Random Fields）模型—专家场模型，并把该模型作为正则化项引入到超分辨率图像重建中。针对该模型直接用于超分辨率重建中会模糊掉图像部分边缘的缺点，构建了一种基于空间信息加权的专家场先验模型并将其用于超分辨率重建。提出的方法利用曲率差算子对图像空间结构进行描述，并定义一个加权函数对专家场模型中通过训练集学习得到的滤波器进行加权，达到在图像的边缘区减弱滤波器的滤波能力、在图像的平坦区增强滤波器的滤波能力，最终实现在图像超分辨率重建中能够更好的抑制噪声和保持边缘的效果。仿真和真实的超分辨率重建实验结果表明，该方法能得到较好的图像视觉效果和较高的峰值信噪比。
（2）分析了传统冲击滤波器在图像增强中的性能，针对传统冲击滤波器对噪声敏感的问题，引入了梯度矢量流场，分别用梯度矢量流场及其与图像梯度的合力场来代替冲击滤波器中的图像梯度场，提出了两种改进的冲击滤波器模型。并对改进的模型进行了图像去噪性能分析，实验中发现，两种模型都能够很好的去除图像的噪声，但合力场模型相对于直接用梯度矢量流场模型具有更好的增强效果，最后将两种改进的模型作为正则化项引入到超分辨率图像重建中。定性和定量的对比分析实验均证明了改进的两种冲击滤波器模型用于超分辨率图像重建的可行性和有效性。
（3）分析了全变分（TV，Total Variation）和四阶偏微分方程（FPDE，FourthPartial Differential Equation）在图像去噪中的优缺点，提出了一种基于混合偏微分方程的图像超分辨率重建方法。该方法通过定义一个加权函数，耦合两种偏微分模型，在图像边缘区对TV模型采用较大权值，保持图像的边缘和纹理细节，在图像的平坦区对FPDE模型采用较大权值，以抑制全变分模型产生的“阶梯效应”，改善重建图像的视觉效果。实验中将混合偏微分方程模型作为正则化项进行真实图像和模拟图像的超分辨率重建，结果表明所提出的混合模型集合了TV和FPDE模型的优点，得到了较好的重建结果。
In the image acquisition process, due to the limitation of imaging conditions andimaging mode, the image resolution acquired usually can not meet the requirementsof practical applications. How to improve the spatial resolution of the image and theimage quality is always the problem to be solved of the image processing technology.The multi-frame image super-resolution reconstruction technique uses the signalprocessing methods to fuse the complementary information between multiple imagesof the same scene so as to obtain a high resolution image. This technology can realizethe observation that is better than the system resolution without changing hardwareconditions, so it is an economic and effective method for improving image resolution.As a result, this technology has a very broad application prospects in many fields andextensive attention by the science and engineering in recent years. Therefore, doingresearch on this topic has a very important theoretical and practical significance.
In this thesis, through the system analysis of image super-resolutionreconstruction technique, we carry out the research on the spatial domainregularization based super-resolution reconstruction algorithm as the main clue. Novelimage edge preserving and image denoising models are proposed, which is developedby employing the image prior information and fully considering the human visualeffects on different regions of the image. Then based on these models, series ofmulti-frame image super-resolution reconstruction algorithms that is based on spatialdomain regularization are presented. The main contributions of this thesis include:
(1) The high order MRF (Markov Random Fields) model i.e. expert model isintroduced into the super-resolution image reconstruction as the regularization term.Meanwhile, in order to overcome the shortcoming of the conventional expert modelthat will blur the image edge when it is directly applied in super-resolutionreconstruction; a weighted expert field based on spatial information is proposed andused for super-resolution reconstruction. The proposed method uses the curvature difference operator to describe the image spatial structure and defines a weightedfunction to describe the filter that is obtained through the training of the expert field.In this case, the filtering capacity is weakened at the image edge, while the filteringcapacity is enhanced in the flat image region. As a result, suppressing noise andpreserving edge can be realized in the proposed super-resolution reconstructionalgorithm. Simulation and real experimental results show that our method can gethigher peak signal to noise ratio and better visual effect compared to severalconventional super-resolution reconstruction methods.
(2) The performance of traditional shock filter in image enhancement is analyzed,and in view of the noise sensitivity problem of it, the gradient vector flow (GVF) isintroduced into super-resolution reconstruction algorithm. Two improved shock filtermodels are proposed, which are formed by separately using the GVF and GVF withimage gradient instead of the image gradient in traditional the shock filter. Thedenoising performance of the improved models is analyzed and its results indicate thatthe two models both have good capacity to remove the image noise, and the combinedmodel has a better effect compared to the direct use of GVF model. Finally, the twoimproved models are incorporated into the image super-resolution reconstructionalgorithm as the regularization term respectively. The Qualitatively and quantitativelycomparative experiments show that the two kinds of modified shock filter models areFeasible and effective for image super-resolution reconstruction.
(3) After analyzing the advantages and disadvantages of the total variation(TV) and the fourth order partial differential equation (FPDE) in the aspect of imagedenoising, this paper proposed a combined PDE based super-resolution reconstructionmethod by defining a weighted function that is used to couple the two PDE models. Inthe method, the weight value is set higher for TV model in the edge region in order tosustain the image edge and texture details well, while the weight value is set higherfor FPDE model in the flat area of the image so that the “step effect” produced by TVmodel can be suppressed and the image visual effects can be improved. The combinedPDE model as a regularization term has been used for super-resolution reconstructionof both real and simulated images. The results show that the proposed method can get better reconstruction results due to the combined model involves the advantages ofboth TV and FPDE models.
本论文通过对图像超分辨率重建技术的系统分析，以空间域正则化方法的超分辨率重建算法为主线，利用图像的先验信息，充分考虑图像不同区域对人眼的视觉影响，研究发展了边缘保持、图像去噪的图像模型，并在此基础上相应地提出了一系列基于空间域正则化方法的多幅图像超分辨率重建算法。论文取得的主要创新成果包括：
（1）分析了高阶MRF（Markov Random Fields）模型—专家场模型，并把该模型作为正则化项引入到超分辨率图像重建中。针对该模型直接用于超分辨率重建中会模糊掉图像部分边缘的缺点，构建了一种基于空间信息加权的专家场先验模型并将其用于超分辨率重建。提出的方法利用曲率差算子对图像空间结构进行描述，并定义一个加权函数对专家场模型中通过训练集学习得到的滤波器进行加权，达到在图像的边缘区减弱滤波器的滤波能力、在图像的平坦区增强滤波器的滤波能力，最终实现在图像超分辨率重建中能够更好的抑制噪声和保持边缘的效果。仿真和真实的超分辨率重建实验结果表明，该方法能得到较好的图像视觉效果和较高的峰值信噪比。
（2）分析了传统冲击滤波器在图像增强中的性能，针对传统冲击滤波器对噪声敏感的问题，引入了梯度矢量流场，分别用梯度矢量流场及其与图像梯度的合力场来代替冲击滤波器中的图像梯度场，提出了两种改进的冲击滤波器模型。并对改进的模型进行了图像去噪性能分析，实验中发现，两种模型都能够很好的去除图像的噪声，但合力场模型相对于直接用梯度矢量流场模型具有更好的增强效果，最后将两种改进的模型作为正则化项引入到超分辨率图像重建中。定性和定量的对比分析实验均证明了改进的两种冲击滤波器模型用于超分辨率图像重建的可行性和有效性。
（3）分析了全变分（TV，Total Variation）和四阶偏微分方程（FPDE，FourthPartial Differential Equation）在图像去噪中的优缺点，提出了一种基于混合偏微分方程的图像超分辨率重建方法。该方法通过定义一个加权函数，耦合两种偏微分模型，在图像边缘区对TV模型采用较大权值，保持图像的边缘和纹理细节，在图像的平坦区对FPDE模型采用较大权值，以抑制全变分模型产生的“阶梯效应”，改善重建图像的视觉效果。实验中将混合偏微分方程模型作为正则化项进行真实图像和模拟图像的超分辨率重建，结果表明所提出的混合模型集合了TV和FPDE模型的优点，得到了较好的重建结果。
In the image acquisition process, due to the limitation of imaging conditions andimaging mode, the image resolution acquired usually can not meet the requirementsof practical applications. How to improve the spatial resolution of the image and theimage quality is always the problem to be solved of the image processing technology.The multi-frame image super-resolution reconstruction technique uses the signalprocessing methods to fuse the complementary information between multiple imagesof the same scene so as to obtain a high resolution image. This technology can realizethe observation that is better than the system resolution without changing hardwareconditions, so it is an economic and effective method for improving image resolution.As a result, this technology has a very broad application prospects in many fields andextensive attention by the science and engineering in recent years. Therefore, doingresearch on this topic has a very important theoretical and practical significance.
In this thesis, through the system analysis of image super-resolutionreconstruction technique, we carry out the research on the spatial domainregularization based super-resolution reconstruction algorithm as the main clue. Novelimage edge preserving and image denoising models are proposed, which is developedby employing the image prior information and fully considering the human visualeffects on different regions of the image. Then based on these models, series ofmulti-frame image super-resolution reconstruction algorithms that is based on spatialdomain regularization are presented. The main contributions of this thesis include:
(1) The high order MRF (Markov Random Fields) model i.e. expert model isintroduced into the super-resolution image reconstruction as the regularization term.Meanwhile, in order to overcome the shortcoming of the conventional expert modelthat will blur the image edge when it is directly applied in super-resolutionreconstruction; a weighted expert field based on spatial information is proposed andused for super-resolution reconstruction. The proposed method uses the curvature difference operator to describe the image spatial structure and defines a weightedfunction to describe the filter that is obtained through the training of the expert field.In this case, the filtering capacity is weakened at the image edge, while the filteringcapacity is enhanced in the flat image region. As a result, suppressing noise andpreserving edge can be realized in the proposed super-resolution reconstructionalgorithm. Simulation and real experimental results show that our method can gethigher peak signal to noise ratio and better visual effect compared to severalconventional super-resolution reconstruction methods.
(2) The performance of traditional shock filter in image enhancement is analyzed,and in view of the noise sensitivity problem of it, the gradient vector flow (GVF) isintroduced into super-resolution reconstruction algorithm. Two improved shock filtermodels are proposed, which are formed by separately using the GVF and GVF withimage gradient instead of the image gradient in traditional the shock filter. Thedenoising performance of the improved models is analyzed and its results indicate thatthe two models both have good capacity to remove the image noise, and the combinedmodel has a better effect compared to the direct use of GVF model. Finally, the twoimproved models are incorporated into the image super-resolution reconstructionalgorithm as the regularization term respectively. The Qualitatively and quantitativelycomparative experiments show that the two kinds of modified shock filter models areFeasible and effective for image super-resolution reconstruction.
(3) After analyzing the advantages and disadvantages of the total variation(TV) and the fourth order partial differential equation (FPDE) in the aspect of imagedenoising, this paper proposed a combined PDE based super-resolution reconstructionmethod by defining a weighted function that is used to couple the two PDE models. Inthe method, the weight value is set higher for TV model in the edge region in order tosustain the image edge and texture details well, while the weight value is set higherfor FPDE model in the flat area of the image so that the “step effect” produced by TVmodel can be suppressed and the image visual effects can be improved. The combinedPDE model as a regularization term has been used for super-resolution reconstructionof both real and simulated images. The results show that the proposed method can get better reconstruction results due to the combined model involves the advantages ofboth TV and FPDE models.
引文
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