图像及视频序列的超分辨率重建
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摘要
图像及视频序列的超分辨率重建,是近年来图像处理领域的一个研究热点,不仅在理论上具有重要意义,在实用中也有迫切需求。本论文的主要工作围绕图像及视频序列的超分辨率重建展开,具体内容包括:
(1)不完全数据重建的病态性及其正则化处理。首先给出了不完全数据超分辨率重建的数学描述,分析了最小二乘估计及其病态性;其次针对不完全数据重建的病态性,分别采用两种不同观点对正则化处理进行了深刻阐述:一是从分析的观点出发,通过对原问题能量泛函的修改,添加正则项,提出了基于变分原理和偏微分方程演化的不完全数据超分辨率重建框架;二是从概率统计的观点出发,利用贝叶斯框架和马尔可夫随机场理论,通过添加先验概率对原问题进行正则化;然后深入讨论了两种正则化观点的相似性和等价性,并详细研究了边缘自适应处理和各向异性演化问题;最后针对正则化参数的选取,提出了一种自适应动态确定正则化参数的方法。
(2)单帧图像的超分辨率重建。主要分为三部分:第一部分讨论基于Hopfield神经网络框架的超分辨率重建算法,针对Paik-Hopfield网络的缺点,提出了基于状态连续变化的Paik-Hopfield网络和基于多精度层离散状态的Paik-Hopfield网络两种改进方法;第二部分研究了变分原理和偏微分方程演化在图像超分辨率重建中的应用,主要包括基于变分和基于各向异性演化的超分辨率重建;第三部分详细分析了图像的小波统计特性,联合空间域和小波域提出了基于小波域隐马尔可夫模型的超分辨率重建算法。L~p(1≤p≤2)
(3)多帧图像或单视频序列的超分辨率重建。主要围绕运动估计和重建算法这两个超分辨率重建的关键问题进行展开:在运动估计部分,首先针对帧间模型为单映变换的视频序列提出了基于带指导的RANSAC特征匹配方法,其次针对普通视频序列提出了一种自适应的光流估计方法;在重建算法部分,首先讨论了基于批处理的静态重建,然后在深入研究帧间运动补偿矩阵和权值矩阵的基础上,发展出一种基于自适应滤波的视频序列超分辨率动态重建算法。
(4)多视频序列的超分辨率重建。主要包括两部分:第一部分为视频序列的时间空间配准,提出了一种基于时空梯度和遗传演化策略相结合的混合等级估计方法;第二部分为视频序列的超分辨率重建,首先提出了一种时空流形模型,可以包括单帧灰度图像、单帧彩色图像、灰度视频和彩色视频,然后将此模型应用到多视频序列的超分辨率重建正则化处理中,得到了一种新型多视频序列的超分辨率重建算法。I
For decades, super-resolution reconstruction is an active topic in image and video processing which is theoretically important as well as practically urgent in many fields. This dissertation focuses on the super-resolution of image and video sequence. And the study is carried out in the following aspects:
(1) The incompleted data reconstruction and its regularization. Because the incompleted data reconstruction is an inverse problem, its least square estimation is ill-posed. To overcome this difficulty, two regularization methods are adopted in the dissertation and their similarity and equality are illustrated vigorously. The one is variation and partial differential equation method, the regularization of ill-posed problem is processed by modifying the original energy functional. The other is the random probability method, using Bayesian and Markov random field theory, the original problem is regularized by adding prior probability item under the MAP frame. Finally, the anisotropic diffusion is introduced to preserve the detail of reconstructed signal, and an adaptive dynamic method is proposed for the choice of regularization parameters.
(2) The super-resolution of single image. This part mainly consists of three irrelevant contents. At first, according to shortcomings of the classic Paik-Hopfield neural network, two modified algorithm are suggested, of which the node state and updating rule are changed continuously and discrete hierarchically, respectively. Secondly, using the variation and partial differential equation method, two super-resolution reconstruction algorithms based on L~p(1≤p≤2) norm and anisotropic diffusion are presented to apply in image super-resolution reconstruction. Lastly, after carefully study on image wavelet domain statistical property, a super resolution reconstruction algorithm is put forward based on wavelet-domain hidden Markov model.
(3) The super-resolution of multi-image or single video sequence. Obviously, there are two key problems to be solved in the super-resolution of multi-image or single video sequence. On the
(1)不完全数据重建的病态性及其正则化处理。首先给出了不完全数据超分辨率重建的数学描述,分析了最小二乘估计及其病态性;其次针对不完全数据重建的病态性,分别采用两种不同观点对正则化处理进行了深刻阐述:一是从分析的观点出发,通过对原问题能量泛函的修改,添加正则项,提出了基于变分原理和偏微分方程演化的不完全数据超分辨率重建框架;二是从概率统计的观点出发,利用贝叶斯框架和马尔可夫随机场理论,通过添加先验概率对原问题进行正则化;然后深入讨论了两种正则化观点的相似性和等价性,并详细研究了边缘自适应处理和各向异性演化问题;最后针对正则化参数的选取,提出了一种自适应动态确定正则化参数的方法。
(2)单帧图像的超分辨率重建。主要分为三部分:第一部分讨论基于Hopfield神经网络框架的超分辨率重建算法,针对Paik-Hopfield网络的缺点,提出了基于状态连续变化的Paik-Hopfield网络和基于多精度层离散状态的Paik-Hopfield网络两种改进方法;第二部分研究了变分原理和偏微分方程演化在图像超分辨率重建中的应用,主要包括基于变分和基于各向异性演化的超分辨率重建;第三部分详细分析了图像的小波统计特性,联合空间域和小波域提出了基于小波域隐马尔可夫模型的超分辨率重建算法。L~p(1≤p≤2)
(3)多帧图像或单视频序列的超分辨率重建。主要围绕运动估计和重建算法这两个超分辨率重建的关键问题进行展开:在运动估计部分,首先针对帧间模型为单映变换的视频序列提出了基于带指导的RANSAC特征匹配方法,其次针对普通视频序列提出了一种自适应的光流估计方法;在重建算法部分,首先讨论了基于批处理的静态重建,然后在深入研究帧间运动补偿矩阵和权值矩阵的基础上,发展出一种基于自适应滤波的视频序列超分辨率动态重建算法。
(4)多视频序列的超分辨率重建。主要包括两部分:第一部分为视频序列的时间空间配准,提出了一种基于时空梯度和遗传演化策略相结合的混合等级估计方法;第二部分为视频序列的超分辨率重建,首先提出了一种时空流形模型,可以包括单帧灰度图像、单帧彩色图像、灰度视频和彩色视频,然后将此模型应用到多视频序列的超分辨率重建正则化处理中,得到了一种新型多视频序列的超分辨率重建算法。I
For decades, super-resolution reconstruction is an active topic in image and video processing which is theoretically important as well as practically urgent in many fields. This dissertation focuses on the super-resolution of image and video sequence. And the study is carried out in the following aspects:
(1) The incompleted data reconstruction and its regularization. Because the incompleted data reconstruction is an inverse problem, its least square estimation is ill-posed. To overcome this difficulty, two regularization methods are adopted in the dissertation and their similarity and equality are illustrated vigorously. The one is variation and partial differential equation method, the regularization of ill-posed problem is processed by modifying the original energy functional. The other is the random probability method, using Bayesian and Markov random field theory, the original problem is regularized by adding prior probability item under the MAP frame. Finally, the anisotropic diffusion is introduced to preserve the detail of reconstructed signal, and an adaptive dynamic method is proposed for the choice of regularization parameters.
(2) The super-resolution of single image. This part mainly consists of three irrelevant contents. At first, according to shortcomings of the classic Paik-Hopfield neural network, two modified algorithm are suggested, of which the node state and updating rule are changed continuously and discrete hierarchically, respectively. Secondly, using the variation and partial differential equation method, two super-resolution reconstruction algorithms based on L~p(1≤p≤2) norm and anisotropic diffusion are presented to apply in image super-resolution reconstruction. Lastly, after carefully study on image wavelet domain statistical property, a super resolution reconstruction algorithm is put forward based on wavelet-domain hidden Markov model.
(3) The super-resolution of multi-image or single video sequence. Obviously, there are two key problems to be solved in the super-resolution of multi-image or single video sequence. On the
引文
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