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图像视频低秩张量表达及恢复算法研究
Alternative TitleImage/Video Representation and Reconstruction via Low-rank Tensor
陈希爱1,2
Department机器人学研究室
Thesis Advisor唐延东 ; 韩志
Keyword低秩稀疏分解 低秩张量分解 三维全变分 多高斯拟合 马尔科夫随机场
Pages119页
Degree Discipline模式识别与智能系统
Degree Name博士
2018-09-19
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract本论文针对具有共享性或者重复性特质的图像视频数据,利用数据中所具有的共享性或重复性特质,开展了相关低秩理论研究。从数据的表达形式、误差建模方法以及恢复算法方面入手,提出了具有创新性的模型算法。论文的主要内容和创新点如下:(1)针对具有相关性的图像序列存在的非对准以及可能同时存在的局部遮挡、噪声污染等问题,在低秩矩阵框架下提出了一种带有二次惩罚函数的低秩稀疏分解方法,用于实现具有相关性的图像序列鲁棒对准。该方法通过低秩矩阵手段来挖掘相关性图像序列中蕴含的共享性或重复性结构信息,对图像中可能存在的局部遮挡以及噪声污染问题,利用稀疏和非稀疏形式的分布对其进行误差建模,从而解决单一分布形式误差建模带来的鲁棒性不足问题。利用非凸优化方式对问题模型进行求解,从而避免了凸优化方式下带来的有偏估计问题。采用局部线性化和增广拉格朗日的思想,设计了有效的求解算法。对比实验验证了所提方法在图像序列鲁棒对准问题上的有效性。(2)针对高光谱图像的空间域低分辨率问题,提出了一种耦合三维全变分的非局部块低秩张量超分辨恢复方法。该方法在数据张量表达以保持图像结构信息基础上,利用非局部块低秩张量来挖掘高光谱图像在谱段域和空间域上的全局相关性以及非局部自相似性,利用三维全变分来描述高光谱图像中蕴含的局部三维结构上的平滑性,同时抑制噪声。采用张量的加权各模矩阵的秩来进行张量秩的凸优化,进而利用局部线性逼近以及交替方向算子的思想设计了有效求解算法。数值实验中的定量和定性结果表明,该方法在高光谱图像空间域超分辨率恢复性能上具有一定的优越性。(3)针对受复杂噪声影响的具有共享性或者重复性结构的图像数据,提出了一种耦合多高斯误差建模的低秩张量图像恢复模型。该模型充分利用两种经典张量分解在不同应用中的性能优势,实现对张量数据的恢复。并利用多高斯所具有的对任意连续分布的拟合特性,提高模型对数据中复杂噪声的鲁棒性。与传统模型的对比实验表明,本文所提模型在单幅彩色图像恢复、多光谱图像恢复以及人脸建模等多种不同实际应用中均取得了较好的恢复效果,显示出该模型更具有一般性和适用性。同时,针对无噪声分布先验的实际高光谱图像恢复问题,该模型能够有效剔除实际未知噪声分布对图像恢复效果的影响,显示了模型所具有的鲁棒性能。(4)针对具有低秩特性的视频背景数据,提出了一种融合马尔科夫随机场和多高斯的低秩张量逼近模型,用于实现不同场景下监控视频背景的有效分离。该模型利用张量对视频数据进行表达以保持视频帧中信息的完整性,并利用低秩理论来挖掘视频背景中蕴含的共享性信息,通过多高斯误差建模来提高模型对不同场景下监控视频中可能存在的干扰因素的鲁棒性,同时采用马尔科夫随机场描述了视频数据在局部时空域上呈现的连续性。在变分期望最大化框架下推导给出了有效求解算法。数值实验结果表明,该模型能够有效地实现不同场景下监控视频的背景分离重建,同时能够去除噪声对视频背景分离的影响,显示了模型的有效性和鲁棒性。
Other AbstractIn this dissertation, by exploiting the shared or repetitive characteristics in image and video data, the main research works focus on the following three low-rank theory related issues: data representation, error modeling and the recovery algorithms. Some novel models and algorithms are proposed based on the low-rank theory. The main contributions of this dissertation are summarized as follows: (1) For dealing with the problem of recovering the data low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises, a nonconvex plus quadratic penalized low-rank and sparse decomposition model is proposed. Nonconvex penalization is applied to remedy the drawbacks of existing convex penalization model and a quadratic penalty is further used to better tackle the nonsparse noises in the data. The local linear approximation (LLA) and the augmented Lagrange multiplier (ALM) are utilized to solve this model. Numerical experiments validated the efficiency of the proposed model in aligning the image sequences with robustness to sparse and nonsparse noise. (2) To handle the problem of Hyperspectral image (HSI) spatial super-resolution, a novel low-rank tensor model with 3D total variation penalization is proposed. By using the data tensor form, the image structure are protected. The low-rank tensor is used to exploit the global correlation and the nonlocal self-similarity across the spectral and spatial domains. In addition, the local smoothness in spatial-spectral domain of the HSI data is characterized by a 3D total variation (3DTV) term. Effective algorithm are developed for solving the resulting optimization by the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments were carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches in improving the spatial resolution of HSI. (3) To solve the problem of noisy image representation and recovery via low-rank tensor, a novel low-rank tensor approximation model with Mixture of Gaussians (MoG) is proposed. It possesses two characteristics: approximating the tensor data by a general low-rank tensor factorization model; employing MoG to the low-rank tensor factorization model for its ability of universal approximation to any continuous distribution, which can improve the robustness of the model. Two typical tensor factorization operations, i.e., CP factorization and Tucker factorization, are incorporated into the proposed model. Compared with traditional processing models, this model improves the model applicability, which can achieve better recovery results in various applications, such as single color image restoration, multispectral image restorationand face modeling. At the same time, for the real noisy hyperspectral image with no noise distribution prior, this model can effectively remove the unknown noise and obtain a relative good reconstruction performance, which demonstrates the robustness of the proposed model. (4) To solve the problem of effective video representation and recovery via low-rank tensor, a low-rank tensor approximation model with MoG and Markov random field (MRF) is proposed. It employs MoG to model a wider range of noise and MRF to model the continuity prior information in the local space in the video data. This model is solved under the variational EM framework. Numerical experiments demonstrates the effectiveness of the proposed model in subtracting the video background and removing the noise in the video data, which validate the effectiveness and robustness of the proposed model.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/23649
Collection机器人学研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院大学
Recommended Citation
GB/T 7714
陈希爱. 图像视频低秩张量表达及恢复算法研究[D]. 沈阳. 中国科学院沈阳自动化研究所,2018.
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