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高维图像特征的低秩表达算法研究
Alternative TitleThe Low-rank Representation of High-dimension Image/Feature
罗琼
Department机器人学研究室
Thesis Advisor唐延东 ; 韩志
Keyword低秩分解 特征空间 张量表达 噪声建模
Pages103页
Degree Discipline模式识别与智能系统
Degree Name博士
2021-05-19
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract本论文以具有潜在低秩性的隐式低秩数据为研究对象,从误差建模,特征空间学习,以及数据的表达形式三个方面,开展了基于低秩理论的数据及特征恢复算法研究。论文的主要研究内容如下:(1)针对单张图像在空间维度和通道维度都不具备显式低秩性,以及基于L1范数的低秩分解由于其非凸性非光滑性难以优化的问题,我们提出基于循环加权中值和非局部低秩聚类的CWM-NLR方法。首先,我们引入聚类特征空间,在具有显式低秩性的类内图像块集合中寻找低维子空间。其次引入了循环加权中值法(CWM)通过求解一系列标量的最小化凸子问题去寻找最优解。所提方法不仅有效解决了单张图像整体显式低秩性弱的问题,而且具备良好的收敛性和较低的计算复杂度。(2)现有把隐式低秩数据转换成显式低秩数据的特征空间大都是人为设计,需要强依赖于人的经验和特定场景。针对这一问题,本文提出了一个基于数据驱动的通用特征空间。相比于原始观测空间,它具有更强低秩性,因而现有低秩模型在这个特征空间中的处理效果优于在观测空间中的处理效果。同时,我们发现转换到该特征空间的数据带来了额外的稀疏性,本文为此提出了特征稀疏正则项Sfea和基于Sfea正则的非局部低秩去噪模型(Sfea-NLR)。试验表明,Sfea-NLR去噪方法优于同类型的低秩恢复模型。(3)针对高光谱图像的恢复问题,本文提出了一种基于LP范数和增强三维全变分正则(E-3DTV)的去噪模型。首先,3DTV正则假设高光谱的梯度特征空间具有独立且相同的稀疏结构。然而,梯度图通常在所有波段上具有不同且相关的稀疏结构。E-3DTV通过把稀疏约束施加在高光谱图像的低维子空间,实现了在编码稀疏结构相关性的同时保留稀疏结构的差异性。其次,目前高光谱图像恢复模型中普遍采用L1范数对噪声建模,这使得模型仅仅针对拉普拉斯噪声有效。为提高模型对噪声的适应能力,本文提出了基于LP范数的E-3DTV去噪模型,该模型和其他低秩方法在公开的高光谱数据集中展开了对比试验,验证了该模型在不同噪声条件下的鲁棒性。(4)传统鲁棒主成分分析(RPCA)模型采用矩阵表达高维张量数据造成结构信息丢失,采用L1范数建模噪声难以应对现实场景中未知而复杂的噪声。针对以上问题,本文提出了基于CP分解和混合高斯(MoG)的张量RPCA模型TenRPCA-MoG。在这一模型中,使用张量结构表达原始张量数据使其能够充分利用数据固有的先验结构,而MoG能够拟合任意连续分布,使得本文方法能够从更广泛范围的噪声分布重新获得低维线性子空间。本文在变分贝叶斯推断框架下提出了一种新的算法可对所提模型有效求解。本文提出的方法在合成数据和真实数据上与现有方法展开了试验对比,试验结果验证了本文方法相对于现有一些主流方法的优越性。
Other AbstractThe main research issue of this dissertation is to find the low-rankness of implicit low-rank data. It contains noise modeling, feature space learning, and data expression for High-dimension Image/Feature Recovery via low-rank methods. The main research contents of this dissertation are as follows: (1) To handle the problem of that a single image does not have explicit low-rankness in both spatial dimension and channel dimension, and the L1 norm based low-rank decomposition is difficult to be optimized due to its non-convexity and non-smoothness. We proposed the cyclic weighted median and nonlocal low-rank clustering based CWM-NLR method. First, we introduce clustering feature space to find low-dimensional subspace in the in-class image patch group with explicit low-rankness. Second, the cyclic weighted median (CWM) method is introduced to find the optimal solution by solving a series of scalar minimized convex subproblems. The proposed method not only solves the problem of weak explicit low-rankness of the single image, but also has good convergence and low computational complexity. (2) Most of the existing feature spaces for converting implicit low-rank data to explicit low-rank data are artificially designed and rely heavily on human experience and specific fields. To solve this problem, a general data-driven feature space is proposed in this dissertation. It has a stronger low-rankness than the original observation space, so the performance of the existing low-rank models can be improved in the feature space. In addition, feature maps also show sparsity, hence we propose the feature sparse measure Sfea, and the Sfea based nonlocal low-rank denoising model (Sfea-NLR). Extensive experiments validate the superiority of our work. (3) This dissertation propose a denoising model based on LP norm and enhanced three-dimensional total variational regularization (E-3DTV) for the restoration of hyperspectral images. First, 3DTV regularization assumes that the gradient feature space of hyperspectral has sparse structure with independent identical distribution. However, gradient maps usually have different and correlated sparse structures in all bands. E-3DTV effectively encodes the correlation and difference of sparse structures by imposing sparse constraints on the low-dimensional subspace of gradient maps. Second, L1 norm is usually used in hyperspectral image restoration task, which makes the model only effective against Laplace noise. In order to improve the adaptability to real scenarios, we proposed a Lp norm based E-3DTV denoising model. Extensive experiments validate the robustness of our method under different noise conditions. (4) The traditional robust principal component analysis (RPCA) model uses matrix to express high-dimensional tensor data, which destroys the inherent structural information. In addition, it is difficult to deal with the unknown and complex real noise via L1 norm. Therefore, this dissertation proposed a tensor RPCA model called TenRPCA-MoG based on Mix of Gaussian (MoG) and CP decomposition. Using tensor structure to express raw tensor data allows us to make full use of the inherent structure priors of data. MoG is a general approximator to any blends of consecutive distributions, which makes our method capable of regaining the low dimensional linear subspace from a wide range of noises or their mixture. The model is solved by a new proposed algorithm under a variational Bayesian inferred framework. The superiority of our approach over the existing state-of-the-art approaches is validated by extensive experiments on both of synthetic and real data.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/29001
Collection机器人学研究室
Affiliation中国科学院沈阳自动化研究所
Recommended Citation
GB/T 7714
罗琼. 高维图像特征的低秩表达算法研究[D]. 沈阳. 中国科学院沈阳自动化研究所,2021.
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