A unified framework for damaged image fusion and completion based on low-rank and sparse decomposition

Image fusion can integrate the complementary information of multiple images. However, when the images to be fused are damaged, the existing fusion methods cannot recover the lost information. Matrix completion, on the other hand, can be used to recover the missing information of the image. Therefore, the step-by-step operation of image fusion and completion can fuse the damaged images, but it will cause artifact propagation. In view of this, we develop a unified framework for image fusion and completion. Within this framework, we first assume that the image is superimposed by low-rank and sparse components. To obtain the separation of different components to fuse and restore them separately, we propose a low-rank and sparse dictionary learning model. Specifically, we impose low-rank and sparse constraints on low-rank dictionary and sparse component respectively to improve the discrimination of learned dictionaries and introduce the condition constraints of low-rank and sparse components to promote the separation of different components. Furthermore, we integrate the low-rank characteristic of the image into the decomposition model. Based on this design, the lost information can be recovered with the decomposition of the image without using any additional algorithm. Finally, the maximum $l_1$-norm fusion scheme is adopted to merge the coding coefficients of different components. The proposed method can achieve image fusion and completion simultaneously in the unified framework. Experimental results show that this method can well preserve the brightness and details of images, and is superior to the compared methods according to the performance evaluation.     

Image fusion using higher order singular value decomposition

A novel higher order singular value decomposition (HOSVD)-based image fusion algorithm is proposed. The key points are given as follows: 1) Since image fusion depends on local information of source images, the proposed algorithm picks out informative image patches of source images to constitute the fused image by processing the divided subtensors rather than the whole tensor; 2) the sum of absolute values of the coefficients (SAVC) from HOSVD of subtensors is employed for activity-level measurement to evaluate the quality of the related image patch; and 3) a novel sigmoid-function-like coefficient-combining scheme is applied to construct the fused result. Experimental results show that the proposed algorithm is an alternative image fusion approach.     

Nonlocal low-rank matrix completion for image interpolation using edge detection and neural network

In this paper, we propose a nonlocal low-rank matrix completion method using edge detection and neural network to effectively exploit the nonlocal inter-pixel correlation for image interpolation and other possible applications. We first interpolate the images using some basic techniques, such as bilinear and edge-directed methods. Then, each image patch is categorized as smooth regions, edge regions, or texture regions and adaptive interpolating mechanisms are applied to each specific type of regions. Finally, for each specific type of regions, neural networks and low-rank matrix completion are employed to accurately update the results. An iteratively re-weighted minimization algorithm is used to solve the low-rank energy minimization function. Our experiments on benchmark images clearly indicate that the proposed method produces much better results than some existing algorithms using a variety of image quality metric in terms of both objective image quality assessment and subjective quality assessment.     

Low-rank tensor completion with spatial-spectral consistency for hyperspectral image restoration

Hyperspectral image (HSI) restoration has been widely used to improve the quality of HSI. HSIs are often impacted by various degradations, such as noise and deadlines, which have a bad visual effect and influence the subsequent applications. For HSIs with missing data, most tensor regularized methods cannot complete missing data and restore it. We propose a spatial-spectral consistency regularized low-rank tensor completion (SSC-LRTC) model for removing noise and recovering HSI data, in which an SSC regularization is proposed considering the images of different bands are different from each other. Then, the proposed method is solved by a convergent multi-block alternating direction method of multipliers (ADMM) algorithm, and convergence of the solution is proved. The superiority of the proposed model on HSI restoration is demonstrated by experiments on removing various noises and deadlines.     

低秩遮挡图像去噪方法

为获得清晰的低秩图像,提出一种将低秩矩阵填充 (LRMC)与低秩矩阵恢 复(LRMR)联合的新模型,基于非精确增广拉格朗日乘子(IALM)法进行求解,运用LRMC去除遮 挡并填充缺失部 分,再利用LRMR去除噪声,得到完整的图像。以恢复时间、信噪比(SNR)、峰 值信噪比(PSNR)、差错率(err)等做评价标准,对3幅受噪声污染的图像的恢复结果表明, 本文提出的联合LRMC与LRMR的新模型,既能去除遮挡又能够填充图像的缺失部 分,能够达到理想的恢复效果。     

自适应算法在地磁张量阻抗重构中的模拟研究

在地磁数据处理中,张量阻抗的估算通常是在频域里使用非参数谱分析方法进行的。本文使用有理函数模型表示张量阻抗,利用自适应参数时域逼近方法进行重构。这种方法可以直接使用观察到的ＭＴ数据,而无需进行频域转换,因而容许在线实时应用。模拟结果表明,利用此法重构的冲激响应函数与实际的相比较,符合性很好。     

基于增量张量子空间学习的自适应目标跟踪

 传统的基于子空间的跟踪方法易于丢失图像所固有的部分结构和邻域信息,从而降低了目标匹配和跟踪的精度.为此,本文提出了一种增量张量子空间学习算法,用于跟踪目标的建模与模型更新.同时,将该模型与贝叶斯推理相结合,提出一种自适应目标跟踪算法:新方法首先对跟踪目标的外观进行建模,然后利用贝叶斯推理获得目标外观状态参数的最优估计,最后利用最优估计的目标观测更新目标张量子空间.实验结果表明,由于保持了目标外观的结构信息,本文提出的自适应目标跟踪方法具有较强的鲁棒性,在跟踪目标在姿态变化、短时遮挡和光照变化等情况下均可有效地跟踪目标.     

Fundamental tensor operations for large-scale data analysis using tensor network formats

We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation techniques including Candecomp/Parafac, Tucker, and tensor train (TT) decompositions with a number of mathematical and graphical representations. We also provide a brief review of mathematical properties of the TT decomposition as a low-rank approximation technique. With the aim of breaking the curse-of-dimensionality in large-scale numerical analysis, we describe basic operations on large-scale vectors, matrices, and high-order tensors represented by TT decomposition. The proposed representations can be used for describing numerical methods based on TT decomposition for solving large-scale optimization problems such as systems of linear equations and symmetric eigenvalue problems.     

An efficient tensor completion method via truncated nuclear norm

Tensor completion aims to recover missing entries from partial observations for multi-dimensional data. Traditional tensor completion algorithms process the dimensional data by unfolding the tensor into matrices, which breaks the inherent correlation and dependencies in multiple channels and lead to critical information loss. In this paper, we propose a novel tensor completion model for visual multi-dimensional data completion under the tensor singular value decomposition (t-SVD) framework. In the proposed method, tensor is treated as a whole and a truncated nuclear norm regularization is employed to exploit the structural properties in a tensor and hidden information existing among the adjacent channels of a tensor. Besides, we introduce a weighted tensor to adjust the residual error of each frontal slices in consideration of their different recovery statistics. It does enhance the sparsity of all unfoldings of the tensor and accelerates the convergence of the proposed method. Experimental results on various visual datasets demonstrate the promising performance of the proposed method in comparison with the state-of-the-art tensor completion methods.     

应用残差总变分和低秩表示的视频去噪算法

为了有效地去除视频当中的高斯噪声和脉冲噪声,提出了一种新的视频去噪算法。该算法通过相似图像块组内的残差值总变分及低秩表示来同时探索图像块内的局部相似性以及图像块之间的相似性。首先,采用块匹配的方式在含噪视频中寻找最相似图像块并组合成图像块组;其次将每个相似图像组表达为一个低秩矩阵及一个稀疏矩阵之和,并同时强调低秩矩阵内的残差总变分范数最小化;最后,通过求解最优化问题获得最终的低秩矩阵,即恢复出的图像块组数据。实验结果表明,本文的算法能够有效去除视频当中含有的高斯噪声和脉冲噪声。与同类算法相比,能够获得显著的峰值信噪比提升。      

张量低秩约束下的多帧图像去模糊

矩阵低秩估计模型在图像处理任务中有着广泛地运用.针对图像去模糊,利用矩阵低秩先验能保留图像的重要边缘信息从而实现去模糊.而对于多帧图像去模糊,基于矩阵的低秩模型并未充分考虑多帧图像间的时序和空间关系.针对该问题,我们提出基于三维张量低秩先验的多帧视频图像盲去模糊模型.在模型中,首先将多帧连续图像按时序维堆叠成张量,显式...     

基于各向异性扩散偏微分方程的图像去模糊

利用图像结构张量导出的各向异性扩散滤波,具有平滑噪声的同时保持细节的特点,提出基于结构张量的能量最小化去卷积正则化模型,并对由此导出的偏微分方程应用于灰度图像和向量值图像去模糊作了分析。灰度图像的各向异性扩散滤波可以由梯度平滑的结构张量实现,相应的偏微分方程取决于平滑结构张量决定的惩罚函数。与其它非线性扩散滤波去模糊的方法比较结果证实所提方法在信噪比和视觉质量上都具有更好的效果。     

基于新的形态学梯度参数的DTI图像分割算法

为了解决传统DTI图像分割中更细致边缘信息的丢失问题,提出了新的张量形态学梯度参数,并基于张量相似性形态学梯度和各向异性形态学梯度,采用标记的分水岭算法对DTI图像进行分割.通过对人脑胼胝体图像的分割实验表明,利用新参数TMG-l2和TMG-RA能够更加快速、准确地对DTI图像进行细致边缘轮廓的定位和分割,保护了重要分割区域的边缘信息.     

基于张量Tucker分解的频谱地图构建算法

该文研究使用少量监测样本数据构建动态电磁环境频谱地图。首先,将动态电磁环境的时变频谱地图建模为3维频谱张量,通过张量Tucker分解提取出具有物理意义的核张量和因子矩阵等低维特征。其次,根据频谱张量时域、空域、频域之间的相关性以及监测样本数据的稀疏性,设计一种基于Tucker分解的低秩张量补全模型,将频谱地图构建任务转化为数据缺失的低秩张量补全问题,并提出两种无需先验信息的频谱地图构建算法：高精度频谱地图构建算法和快速频谱地图构建算法。前者采用交替最小二乘法对核张量和因子矩阵交替求解,通过“补全-分解”的迭代过程实现对频谱地图的高精度构建。后者采用序列截断高阶奇异值分解法,对潜在多个低秩近似张量加权平均,该算法具有收敛快速和计算复杂度低的优势,在牺牲少量构建精度的情况下能够快速构建频谱地图。仿真实验结果表明,该文提出的两种算法能够精确构建频谱地图,在构建精度、运行时间消耗和噪声鲁棒性上均优于对比算法。     

基于张量四元数极化平滑的极化-DOA估计

为了解决相干信号的极化平滑算法在小快拍数和低信噪比条件下估计性能较差的问题,结合四元数的正交特性和协方差张量方法,提出了一种基于张量四元数的极化平滑多重信号分类（Multiple Signal Classification,MUSIC）解相干算法。首先,为了充分利用接收数据样本中的多维结构信息,建立了由张量四元数表示的柱面共形阵列极化平滑信号模型;其次,将平滑后的张量协方差矩阵通过高阶奇异值分解得到信号子空间;最后,通过极化秩亏MUSIC算法对入射相干信号分别进行二维波达方向（Direction of Arrival,DOA）估计和极化参数估计。仿真结果表明,该算法在小快拍数和低信噪比条件下具有更高的估计精度和分辨能力。     

Weighted truncated nuclear norm regularization for low-rank quaternion matrix completion

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image processing. Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color channel separately, QMC models retain the connection of three channels and process them as a whole. Most of the existing quaternion-based methods formulate low-rank QMC (LRQMC) as a quaternion nuclear norm (a convex relaxation of the rank) minimization problem. The main limitation of these approaches is that they minimize the singular values simultaneously such that cannot approximate low-rank attributes efficiently. To achieve a more accurate low-rank approximation, we introduce a quaternion truncated nuclear norm (QTNN) for LRQMC and utilize the alternating direction method of multipliers (ADMM) to get the optimization in this paper. Further, we propose weights to the residual error quaternion matrix during the update process for accelerating the convergence of the QTNN method with admissible performance. The weighted method utilizes a concise gradient descent strategy which has a theoretical guarantee in optimization. The effectiveness of our method is illustrated by experiments on real visual data sets.     

基于低秩分解的联合动态稀疏表示多观测样本分类算法

通过互联网易获得同一对象的多个无约束的观测样本,针对如何解决无约束观测样本带来的识别困难及充分利用多观测样本数据信息提高其分类性能问题,提出基于低秩分解的联合动态稀疏表示多观测样本分类算法.该算法首先寻找到一组最佳的图像变换域,使得变换图像可以分解成一个低秩矩阵和一个相关的稀疏误差矩阵;然后对低秩矩阵和稀疏误差矩阵分别进行联合动态稀疏表示,以便充分利用类级的相关性和原子级的差异性,即使多观测样本的稀疏表示向量在类级别上分享相同的稀疏模型,而在原子级上采用不同的稀疏模型;最后利用总的稀疏重建误差进行类别判决.在CMU-PIE人脸数据库、ETH-80物体识别数据库、USPS手写体数字数据库和UMIST人脸数据库上进行对比实验,实验结果表明本方法的优越性.     

基于差分阵列的双基地EMVS-MIMO雷达高分辨多维参数估计

为提升双基地EMVS-MIMO雷达的多维参数估计性能,该文提出利用发射/接收EMVS的差分阵列结构来实现多维参数的高分辨估计。对于阵列接收数据,可以利用高阶张量来实现对发射/接收EMVS的差分阵列的构建。首先,利用高阶张量的交换和缩并规则来构建一个包含原始发射/接收EMVS差分阵列结构的5阶张量模型;通过利用两个选择矩阵,可以剔除该张量模型中差分阵列的重复元素,且获得的差分阵列的自由度为原始阵列自由度的两倍。然后,对新构建的5阶张量模型再次进行张量的缩并处理可以获得一个第3个维度为36的3阶张量模型。最后,通过利用平行因子分解算法可以实现对发射4维参数和接收4维参数进行有效的求解。仿真实验表明,该文对差分阵列的构建有效地实现了双基地EMVS-MIMO雷达中多维参数估计性能的提升。     

基于特征点轨迹增长的视频稳像算法

现今的特征点轨迹稳像算法都是基于网格变形达到稳定视频的最终目的,而保证结果不扭曲失真且稳定的网格变形需要由一定数量的长特征轨迹通过相应最优算法来实现.目前所提出的算法无法在保证良好时间性能下达到这一要求,针对这个问题,提出一种基于特征点轨迹增长的视频稳像算法.首先提取特征轨迹,为避免算法优先选择较长轨迹而导致轨迹分布过于集中造成局部抖动的问题出现,将特征点位置分布与轨迹长度相结合作为选择策略使特征点轨迹分布更加均匀;接着利用低秩矩阵迭代逼近原理生成虚拟轨迹来实现轨迹增长;最后利用网格变形生成稳定帧.将本文的算法与另外两种典型的特征点轨迹稳像算法相比较,其中包括基于对极几何点转移的稳像算法以及基于三焦点张量重投影的特征点轨迹稳像算法.实验结果表明,本文算法的特征点分布均匀且轨迹利用率高,与基于对极几何点转移的稳像算法相比,稳像效果更稳定并且时间复杂度更低,与基于三焦点张量重投影的特征点轨迹稳像算法相比,在保证稳像效果的同时时间复杂度更低.     

Joint recommendation algorithm based on tensor completion and user preference

Aiming at the problem that existing recommendation algorithms have little regard for user preference,and the recommendation result is not satisfactory,a joint recommendation algorithm based on tensor completion and user preference was proposed.First,a user-item-category 3-dimensional tensor was built based on user-item scoring matrix and item-category matrix.Then,the Frank-Wolfe algorithm was used for iterative calculation to fill in the missing data of the tensor.At the same time,a user category preference matrix and a scoring preference matrix were built based on the 3-dimensional tensor.Finally,a joint recommendation algorithm was designed based on the completed tensor and the two preference matrices,and the differential evolution algorithm was used for parameter tuning.The experimental results show that compared with some typical and newly proposed recommendation algorithms,the proposed algorithm is superior to the compare algorithms,the precision is improved by 1.96% ~ 3.44% on average,and the recall rate is improved by 1.35%~2.40% on average.