基于低秩矩阵二元分解的快速显著性目标检测算法

近年来,基于矩阵低秩表示模型的图像显著性目标检测受到了广泛关注。在传统模型中通常对秩最小化问题进行凸松弛,即引入最小化核范数将原始输入图像分解为低秩矩阵和稀疏矩阵。但是,这种方法在每次迭代中必须执行矩阵奇异值分解（SVD）,计算复杂度较高。为此,本文提出了一种低秩矩阵双因子分解和结构化稀疏矩阵分解联合优化模型,并应用于显著性目标检测。算法不仅利用低秩矩阵双因子分解和交替方向法（ADM）来降低时间开销,而且引入分层稀疏正则化刻画稀疏矩阵中元素之间的空间关系。此外,所提算法能够无缝集成高层先验知识指导矩阵分解过程。实验结果表明,提出模型和算法的检测性能优于当前主流无监督显著性目标检测算法,且具有较低的时间复杂度。     

基于lP范数的非凸低秩张量最小化

在低秩矩阵、张量最小化问题中,凸函数容易求得最优解,而非凸函数可以得到更低秩的局部解.文中基于非凸替换函数的低秩张量恢复问题,提出基于l_p范数的非凸张量模型.采用迭代加权核范数算法求解模型,实现低秩张量最小化.在合成数据和真实图像上的大量实验验证文中方法的恢复性能.     

基于模板校正与低秩分解的纺织品瑕疵检测方法

针对周期性纺织品存在的拉伸变形问题,提出结合模板校正与低秩分解的纺织品瑕疵检测方法.首先对原图像进行模板校正,减少图像拉伸变形对检测结果的影响.然后提出低秩校正分解模型,包含低秩项、稀疏项和校正项,通过交替方向法优化求解,生成低秩矩阵和稀疏矩阵.最后利用最优阈值分割算法,分割由稀疏矩阵产生的显著图,完成瑕疵检测.在标准数据库上的实验表明,文中方法的查全率有所提高.     

Discriminative low-rank representation with Schatten-p norm for image recognition

Low-rank representation (LRR) has attracted much attention recently due to its efficacy in a rich variety of real world applications. Recently, the non-convex regularization has become widely used in the rank minimization problem. In this paper, we propose a discriminative low-rank representation with Schatten-p norm (DLRR-SPN) to learn a robust and discriminative affinity matrix for image recognition. To this end, we first impose the Schatten-p norm regularization on the representation matrix to learn the global structure of data. Moreover, the adaptive distance penalty is used to preserve the local neighbor relationship of data. The objective function is formulated as a Schatten-p norm minimization problem, which can be solved via alternating direction method of multipliers (ADMM). To enhance the separation ability of the discriminative affinity matrix for semi-supervised recognition problem, the angular information of the principal directions of the low-rank representation is further exploited. Finally, an effective semi-supervised classifier is utilized on the learned affinity matrix for final prediction. Extensive experimental results on image recognition demonstrate the effectiveness of the proposed method and its superiority in performance over the related state-of-the-art methods.

     

Salient object detection with low-rank approximation and ℓ2,1-norm minimization

Salient object detection is an important issue in computer vision and image procession in that it can facilitate humans to locate conspicuous visual regions in complex scenes rapidly and improve the performance of object detection and video tracking. In recent years, low-rank matrix approximation has been proved to be favorable in image saliency detection and gained a great deal of attention. An underlying assumption of low-rank recovery is that an image is a combination of background regions being low-rank and salient objects being sparse, which corresponds to tough non-smooth optimization problems. In this paper, by incorporating ℓ_2,1-norm minimization, we obtain the corresponding smooth optimization problems and propose two effective algorithms with proved convergence. To guarantee the robustness of the proposed methods, the input image is divided into patches and each patch is approximately represented by its mean value. Besides, multi-scale visual features of each patch of the given image are extracted to capture common low-level features such as color, edge, shape and texture. The salient objects of a given image are indicated with sparse coefficients solved by the low-rank matrix approximation problem. Saliency maps are further produced with integration of the high-level prior knowledge. Finally, extensive experiments in four real-world datasets demonstrate that the proposed methods come with competitive performance over the eight compared state-of-the-arts.     

Decomposition into low-rank plus additive matrices for background/foreground separation: A review for a comparative evaluation with a large-scale dataset

Background/foreground separation is the first step in video surveillance system to detect moving objects. Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit (PCP) which decomposes a data matrix into a low-rank matrix and a sparse matrix. However, similar robust implicit or explicit decompositions can be made in the following problem formulations: Robust Non-negative Matrix Factorization (RNMF), Robust Matrix Completion (RMC), Robust Subspace Recovery (RSR), Robust Subspace Tracking (RST) and Robust Low-Rank Minimization (RLRM). The main goal of these similar problem formulations is to obtain explicitly or implicitly a decomposition into low-rank matrix plus additive matrices. These formulation problems differ from the implicit or explicit decomposition, the loss function, the optimization problem and the solvers. As the problem formulation can be NP-hard in its original formulation, and it can be convex or not following the constraints and the loss functions used, the key challenges concern the design of efficient relaxed models and solvers which have to be with iterations as few as possible, and as efficient as possible. In the application of background/foreground separation, constraints inherent to the specificities of the background and the foreground as the temporal and spatial properties need to be taken into account in the design of the problem formulation. Practically, the background sequence is then modeled by a low-rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. Although, many efforts have been made to develop methods for the decomposition into low-rank plus additive matrices that perform visually well in foreground detection with reducing their computational cost, no algorithm today seems to emerge and to be able to simultaneously address all the key challenges that accompany real-world videos. This is due, in part, to the absence of a rigorous quantitative evaluation with synthetic and realistic large-scale dataset with accurate ground truth providing a balanced coverage of the range of challenges present in the real world. In this context, this work aims to initiate a rigorous and comprehensive review of the similar problem formulations in robust subspace learning and tracking based on decomposition into low-rank plus additive matrices for testing and ranking existing algorithms for background/foreground separation. For this, we first provide a preliminary review of the recent developments in the different problem formulations which allows us to define a unified view that we called Decomposition into Low-rank plus Additive Matrices (DLAM). Then, we examine carefully each method in each robust subspace learning/tracking frameworks with their decomposition, their loss functions, their optimization problem and their solvers. Furthermore, we investigate if incremental algorithms and real-time implementations can be achieved for background/foreground separation. Finally, experimental results on a large-scale dataset called Background Models Challenge (BMC 2012) show the comparative performance of 32 different robust subspace learning/tracking methods.     

牛顿-软阈值迭代鲁棒主成分分析算法

针对鲁棒主成分分析（RPCA）问题，为了降低RPCA算法的时间复杂度，提出了牛顿-软阈值迭代（NSTI）算法。首先，使用低秩矩阵的Frobenius范数与稀疏矩阵的l₁-范数的和来构造NSTI算法的模型；其次，同时使用两种不同的优化方式求解模型的不同部分，即用牛顿法快速计算出低秩矩阵，用软阈值迭代算法快速计算出稀疏矩阵，交替使用这两种方法计算出原数据的低秩矩阵和稀疏矩阵的分解；最后，得到原始数据的低秩特征。在数据规模为5 000×5 000，低秩矩阵的秩为20的情况下，NSTI算法和梯度下降（GD）算法、低秩矩阵拟合（LMaFit）算法相比，时间效率分别提高了24.6%、45.5%。对180帧的视频前景背景进行分离，NSTI耗时3.63 s，时间效率比GD算法、LMaFit算法分别高78.7%、82.1%。图像降噪实验中，NSTI算法耗时0.244 s，所得到的降噪后的图像与原始图像的残差为0.381 3，与GD算法、LMaFit算法相比，时间效率和精确度分别提高了64.3%和45.3%。实验结果证明，NSTI算法能够有效解决RPCA问题并提升RPCA算法的时间效率。     

牛顿-软阈值迭代鲁棒主成分分析算法

针对鲁棒主成分分析（RPCA）问题,为了降低RPCA算法的时间复杂度,提出了牛顿-软阈值迭代（NSTI）算法。首先,使用低秩矩阵的Frobenius范数与稀疏矩阵的l₁-范数的和来构造NSTI算法的模型;其次,同时使用两种不同的优化方式求解模型的不同部分,即用牛顿法快速计算出低秩矩阵,用软阈值迭代算法快速计算出稀疏矩阵,交替使用这两种方法计算出原数据的低秩矩阵和稀疏矩阵的分解;最后,得到原始数据的低秩特征。在数据规模为5 000×5 000,低秩矩阵的秩为20的情况下,NSTI算法和梯度下降（GD）算法、低秩矩阵拟合（LMaFit）算法相比,时间效率分别提高了24.6%、45.5%。对180帧的视频前景背景进行分离,NSTI耗时3.63 s,时间效率比GD算法、LMaFit算法分别高78.7%、82.1%。图像降噪实验中,NSTI算法耗时0.244 s,所得到的降噪后的图像与原始图像的残差为0.381 3,与GD算法、LMaFit算法相比,时间效率和精确度分别提高了64.3%和45.3%。实验结果证明,NSTI算法能够有效解决RPCA问题并提升RPCA算法的时间效率。     

基于判别低秩矩阵恢复和协同表示的遮挡人脸识别

针对训练样本和测试样本均受到严重的噪声污染的人脸识别问题,传统的子空间学习方法和经典的基于稀疏表示的分类(SRC)方法的识别性能都将急剧下降。另外,基于稀疏表示的方法也存在算法复杂度较高的问题。为了在一定程度上缓解上述问题,提出一种基于判别低秩矩阵恢复和协同表示的遮挡人脸识别方法。首先,低秩矩阵恢复可以有效地从被污损的训练样本中恢复出干净的、具备低秩结构的训练样本,而结构非相关性约束的引入可以有效提高恢复数据的鉴别能力。然后,通过学习原始污损数据与恢复出的低秩数据之间的低秩投影矩阵,将受污损的测试样本投影到相应的低维子空间,以修正污损测试样本。最后,利用协同表示的分类方法(CRC)对修正后的测试样本进行分类,获取最终的识别结果。在Extended Yale B和AR数据库上的实验结果表明,本文方法对遮挡人脸识别具有更好的识别性能。     

Exact Low-Rank Matrix Completion from Sparsely Corrupted Entries Via Adaptive Outlier Pursuit

Recovering a low-rank matrix from some of its linear measurements is a popular problem in many areas of science and engineering. One special case of it is the matrix completion problem, where we need to reconstruct a low-rank matrix from incomplete samples of its entries. A lot of efficient algorithms have been proposed to solve this problem and they perform well when Gaussian noise with a small variance is added to the given data. But they can not deal with the sparse random-valued noise in the measurements. In this paper, we propose a robust method for recovering the low-rank matrix with adaptive outlier pursuit when part of the measurements are damaged by outliers. This method will detect the positions where the data is completely ruined and recover the matrix using correct measurements. Numerical experiments show the accuracy of noise detection and high performance of matrix completion for our algorithms compared with other algorithms.     

基于背景先验与低秩恢复的显著性目标检测方法

显著性检测是指计算机通过算法自动识别出图像中的显著性目标，广泛应用于目标识别、图像检索与图像分类等领域。针对现有基于稀疏与低秩矩阵恢复的显著性检测模型中低秩转换矩阵的获取、前景稀疏矩阵的处理以及超像素块之间的关系，需对现有的稀疏与低秩矩阵恢复模型进行优化，使之更好地适用于图像的显著性检测。首先，根据背景的对比度和连通度原则获取图像低秩的背景字典，采用3种尺度分割图像的多个特征矩阵获得图像的前景稀疏矩阵；其次，通过计算邻居像素点之间的影响因子矩阵与置信度矩阵对显著图的结果进行结构约束，并且采用稀疏与低秩矩阵恢复模型对图像进行显著性检测；最后，利用K-means聚类算法的传播机制优化得到的显著图。在公开数据集上进行实验验证,结果证明本文方法能够准确有效地检测出显著性目标。     

求解低秩矩阵融合高动态范围图像

目的 利用低秩矩阵恢复方法可从稀疏噪声污染的数据矩阵中提取出对齐且线性相关低秩图像的优点,提出一种新的基于低秩矩阵恢复理论的多曝光高动态范围（HDR）图像融合的方法,以提高HDR图像融合技术的抗噪声与去伪影的性能。方法 以部分奇异值（PSSV）作为优化目标函数,可构建通用的多曝光低动态范围（LDR）图像序列的HDR图像融合低秩数学模型。然后利用精确增广拉格朗日乘子法,求解输入的多曝光LDR图像序列的低秩矩阵,并借助交替方向乘子法对求解算法进行优化,对不同的奇异值设置自适应的惩罚因子,使得最优解尽量集中在最大奇异值的空间,从而得到对齐无噪声的场景完整光照信息,即HDR图像。结果 本文求解方法具有较好的收敛性,抗噪性能优于鲁棒主成分分析（RPCA）与PSSV方法,且能适用于多曝光LDR图像数据集较少的场合。通过对经典的Memorial Church与Arch多曝光LDR图像序列的HDR图像融合仿真结果表明,本文方法对噪声与伪影的抑制效果较为明显,图像细节丰富,基于感知一致性（PU）映射的峰值信噪比（PSNR）与结构相似度（SSIM）指标均优于对比方法：对于无噪声的Memorial Church图像序列,RPCA方法的PSNR、SSIM值分别为28.117 dB与0.935,而PSSV方法的分别为30.557 dB与0.959,本文方法的分别为32.550 dB与0.968。当为该图像序列添加均匀噪声后,RPCA方法的PSNR、SSIM值为28.115 dB与0.935,而PSSV方法的分别为30.579 dB与0.959,本文方法的为32.562 dB与0.967。结论 本文方法将多曝光HDR图像融合问题与低秩最优化理论结合,不仅可以在较少的数据量情况下以较低重构误差获取到HDR图像,还能有效去除动态场景伪影与噪声的干扰,提高融合图像的质量,具有更好的鲁棒性,适用于需要记录场景真实光线变化的场合。     

基于低秩稀疏分解的自适应运动目标检测算法

传统的低秩稀疏分解方法使用[l1]范数把场景中的运动目标建模为稀疏离群值,分离出低秩的背景成分与稀疏的运动目标成分。然而,在许多实际场景中往往会有动态背景的情形（例如水面波纹、树木摇动）,[l1]范数并不能区分出这些干扰与真实目标,从而大大影响检测效果。实际上,运动目标区域中的像素不仅仅具有稀疏性,还具有空间分布上的连续性。通过引入空间融合稀疏约束,在空间连续性和稀疏性两方面对运动目标进行建模,使模型更符合目标像素的分布规律。同时,设计了一种自适应的参数更新方法,使算法的鲁棒性进一步提升。在公共数据集上的大量实验表明,相比于传统方法,该算法在准确率和鲁棒性方法有很大提高。     

A nonconvex nonsmooth regularization method for compressed sensing and low rank matrix completion

In this paper, a nonconvex and nonsmooth method for compressed sensing and low-rank matrix completion is studied. The proposed model is formulated as nonconvex regularized least square optimization problem. At first, an alternating minimization scheme is developed in which the problem can be decomposed into three subproblems, two of them are convex and the remaining one is smooth. Then, the convergence of the sequence which is generated by the alternating minimization algorithm is proved. In addition, some recovery guarantees are also analyzed. Finally, various numerical simulations are performed to test the efficiency of the method.     

结合低秩和结构化稀疏的大雾图像小目标检测

针对传统的低秩稀疏分解模型不能直接应用到单幅图像进行目标检测,且忽略了目标像素的空间结构性导致检测精度不高等问题,提出一种基于低秩和结构化稀疏的单幅大雾图像小目标检测算法。首先,对原始大雾图像进行预处理得到由局部子图像构成的大雾补片图像,将小目标检测问题转化为低秩和稀疏分解问题。然后,考虑到目标像素间的空间结构关系,在对大雾补片图像进行矩阵分解时,引入结构化稀疏诱导范数对目标进行约束。最后,将矩阵分解得到的补片图像进行后处理得到背景图像和目标图像。通过对单幅大雾图像实验仿真表明,所提算法确保了小目标检测的完整性并且提高了检测精度。     

大气湍流下退化序列图像的目标检测方法

为解决大气湍流退化序列中运动目标检测困难的问题,提出了一种结合低秩分解和检测融合的目标检测方法。首先,根据退化视频中湍流运动分量的稀疏分布特点,采用低秩矩阵描述法将每帧图像分解为低秩稳像和稀疏运动两部分,初步实现场景和湍流运动的粗分离。其次,由于稀疏部分中包含目标在内的整个场景的稀疏运动量,引入自适应阈值法剔除干扰量,分割目标并填补其中空洞;对于无湍流偏移干扰的低秩部分,采用高斯建模获得低秩中的前景区域。最后,对两部分检测结果进行联合判定,从而获得准确的目标检测结果。实验表明,本文方法目标提取的准确度较高,明显优于当前经典检测方法,在强湍流条件下检测结果仍较为理想。     

CUSTOM: A Calibration Region Recovery Approach for Highly Subsampled Dynamic Parallel Magnetic Resonance Imaging

We propose a recovery approach for highly subsampled dynamic parallel MRI image without auto-calibration signals (ACSs) or prior knowledge of coil sensitivity maps. By exploiting the between-frame redundancy of dynamic parallel MRI data, we first introduce a new low-rank matrix recovery-based model, termed as calibration using spatial–temporal matrix (CUSTOM), for ACSs recovery. The recovered ACSs from data are used for estimating coil sensitivity maps and further dynamic image reconstruction. The proposed non-convex and non-smooth minimization for the CUSTOM step is solved by a proximal alternating linearized minimization method, and we provide its convergence result for this specific minimization problem. Numerical experiments on several highly subsampled test data demonstrate that the proposed overall approach outperforms other state-of-the-art methods for calibrationless dynamic parallel MRI reconstruction.     

基于稀疏和低秩先验分离的快速动态MRI重建

为了加速动态核磁共振成像（MRI）的重建,并提取动态组织部分,提出一种基于将稀疏和低秩先验分离的重建方法。算法利用鲁棒主成分分析法（RPCA）,将动态MRI看作静态背景和动态组织的合成,建立相应的低秩矩阵和x-f域稀疏模型,再通过交替方向拉格朗日乘子法（ADMM）求解优化问题。与经典的k-t FOCUSS算法和k-t SLR算法进行对比,此算法能保证重建质量,即峰值信噪比（PSNR）、结构相似性（SSIM）等评价指标。实验结果表明,该算法能实现快速动态MRI的成像,减少运动伪影,同时更利于提取动态信息。     

结构图正则低秩子空间聚类

针对结构稀疏子空间聚类中不能很好地保证相似度矩阵连接性的问题,给出了一个新的统一优化模型。首先,引入了表示系数矩阵的子空间结构范数,增加了低秩表示来揭示高维数据的全局结构。其次,为了使相似度矩阵具有类内统一,类间稀疏的作用,还定义了分组效应来捕获数据的内部几何结构,提出了结构图正则低秩子空间聚类模型。最后使用自适应惩罚的线性化交替法（LADMAP）来得到最优解。实验结果表明,该模型不但可以捕获数据的全局结构,而且还可以捕获数据的内在几何结构,迫使相关数据紧密结合,不相关数据松散分离,从而使得相似度矩阵与分割矩阵变得更加一致。     

隐式低秩稀疏表示的多视角子空间聚类

针对多视角子空间聚类问题,提出基于隐式低秩稀疏表示的多视角子空间聚类算法(LLSMSC).算法构建多个视角共享的隐式结构,挖掘多视角之间的互补性信息.通过对隐式子空间的表示施加低秩约束和稀疏约束,捕获数据的局部结构和稀疏结构,使聚类结果更准确.同时,使用基于增广拉格朗日乘子交替方向最小化算法高效求解优化问题.在6个不同数据集上的实验验证LLSMSC的有效性和优越性.