基于低秩表示动态更新投影的在线运动目标检测

视频图像中运动目标检测是机器视觉领域的重要研究内容,旨在将序列图像中的背景和前景进行有效分离。在研究几种典型运动目标检测算法的基础上,提出了一种基于低秩表示动态更新投影的在线运动目标检测算法。采用低秩表示方法对若干连续视频帧进行低秩分解,并将分解所获得的低秩部分对应的左奇异值矩阵的正交补引为投影矩阵;再构建投影模型,拟合出数据的稀疏前景;最后采用视频分段分析法则对投影矩阵进行动态更新,从而保证所分离的背景以及前景的有效性。在Curtain等多个视频数据库上与其他算法进行了对比实验,实验结果表明所提算法具有很好的检测效果,对复杂的运动前景和动态背景的处理表现出很强的鲁棒性。     

自适应低秩稀疏分解在运动目标检测中的应用

针对视频处理中运动目标的精确检测这一问题,提出了一种自适应的低秩稀疏分解算法。该算法首先用背景模型与待求解的帧向量构建增广矩阵,然后使用鲁棒的主成分分析(robust principal component analysis,RPCA)对降维后的增广矩阵进行低秩稀疏分解,分离出的低秩部分和稀疏噪声分别对应于视频帧的背景和运动前景,然后使用增量奇异值分解方法用当前得到的背景向量更新背景模型。实验结果表明,该算法能更好地处理光线变化、背景运动等复杂场景,并有效降低算法的延迟和内存的占用。     

基于DFT基的矿井视频监控图像分块压缩感知方法

针对矿井视频监控图像受噪声干扰影响大,采用常规的图像采样和压缩方法存在图像模糊和传输时间过长等问题,提出了一种矿井视频监控图像分块压缩感知方法。该方法通过建立矿井视频监控图像分块压缩感知模型,在井下图像采集节点利用稀疏随机矩阵进行压缩采样,然后在地面监控中心利用正交匹配追踪( OMP )算法重构图像。研究结果表明,采用本文算法的重构图像误差小、重构时间短,所需信号采样点数少;与扰频Hadamard矩阵相比,采用稀疏随机矩阵和高斯随机矩阵作为观测矩阵对图像信号重构的峰值信噪比( PSNR)提高4 dB~5 dB;本文算法与基于小波基的算法相比,信号重构的PSNR提高1 dB~4 dB,重构时间缩短至少80％以上。     

非局部低秩正则化视频压缩感知重构

视频压缩感知在采样资源受限的视频采集领域具有重要研究意义,重构算法是视频压缩感知系统的关键技术.为了更好地从压缩采样数据中重构视频信号,提出一种基于全变分与非局部低秩正则化的视频重构算法,为视频重构提供一种新的思路.算法第1步考虑视频帧内和帧间的局部相关性,应用全变分模型作为先验约束得到初步恢复的视频帧;第2步考虑视频帧内与帧间的非局部自相似性,应用改进的非局部低秩正则化算法对其进一步重构,该步骤针对初步恢复的图像帧分块在本帧和关键帧中寻找相似块,构建低秩矩阵进行低秩正则化重构.仿真结果表明,所提出算法能够精确重构视频信号,相比主流的视频压缩感知重构算法具有更高的重构质量.     

语音压缩感知研究进展与展望

压缩感知技术,特别是语音压缩感知技术逐渐成为信号处理领域的研究热点。当前的语音压缩感知关键技术主要包括适合语音信号的稀疏分解矩阵构造,观测矩阵的选择和重构算法的设计。稀疏分解矩阵的重要代表是正交基、基于语音特性的线性预测矩阵和过完备字典。观测矩阵方面主要采用随机观测矩阵分析语音压缩感知性能;重构算法方面重点研究当观测序列或语音信号本身含有噪声时鲁棒的语音压缩感知重构算法。本文对上述语音压缩感知的3大关键技术进行了介绍和对比分析,并对语音压缩感知的应用进行了总结,最后对未来可能的研究热点进行了展望。     

基于改进循环观测的线性预测语音压缩感知

利用语音信号线性预测残差的稀疏性特点可对语音信号进行压缩感知,但需要信号的线性预测系数来构造稀疏变换矩阵,从而增加预测系数传输的数据量。为此,提出将线性预测系数存入对角阵向量中构造循环矩阵,由此得到循环观测矩阵,再对语音信号进行观测。提取该循环矩阵中的线性预测系数构造残差域稀疏变换矩阵,利用正交匹配追踪算法对观测信号进行重构。仿真实验结果表明,与传统线性预测方法相比,该方法减少了3.9%以上的数据量,且比将高斯随机矩阵作为观测矩阵的方法具有更高的帧平均重构信噪比。     

基于P-Ifourier观测矩阵的宽带压缩感知方法

针对压缩感知理论在宽带频谱感知领域应用时重构精度差的问题,根据平稳信号在频域所表现出的稀疏特性,提出了一种基于P-Ifourier(Partial-Inverse fourier)观测矩阵的宽带压缩频谱感知方法。新方法首先将频谱感知问题建模为一个典型的压缩感知问题,利用相关性能优良的标准正交傅里叶基构造观测矩阵,使观测矩阵具有良好的重构性能和重构精度。仿真结果表明,相比于高斯随机观测矩阵和嵌入式混沌序列-循环Toeplitz结构观测矩阵,该方法在较低信噪比环境下能够明显降低信号重构的均方误差,并且在相同条件下的重构概率得到了明显改善。     

一种近似奇异值分解的观测矩阵优化方法

压缩感知观测矩阵的优化通常采用迭代或最优化的思想,其主要缺点是运算复杂度高。针对这种情况,提出一种基于奇异值分解的观测矩阵优化方法。首先对随机矩阵进行奇异值分解,其次减小随机矩阵的奇异值到适定的范围,进而得到条件数相对小的观测矩阵。理论分析和实验结果表明,该方法得到的观测矩阵与稀疏基的互干性较小,能够精确重构信号。与现有的其他优化方法相比,该方法具有实现简单,计算复杂度低和重构精度高的特点。     

基于稀疏预处理和循环观测的语音压缩感知

基于压缩感知原理提出将语音信号DCT域上的小系数在一定阈值下置零预处理来改善变换域稀疏性;用三种方法构造循环观测矩阵作为观测矩阵来代替高斯随机矩阵,并证明了构造的观测矩阵与DCT基之间的非相关性;利用OMP正交匹配追踪方法对观测信号进行恢复。仿真实验结果表明,预处理后使用循环观测在不同压缩率下有更低的重构误差,同时分析各帧信噪比情况保证在比较低的压缩率下仍能得到良好的主观评估。     

语音信号处理中鲁棒性压缩感知关键技术

压缩感知技术在 许多领域都有广阔的应用前景。压缩感知关键技术主要包括稀疏矩阵的选取,观测矩阵的构造以及重构算法的设计。语音信号不同于一般信号,通常在观测矩阵和重构算法中有特殊的结构特征。在实际的应用中,噪声难以避免,而压缩感知系统中,重构系统是非线性的,且对噪声敏感,因而研究具有抗噪能力的鲁棒性压缩感知系统具有重要意义,也是压缩感知技术能否真正实用的关键之一。本文首先介绍了压缩感知的基本概念,然后分析各种噪声对压缩感知带来的影响,侧重从语音信号的观测矩阵和重构技术入手,介绍具有鲁棒性的压缩感知投影算子和重构算法,最后对未来可能的研究方向进行了展望。     

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.     

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。     

Textile fabric defect detection based on low-rank representation

In this paper, we propose a novel and robust fabric defect detection method based on the low-rank representation (LRR) technique. Due to the repeated texture structure we model a defects-free fabric image as a low-rank structure. In addition, because defects, if exist, change only the texture of fabric locally, we model them with a sparse structure. Based on the above idea, we represent a fabric image into the sum of a low-rank matrix which expresses fabric texture and a sparse matrix which expresses defects. Then, the LRR method is applied to obtain the corresponding decomposition. Especially, in order to make better use of low-rank structure characteristics we propose LRREB (low-rank representation based on eigenvalue decomposition and blocked matrix) method to improve LRR. LRREB is implemented by dividing a image into some corresponding blocked matrices to reduce dimensions and applying eigen-value decomposition (EVD) on blocked matrix instead of singular value decomposition (SVD) on original fabric image, which improves the accuracy and efficiency. No training samples are required in our methods. Experimental results show that the proposed fabric defect detection method is feasible, effective, and simple to be employed.

     

基于非凸低秩分解判别的叠加线性稀疏人脸识别

目的 针对因采集的人脸图像样本受到污染而严重干扰人脸识别及训练样本较少（小样本）时会由于错误的稀疏系数导致性能急剧下降从而影响人脸识别的问题,提出了一种基于判别性非凸低秩矩阵分解的叠加线性稀疏表示算法。方法 首先由γ范数取代传统核范数,克服了传统低秩矩阵分解方法求解核范数时因矩阵奇异值倍数缩放导致的识别误差问题;然后引入结构不相干判别项,以增加不同类低秩字典间的非相干性,达到抑制类内变化和去除类间相关性的目的;最后利用叠加线性稀疏表示方法完成分类。结果 所提算法在AR人脸库中的识别率达到了98.67±0.57%,高于SRC（sparse representation-based classification）、ESRC（extended SRC）、RPCA（robust principal component analysis）+SRC、LRSI（low rank matrix decomposition with structural incoherence）、SLRC（superposed linear representation based classification）-l₁等算法;同时,遮挡实验表明,算法对遮挡图像具有更好的鲁棒性,在不同遮挡比例下,相比其他算法均有更高的识别率。在CMU PIE人脸库中,对无遮挡图像添加0、10%、20%、30%、40%的椒盐噪声,算法识别率分别达到90.1%、85.5%、77.8%、65.3%和46.1%,均高于其他算法。结论 不同人脸库、不同比例遮挡和噪声的实验结果表明,所提算法针对人脸遮挡、表情和光照等噪声因素依然保持较高的识别率,鲁棒性更好。     

基于亚高斯随机投影的图像重建方法

将亚高斯随机投影引入可压缩传感CS(compressed sensing)理论,给出了两种新类型的CS测量矩阵:稀疏投影矩阵和非常稀疏投影矩阵.利用亚高斯分布尾部的有界性,证明了这两种矩阵满足CS测量矩阵的必要条件.同时,进一步说明由于这两种矩阵构成元素的稀疏性可以简化图像重建过程中的投影计算,从而提高重建速度.实验结果表明新的测量矩阵均有较好的测量效果,在满足一定测量数目要求的条件下可以精确重建.最后给出了这两种矩阵与一般采用的高斯测量矩阵的重建结果比较和分析.     

结合全变差与自适应低秩正则化的图像压缩感知重构

针对基于固定变换基的协同稀疏图像压缩感知(CS)重构算法不能充分利用图像自相似特性的问题,提出了一种改进的联合全变差与自适应低秩正则化的压缩感知重构方法。首先,通过图像块匹配法寻找结构相似块,并组成非局部相似块组;然后,以非局部相似块组加权低秩逼近替代协同稀疏表示中的三维小波变换域滤波;最后,结合梯度稀疏与非局部相似块组低秩先验构成重构模型的正则化项,并采用交替方向乘子法求解实现图像重构。实验结果表明,相比协同稀疏压缩感知重构(RCoS)算法,该方法重构图像的峰值信噪比平均可提升约2 dB,所提算法在准确描述图像非局部自相似结构特征的前提下显著提高了重构质量,更好地保留了图像的纹理细节信息。     

A spectral-spatial method based on low-rank and sparse matrix decomposition for hyperspectral anomaly detection

Recently, some methods based on low-rank and sparse matrix decomposition (LRASMD) have been developed to improve the performance of hyperspectral anomaly detection (AD). However, these methods mainly take advantage of the spectral information in hyperspectral imagery (HSI), and ignore the spatial information. This article proposes an LRASMD-based spectral-spatial (LS-SS) method for hyperspectral AD. First, the Go Decomposition (GoDec) algorithm is employed to solve the low-rank background component and the sparse anomaly component. Next, the sparse component is explored to calculate the spectral sparsity divergence index (SDI). Based on spectral SDI, the detection result in the spectral domain and the reliable background points, which are employed as training data to construct the background manifold by linear local tangent space alignment (LLTSA), can also be obtained. Then, based on the background manifold and the transformation matrix, the low-dimensional manifold of the whole data is computed by linear mapping. After that, the kernel collaborative representation detector (KCRD) is used in the low-dimensional manifold of the whole data for the spatial SDI. Finally, SS SDI is computed for the final detection result. The theoretical analysis and experimental results demonstrate that the proposed LS-SS can achieve better performance when compared with the comparison algorithms.     

基于Contourlet变换的图像压缩感知重构

根据图像信号在Contourlet变换域的稀疏特性,分析Contourlet变换的基本原理,提出一种基于Contourlet变换的压缩感知重构方法。针对Contourlet变换的基函数并不严格规范正交、无法构造正交变换矩阵的问题,采用改进梯度投影算法恢复稀疏处理后的系数,在保证图像质量的情况下,实现图像的低速率重构。实验结果表明,该算法的鲁棒性较好。     

基于运动和亮度显著性的森林烟雾分割方法

本文提出了一种基于运动和亮度显著性检测的烟雾区域分割方法,目的是解决传统的运动检测方法对于树叶抖动、摄像机抖动等不显著的运动区域比较敏感的问题.采用低秩结构化稀疏分解方法提取前景区域,然后计算烟雾的显著性,以便进一步分离.我们提出一种基于自适应参数的群稀疏鲁棒标准正交子空间学习(ROSL)的显著性测量方法.实验表明,该...     

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。