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Design, Automation and Test in Europe Conference and Exhibition (DATE)

作者： Hatami, Safar Pedram, Massoud Univ Southern Calif Dept Elect Engn Los Angeles CA 90089 USA

ISBN: (纸本)9783981080162

In deep sub-micron technology, accurate modeling of output waveforms of library cells under different input slew and load capacitance values is crucial for precise timing and noise analysis of VLSI circuits. Construction of a compact and efficient model of such waveforms becomes even more challenging when manufacturing process and environmental variations are considered. This paper introduces a rigorous and robust foundation to mathematically model output waveforms under sources of variability and to compress the library data. The proposed approach is suitable for today's current source model (CSM) based ASIC libraries. It employs an orthonormal transformation to represent the output waveforms as a linear combination of some appropriately-derived basis waveforms. More significantly robust principle component analysis (RPCA) is used to stratify the library waveforms into a small number of groups for which different sets of principle components are calculated. This stratification results in a very high compression ratio for the variational CSM library while meeting a maximum error tolerance. Interpolation and further compression is obtained by representing the coefficients as signomial functions of various parameters, e.g., input slew, load capacitance, supply voltage, and temperature. We propose a procedure to calculate the coefficients and power of the signomial functions. Experimental results demonstrate the effectiveness of the proposed variational CSM modeling framework and the stratification-based compression approach.

关键词： Current Source Model robust principle component analysis Stratification signomial

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Background Subtraction Based on robust principle component analysis and Its Implementation Using CUDA

Background Subtraction Based on Robust Principle Component A...

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作者： Zhe Zhang 华中师范大学

学位级别：硕士

本文中,我基于现有的鲁棒性主成分分析算法提出了一个基于鲁棒性主成分分析的在线算法并描述了它的GPU实现和优化。全文一共有四个部分:绪论、理论基础、新算法的提出和新算法的GPU实现方法。第一部分中文章主要介绍了背景提取的概念、... 详细信息

本文中,我基于现有的鲁棒性主成分分析算法提出了一个基于鲁棒性主成分分析的在线算法并描述了它的GPU实现和优化。全文一共有四个部分:绪论、理论基础、新算法的提出和新算法的GPU实现方法。第一部分中文章主要介绍了背景提取的概念、研究意义和研究现状。第二部分从背景提取的基本步骤和方法讲起,然后到基于主成分分析的背景提取算法到基于鲁棒主成分分析的背景提取算法的发展进化历程。新算法的提出部分我主要介绍了新算法的整体框架和一些具体的实现细节。在最后一部分GPU实现方法部分中,我介绍了如何将新的在线鲁棒性主成分分析算法通过CUDA技术来实现在GPU上的运行和优化。随着人工智能的不断发展,对机器视觉的需求也越来越大。而对于任何机器人来说,获取视觉信息的最便宜最直接的方式就是使用视频。目前,视频和摄像机已经被使用在视频游戏,安全监控,人体健康检测等诸多领域。对智能机器人来说,最重要的不是对视频的提取,而是通过机器的处理去理解视频中的各种元素。这就需要视频中运动对象的识别和分离,也就是对视频的前后景的分离:对视频中的图像序列进行分析和处理,检测或者识别视频中的运动的对象然后提取出视频中的完整的背景信息。因此,背景提取或者前景追踪是人工智能的重要基础。同时通过背景提取和前景提取的预处理,还可以大大增加模式识别等问题的准确率。因此背景提取有着重要的研究前景。在过去的几十年中,在背景提取领域有着很多论文,但是当观测到的视频中含有大量的运动物体或者视频中有着大量的干扰信号的时候,模型生成的背景矩阵往往不够准确。我从最新的学术论文中发现,一种新的子空间学习算法可能在这一领域有着极好的前景。这一方法常被称为鲁棒性主成分分析。这是一个对传统主成分分析方法的鲁棒性改进,他比传统的主成分分析更加适合用于背景提取任务。虽然鲁棒性主成分分析方法在背景提取领域显示出来非常大的潜力,现有的大部分鲁棒性主成分分析模型都是基于批处理算法。而现实生活中对背景提取的应用比如说视频安全监控需要一个足够鲁棒的在线算法。因此,迫切需要改进现有的批处理算法并将其发展为足够优秀的在线背景提取算法以适应实际应用的需求。同时使得算法更加实用,我还将再现鲁棒主成分分析算法使用GPU来实现以大大降低算法实现和部署的硬件成本。最简单的实现背景建模的方法是使用没有任何前景对象的图像来建模。但是在现实生活中,背景并不总是可以直接用静态的图像来表示的,因为背景可能会随着时间而改变。比如说摇晃的树和各种物体的阴影。因此我们需要使用一些更加鲁棒的模型来描述背景,比如说在鲁棒主成分分析方法中使用的背景矩阵。同时,背景建模的研究还建立在一个前提条件上,就是说前景也就是运动物体的移动会导致当前图像与背景模型或者背景图像之间产生偏差。我们的背景提取模型初次之外还需要满足这些前提条件:相机位置是固定的,存在一个背景模型可以拟合。一个完整的背景提取算法通常包括三个部分:第一个部分是背景建模,也就是寻找一个合适的可以用来描述当前处理问题的背景的模型,也可以被称作背景表示。第二个部分是背景初始化,也就是通过视频或者其他数据来提取出背景模型中需要的参数和数据。第三个部分是背景维护,是通过适时地更新背景模型中的数据来保持背景可以被动态的调整和更新。在这篇文章的算法的根基是基于鲁棒主成分分析的背景提取方法。这一方法由基于主成分分析的背景提取方法发展而来。传统的主成分分析方法作为一个基本的计算机机器学习的算法,在图像加工,数据预处理等方面有着非常广泛的用途。对于主成分分析,我们考虑对于一个集合x0,…,xn。集合中的每个向量代表视频中的一帧图像包含的数据。也就是说集合x0，…xn就代表一系列的图片,也就是视频。对于给定的这么一个集合x0,…,xn如,主成分分析的主要目的是计算一个集合x0，…xn的关于低纬子空间的线性映射。为了计算主成分分析的结果,我们取这样[x0，…xn]=Xn∈Rm×n∈一个矩阵,通过最小化下式来计算目标k维子空间:（？）也就是说将一个矩阵X分解为一个稀疏矩阵L和一个低秩矩阵X的和。但是主成分分析方法有一个主要的缺点是:它对于异常值或者一些噪声过于敏感。这个缺点对它在背景提取领域的应用造成了一定限制。因此在原有的主成分分析的基础上，有人提出了鲁棒性主成分分析的方法,这种新的方法常常用在数据丢失的情况下恢复原始数据。鲁棒主成分分析的主要思路如下:给定一个矩阵X,鲁棒主成分分析可以转化为如下优化问题:（？）然而鲁棒性主成分分析引来了新的问题:我们没有对于上式的确定的解。甚至我们因为矩阵过大,所以简单的蛮力搜索方法也因为计算复杂度过高的问题而不可行。因此有些研究人员提出了该问题的近似问题:（？）为了将传统的鲁棒主成分分析方法适用于背景提取,我们将原始的鲁棒主成分分析问题改为:用X来表示原始的视频矩阵,然后将原始的视频矩

关键词： Background Subtraction robust principle component analysis CUDA

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Fast, Efficient, and Viable Compressed Sensing, Low-Rank, and robust principle component analysis Algorithms for Radar Signal Processing

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REMOTE SENSING 2023年第8期15卷 2216页

作者： Panhuber, Reinhard Fraunhofer Inst High Frequency Phys & Radar Tech F Fraunhofer FHR D-53343 Wachtberg Germany

Modern radar signal processing techniques make strong use of compressed sensing, affine rank minimization, and robust principle component analysis. The corresponding reconstruction algorithms should fulfill the following desired properties: complex valued, viable in the sense of not requiring parameters that are unknown in practice, fast convergence, low computational complexity, and high reconstruction performance. Although a plethora of reconstruction algorithms are available in the literature, these generally do not meet all of the aforementioned desired properties together. In this paper, a set of algorithms fulfilling these conditions is presented. The desired requirements are met by a combination of turbo-message-passing algorithms and smoothed l(0)-refinements. Their performance is evaluated by use of extensive numerical simulations and compared with popular conventional algorithms.

关键词： compressed sensing affine rank minimization robust principle component analysis complex valued radar signal processing

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robust principal component analysis with intra-block correlation

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NEUROCOMPUTING 2020年 386卷 165-178页

作者： Can Jiang Feng Zhang Jianjun Wang Chan-Yun Yang Wendong Wang Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Southwest Univ Coll Artificial Intelligence Chongqing 400715 Peoples R China Natl Taipei Univ Dept Elect Engn 151 Univ Rd New Taipei 23741 Taiwan Southwest Univ Res Inst Intelligent Finance & Platform Econ Chongqing 400715 Peoples R China

This paper proposes a novel optimization program for solving the robust principle component analysis (RPCA) problem, which decomposes a data matrix into a conventional low-rank part plus a particular block-sparse residual. This kind of block-sparse residual often scattered in the source signal scope as contaminants, and often existed in many practical applications, such as an ordinary imaging system, a Hyper Spectral Imaging system, EEG and MEG, and types of physiological signals. Different from most currently existing approaches, the study perceived especially a highly spatial correlation among the inner structure of the neighbouring pixels in this contiguously block-sparse residual. The high intra-block correlation is then introduced as prior information to deal the governing optimization problem. In order to enhance the block-sparsity and maintain the local smoothness simultaneously, a localized low-rank promoting method is introduced with a theoretical guarantee. An efficient solving algorithm is designed accordingly with a convergence analysis by adopting the classical Alternating Direction Method of Multipliers (ADMM) framework. In addition to the theoretical model derivation, several synthetic simulations together with a real application on image denoising experiment have been conducted to validate the proposed model. As expected, the models outperforms significantly the compared state-of-the-arts. (c) 2019 Elsevier B.V. All rights reserved.

关键词： robust principle component analysis Block sparse Intra-block correlation Localized low-rank promoting method Alternating direction method of multipliers Image denoising

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Structural damage detection by integrating robust PCA and classical PCA for handling environmental variations and imperfect measurement data

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ADVANCES IN STRUCTURAL ENGINEERING 2022年第8期25卷 1815-1828页

作者： Xu, Mingqiang Li, Jun Wang, Shuqing Hao, Hong Tian, Huiyuan Han, Jie Ocean Univ China Shandong Prov Key Lab Ocean Engn Qingdao Peoples R China Univ Hong Kong Dept Civil Engn Hong Kong Peoples R China Curtin Univ Ctr Infrastruct Monitoring & Protect Sch Civil & Mech Engn Perth WA Australia Shanghai Invest Design & Res Inst Co Ltd Shanghai Peoples R China

This paper proposes a vibration-based structural damage detection approach considering the effects of uncertainties, including environmental variations and random errors that possibly stem from measurement and automatic modal identification. The existing methods that only employ the classical principle component analysis (PCA) have been demonstrated effective to remove the effects of environmental variations while extremely sensitive to random errors. Therefore, the robust PCA is firstly introduced to remove the random errors, especially outliers, that significantly corrupt the low-rank property of the stacked damage sensitive feature (DSF) matrix. Then, the classical PCA is used to extract the environmental variation-free residues, which are inherently damage-dependent and can be used to detect the existence of damage. The problem of missing data is also considered in this study. It is tackled by adding virtual random errors to the locations of missing entities and thus can be addressed by the introduced robust PCA. The advantages of the proposed approach include: (1) Handling the random error-contaminated DSF data regardless of the error's amplitude, which is an intractable problem for the existing classical PCA-based methods to consider the environmental effects;(2) Damage detection process can be automatic since the missing data can be automatically predicted and the random errors are not required to be manually distinguished. The effectiveness and performance of the proposed method are demonstrated on a numerical beam structure and an experimentally tested wooden bridge model.

关键词： structural damage detection environmental variation uncertainties missing data classical principle component analysis robust principle component analysis

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Moving object detection by low rank approximation and l₁-TV regularization on RPCA framework

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2018年 56卷 188-200页

作者： Shijila, B. Tom, Anju Jose George, Sudhish N. Natl Inst Technol Calicut Dept Elect & Commun Engn Calicut 673601 Kerala India

The detection of moving objects and the subtraction of the scene background are significant tasks for intelligent video surveillance systems as it is one among the fundamental steps. Inspired by the challenging cases yet to be resolved in Moving Object Detection (MOD), a new formulation is done to detect moving objects from video sequences based on robust Principal component analysis (RPCA) principle by adopting the regularization of Total Variation (TV) norm using a convergent convex optimization algorithm. While the nuclear norm exploits the low-rank property of background, the sparsity is enhanced by the l(1)-norm and the foreground spatial smoothness is explored by TV regularization. The goodness of this method lies in the reduced computational complexity, quickness and on the superiority acquired in quantitative evaluation based on F-measure, Recall and Precision with respect to the state of the art methods. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Moving object detection Low rank recovery Background subtraction robust principle component analysis

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Simultaneous denoising and moving object detection using low rank approximation

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2019年 90卷 198-210页

作者： Shijila, B. Tom, Anju Jose George, Sudhish N. Natl Inst Technol Calicut Dept Elect & Commun Engn Calicut Kerala India

Moving Object Detection (MOD) and Background Subtraction (BS) are the fundamental tasks in video surveillance systems. But, one of the major challenges which badly affects the accuracy of detection is the presence of noise in the captured video sequence. In this work, we propose a new moving object detection method from noisy video data named as De-Noising and moving object detection by Low Rank approximation and l(1) -TV regularization (DNLRl(1) TV). In general, background of videos are assumed to lie in a low-rank subspace and moving objects are assumed to be piecewise smooth in the spatial and temporal direction. The proposed method consolidates the nuclear norm, l(2)-norm, l(1)-norm and Total Variation (TV) regularization in a unified framework to obtain simultaneous denoising and MOD performance. The nuclear norm exploits the low-rank property of the background, the sparsity is enhanced by the l(1)-norm, TV regularization is used to explore the foreground spatial smoothness and noise is detected and removed by the l(2)-norm regularization. Extensive experiments demonstrate that the proposed method outperforms the state-of-the-art approaches in terms of denoising capability and detection accuracy. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Moving object detection Low rank recovery Background subtraction robust principle component analysis

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Cold-start link prediction in multi-relational networks based on network dependence analysis

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 515卷 558-565页

作者： Wu, Shun-yao Zhang, Qi Xue, Chuan-yu Liao, Xi-yang Qingdao Univ Qingdao 266071 Peoples R China Ping An Technol Shenzhen Co Ltd Shenzhen 518000 Peoples R China

Cold-start link prediction has been a hot issue in complex network. Different with most of existing methods, this paper utilizes multiple interactions to predict a specific type of links. In this paper, multiple interactions are abstracted as multi-relational networks, and robust principle component analysis is employed to extract low-dimensional latent factors from sub-networks. Then a distribution free independence test, projection correlation, is introduced to efficiently analyze dependence between target and auxiliary sub-networks. Furthermore, associated auxiliary networks are exploited for cold-start link prediction, which aims to forecast potential links for new/isolated nodes in target sub-networks. Experimental results on 8 bioinformatics datasets validate rationality and effectiveness of the method. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Cold-start link prediction Network dependence analysis Projection correlation statistics robust principle component analysis

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Low rank and sparse decomposition based on extended LLp norm

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第9期83卷 26107-26130页

作者： Keshavarzian, Razieh Aghagolzadeh, Ali Islamic Azad Univ Dept Elect Engn Heris Branch Heris Iran Babol Noshirvani Univ Technol Fac Elect & Comp Engn Babol Iran

The problem of decomposing a given matrix into its low-rank and sparse components, known as robust principle component analysis (RPCA), has found many applications in variety of fields. In this problem, the goal is to recover the two components through constrained minimization of a combination of the rank function and l(0) norm. Oftentimes, exact recovery of the low-rank component is desired. Since the problem is NP-Hard, a convex relaxation where nuclear norm and l(1) norm are utilized to induce low-rank and sparsity is used. However, it may obtain suboptimal results since the nuclear norm cannot well approximate the rank function. This paper addresses the low-rank and sparse decomposition (LRSD) problem by utilizing a new nonconvex approximation function for the rank. In our LRSD approach, the nonconvex LLp norm is extended on singular values to obtain a new surrogate, called eLL(p), for the rank function. To solve the associated minimization problem, an efficient algorithm based on alternating direction multiplier method (ADMM) and Majorization-Minimization (MM) algorithm is developed. To verify the effectiveness of the proposed method, it is applied to the synthetic data and real applications including face image shadow removal and image denoising. Experimental results show the effectiveness of the proposed method compared with the other methods in terms of the recovery errors and objective evaluations. In real applications of the images, our proposed method achieves higher recovery accuracy in a less time.

关键词： Alternating direction multiplier method Low-rank and sparse decomposition LLp norm robust principle component analysis

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An Effective Optimization Scheme for ECG Signal Denoising via Low-Rank Matrix Decomposition

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2019年第1期38卷 138-152页

作者： Ye, Qian Cai, Nian Xia, Hao Cen, Guandong Chen, Xindu Wang, Han Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Guangdong Peoples R China Guangdong Univ Technol Sch Electromech Engn Guangzhou 510006 Guangdong Peoples R China

Electrocardiogram (ECG) signal denoising is an important preprocessing for ECG signal analysis. The contaminated ECG signal can be considered as the combination of the desired clean signal and the noise. Thus, ECG signal denoising can be considered as a problem of obtaining an optimal solution to the desired clean signal. In this paper, an effective optimization scheme for ECG signal denoising is presented based on low-rank matrix decomposition. First, the ECG denoising problem is formulated as low-rank matrix decomposition. So, an ECG beats matrix is assumed to be the combination of a sparse noise matrix and a low-rank matrix. Considering the repeatability of ECG signal, the rank of the ECG beats matrix is assumed to be one. Then, to fully exploit the low-rank property of the ECG signal, the matrix decomposition is modified by means of adding different weights to different singular values. Finally, the desired clean ECG signal is reconstructed by the low-rank component. The experimental results show that the proposed denoising method achieves the best performance of suppressing the electromyographic noise in the ECG signals compared with other optimization models.

关键词： Electrocardiographic signal Low-rank decomposition robust principle component analysis Weighted nuclear norm minimization Electromyographic noise

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