凸优化在信号处理与通信中的应用Convex Optimization in Signal Processing and Communications
凸优化理论在信号处理以及通信系统中的应用 比较经典的通信系统凸优化入门教程ContentsList of contributorspage IxPrefaceAutomatic code generation for real- time convex optimizationJacob Mattingley and stephen Boyd1.1 Introduction1.2 Solvers and specification languages61. 3 Examples121. 4 Algorithm considerations1.5 Code generation261.6 CVXMOD: a preliminary implementation281.7 Numerical examples291. 8 Summary, conclusions, and implicationsAcknowledgments35ReferencesGradient-based algorithms with applications to signal-recoveryproblemsAmir beck and marc teboulle2.1 Introduction422.2 The general optimization model432.3 Building gradient-based schemes462. 4 Convergence results for the proximal-gradient method2.5 A fast proximal-gradient method2.6 Algorithms for l1-based regularization problems672.7 TV-based restoration problems2. 8 The source-localization problem772.9 Bibliographic notes83References85ContentsGraphical models of autoregressive processes89Jitkomut Songsiri, Joachim Dahl, and Lieven Vandenberghe3.1 Introduction893.2 Autoregressive processes923.3 Autoregressive graphical models983. 4 Numerical examples1043.5 Conclusion113Acknowledgments114References114SDP relaxation of homogeneous quadratic optimization: approximationbounds and applicationsZhi-Quan Luo and Tsung-Hui Chang4.1 Introduction1174.2 Nonconvex QCQPs and sDP relaxation1184.3 SDP relaxation for separable homogeneous QCQPs1234.4 SDP relaxation for maximization homogeneous QCQPs1374.5 SDP relaxation for fractional QCQPs1434.6 More applications of SDP relaxation1564.7 Summary and discussion161Acknowledgments162References162Probabilistic analysis of semidefinite relaxation detectors for multiple-input,multiple-output systems166Anthony Man-Cho So and Yinyu Ye5.1 Introduction1665.2 Problem formulation1695.3 Analysis of the SDr detector for the MPsK constellations1725.4 Extension to the Qam constellations1795.5 Concluding remarks182Acknowledgments182References189Semidefinite programming matrix decomposition, and radar code design192Yongwei Huang, Antonio De Maio, and Shuzhong Zhang6.1 Introduction and notation1926.2 Matrix rank-1 decomposition1946.3 Semidefinite programming2006.4 Quadratically constrained quadratic programming andts sdp relaxation201Contents6.5 Polynomially solvable QCQP problems2036.6 The radar code-design problem2086.7 Performance measures for code design2116.8 Optimal code design2146.9 Performance analysis2186.10 Conclusions223References226Convex analysis for non-negative blind source separation withapplication in imaging22Wing-Kin Ma, Tsung-Han Chan, Chong-Yung Chi, and Yue Wang7.1 Introduction2297.2 Problem statement2317.3 Review of some concepts in convex analysis2367.4 Non-negative, blind source-Separation criterion via CAMNS2387.5 Systematic linear-programming method for CAMNS2457.6 Alternating volume-maximization heuristics for CAMNS2487.7 Numerical results2527.8 Summary and discussion257Acknowledgments263References263Optimization techniques in modern sampling theory266Tomer Michaeli and yonina c. eldar8.1 Introduction2668.2 Notation and mathematical preliminaries2688.3 Sampling and reconstruction setup2708.4 Optimization methods2788.5 Subspace priors2808.6 Smoothness priors2908.7 Comparison of the various scenarios3008.8 Sampling with noise3028. 9 Conclusions310Acknowledgments311References311Robust broadband adaptive beamforming using convex optimizationMichael Rubsamen, Amr El-Keyi, Alex B Gershman, and Thia Kirubarajan9.1 Introduction3159.2 Background3179.3 Robust broadband beamformers3219.4 Simulations330Contents9.5 Conclusions337Acknowledgments337References337Cooperative distributed multi-agent optimization340Angelia Nedic and asuman ozdaglar10.1 Introduction and motivation34010.2 Distributed-optimization methods using dual decomposition34310.3 Distributed-optimization methods using consensus algorithms35810.4 Extensions37210.5 Future work37810.6 Conclusions38010.7 Problems381References384Competitive optimization of cognitive radio MIMO systems via game theory387Gesualso Scutari, Daniel P Palomar, and Sergio Barbarossa11.1 Introduction and motivation38711.2 Strategic non-cooperative games: basic solution concepts and algorithms 39311.3 Opportunistic communications over unlicensed bands411.4 Opportunistic communications under individual-interferenceconstraints4151.5 Opportunistic communications under global-interference constraints43111.6 Conclusions438Ackgment439References43912Nash equilibria: the variational approach443Francisco Facchinei and Jong-Shi Pang12.1 Introduction44312.2 The Nash-equilibrium problem4412. 3 EXI45512.4 Uniqueness theory46612.5 Sensitivity analysis47212.6 Iterative algorithms47812.7 A communication game483Acknowledgments490References491Afterword494Index49ContributorsSergio BarbarossaYonina c, eldarUniversity of rome-La SapienzaTechnion-Israel Institute of TechnologyHaifaIsraelAmir beckTechnion-Israel instituteAmr El-Keyiof TechnologyAlexandra universityHaifEgyptIsraelFrancisco facchiniStephen boydUniversity of rome La sapienzaStanford UniversityRomeCaliforniaItalyUSAAlex b, gershmanTsung-Han ChanDarmstadt University of TechnologyNational Tsing Hua UniversityDarmstadtHsinchuGermanyTaiwanYongwei HuangTsung-Hui ChangHong Kong university of scienceNational Tsing Hua Universityand TechnologyHsinchuHong KongTaiwanThia KirubarajanChong-Yung chiMcMaster UniversityNational Tsing Hua UniversityHamilton ontarioHsinchuCanadaTaiwanZhi-Quan LuoJoachim dahlUniversity of minnesotaanybody Technology A/sMinneapolisDenmarkUSAList of contributorsWing-Kin MaMichael rebsamenChinese University of Hong KongDarmstadt UniversityHong KonTechnologyDarmstadtAntonio de maioGermanyUniversita degli studi di napoliFederico iiGesualdo scutariNaplesHong Kong University of Sciencealyand TechnologyHong KongJacob MattingleyAnthony Man-Cho SoStanford UniversityChinese University of Hong KongCaliforniaHong KongUSAJitkomut songsinTomer michaeliUniversity of californiaTechnion-Israel instituteLoS Angeles. CaliforniaogyUSAHaifaMarc teboulleTel-Aviv UniversityAngelia NedicTel-AvUniversity of Illinois atIsraelUrbana-ChampaignInoSLieven VandenbergheUSAUniversity of CaliforniaLos Angeles, CaliforniaUSAAsuman OzdaglarMassachusetts Institute of TechnologyYue WangBoston massachusettsVirginia Polytechnic InstituteUSAand State UniversityArlingtonDaniel p palomarUSAHong Kong University ofScience and TechnologyYinyu YeHong KongStanford UniversityCaliforniaong-Shi PangUSAUniversity of illinoisat Urbana-ChampaignShuzhong zhangIllinoisChinese university of Hong KongUSAHong KongPrefaceThe past two decades have witnessed the onset of a surge of research in optimization.This includes theoretical aspects, as well as algorithmic developments such as generalizations of interior-point methods to a rich class of convex-optimization problemsThe development of general-purpose software tools together with insight generated bythe underlying theory have substantially enlarged the set of engineering-design problemsthat can be reliably solved in an efficient manner. The engineering community has greatlybenefited from these recent advances to the point where convex optimization has nowemerged as a major signal-processing technique on the other hand, innovative applica-tions of convex optimization in signal processing combined with the need for robust andefficient methods that can operate in real time have motivated the optimization commu-nity to develop additional needed results and methods. The combined efforts in both theoptimization and signal-processing communities have led to technical breakthroughs ina wide variety of topics due to the use of convex optimization This includes solutions tonumerous problems previously considered intractable; recognizing and solving convex-optimization problems that arise in applications of interest; utilizing the theory of convexoptimization to characterize and gain insight into the optimal-solution structure and toderive performance bounds; formulating convex relaxations of difficult problems; anddeveloping general purpose or application-driven specific algorithms, including thosethat enable large-scale optimization by exploiting the problem structureThis book aims at providing the reader with a series of tutorials on a wide varietyof convex-optimization applications in signal processing and communications, writtenby worldwide leading experts, and contributing to the diffusion of these new developments within the signal-processing community. The goal is to introduce convexoptimization to a broad signal-processing community, provide insights into how convexoptimization can be used in a variety of different contexts, and showcase some notablesuccesses. The topics included are automatic code generation for real-time solvers, graphical models for autoregressive processes, gradient-based algorithms for signal-recoveryapplications, semidefinite programming(SDP)relaxation with worst-case approximationperformance, radar waveform design via SDP, blind non-negative source separation forimage processing, modern sampling theory, robust broadband beamforming techniquesdistributed multiagent optimization for networked systems, cognitive radio systems viagame theory, and the variational-inequality approach for Nash-equilibrium solutionsPrefaceThere are excellent textbooks that introduce nonlinear and convex optimization, providing the reader with all the basics on convex analysis, reformulation of optimizationproblems, algorithms, and a number of insightful engineering applications. This book istargeted at advanced graduate students, or advanced researchers that are already familiarwith the basics of convex optimization. It can be used as a textbook for an advanced graduate course emphasizing applications, or as a complement to an introductory textbookthat provides up-to-date applications in engineering. It can also be used for self-study tobecome acquainted with the state of-the-art in a wide variety of engineering topicsThis book contains 12 diverse chapters written by recognized leading experts worldwide, covering a large variety of topics. Due to the diverse nature of the book chaptersit is not possible to organize the book into thematic areas and each chapter should betreated independently of the others. a brief account of each chapter is given nextIn Chapter 1, Mattingley and Boyd elaborate on the concept of convex optimizationin real-time embedded systems and automatic code generation. As opposed to genericsolvers that work for general classes of problems, in real-time embedded optimization thesame optimization problem is solved many times, with different data, often with a hardreal-time deadline. Within this setup the authors propose an automatic code-generationsystem that can then be compiled to yield an extremely efficient custom solver for theproblem familyIn Chapter 2, Beck and Teboulle provide a unified view of gradient-based algorithmsfor possibly nonconvex and non-differentiable problems, with applications to signalrecovery. They start by rederiving the gradient method from several different perspectives and suggest a modification that overcomes the slow convergence of the algorithmThey then apply the developed framework to different image-processing problems suchas e1-based regularization, TV-based denoising, and Tv-based deblurring, as well ascommunication applications like source localizationIn Chapter 3, Songsiri, Dahl, and Vandenberghe consider graphical models for autore-gressive processes. They take a parametric approach for maximum-likelihood andmaximum-entropy estimation of autoregressive models with conditional independenceconstraints, which translates into a sparsity pattern on the inverse of the spectral-densitymatrix. These constraints turn out to be nonconvex. To treat them the authors proposea relaxation which in some cases is an exact reformulation of the original problem. Theproposed methodology allows the selection of graphical models by fitting autoregressiveprocesses to different topologies and is illustrated in different applicationsThe following three chapters deal with optimization problems closely related to SDPand relaxation techniquesIn Chapter 4, Luo and Chang consider the SDP relaxation for several classes ofquadratic-optimization problems such as separable quadratically constrained quadraticprograms(QCQPs)and fractional QCQPs, with applications in communications and signal processing. They identify cases for which the relaxation is tight as well as classes ofquadratic-optimization problems whose relaxation provides a guaranteed, finite worstcase approximation performance. Numerical simulations are carried out to assess theefficacy of the SDP-relaxation approach
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OpenCV中文参考手册
OpenCV中文参考文件，应用程序接口（API）中文参考资料al OpenCV参考手册·ΩpencⅤ编程简介(矩阵/图像/姒频的基本·Ω中文参考手册读写操作)入门必读· OpenCV概述1.图像处理2.结构分析CXCore中文参考手册3.运动分析与对象跟踪4.模式识别1.基础结构5.照相机定标和三维重建2.数组操作3.动态结构HgGU中文参考手册4.绘图函数5.数椐保存和运行时类型信息1. HighGUI概述6,其它混合函数2.简单图形界面7.錯误处理和系统函数3.读取与保存图傯4.视频读写数机器学习中文参考手册5.实用涵数与系统函数OpencⅤ编码样式指南(阅读 Opencv代码前必CIMage类参考手册读CiMage中的陷阱和BUGOpenCV的Phon接口Opengν编程简介(矩阵/图像/视频的基本读写操作)Wikipedia,自由的百科全书Introduction to programming with OpenCVOpencv编程简介作者: Gady AgamDepartment of Computer ScienceJanuary 27, 2006Illinois Institute of TechnologyUrl:http://www.cs.it.edu/ragam/cs512/lect-notes/opency-intro/opency-intro. html#SECTION00040000000000000000翻译: chenyusiyuanJanuary 26, 2010.http:/blog.csdn.net/chenyusiyuan/archive/2010/01126/5259060.aspx摘要:本文旨在帮助读者快速入门 Openc,而无需阅读冗长的参考手册。掌握了 Opencv的以下基础知识后,有需要的话再查阅相关的参考手册。目录[原]1二、简介o1.11、 Openc的特点1.1.1(1)总体描述(2)功能113(3) OpenCv模块122、有用的学习资源2.1(1)参考手册;122(2)网络资源1.23(3)书籍124(4)视瓶处理例程(在< openly-root>/ samples/c/)125(5)图像处理例程(在< openly-root>/ samples/c/0133、 openc命名规则2(2)矩阵数据类型:■1.33(3)图像数据类型134(4)头文件:o144、编译建议.14.1(lInux;1.4.2(2) Windowso155、C例程2二、GUI指令2.11、窗口管理2.1.1(1)创建和定位一个新窗口∶2.12(2)载入图像2.13(3)显示图後2.14(4)关团窗口2.15(5)改变窗o222、输入处理2.2.1(1)处理鼠标事件222(2)处理键盘事件■2.23(3)处理滑动条事件·3三、 OpenCV的基本数据结构o3.11、图像数据结构3.1.1322、知阵与向量3.2,1(1)矩阵3232).元批333、其它结构类型33.1(1)点332(2)矩框大小(以像素为精度)∵■333(3)矩形框的偏置和大4四、图像处理4,11、图像的内存分配与释放411(1)分配内存给一幅新图像4.1.2(2)释放图像■4.13(3)复制图像414(4)设置/获取感兴趣区域ROI415〈5)设置/获取感兴趣通道COI422、图像读写4.2,1(1)从文件中读入图像4.2.2(2)保存图o433、访回图像像素4.3.1(1)假设你要访间第k通道、翦列的像素43,2(2)间接访间;(通用,但效可访间任意格式的图像)433(3)直接访间:(效率高,但容易岀错)434(4)基于指针的直接访闻:(简单高效435(5)基于c++ wrapper的直接访间(更简单高效a444、图像转换441(1)字节型图像的灰度-彩色转换442(2)彩色图像->灰度图像44不同彩色空间之间的转換a455、绘图指令4.5,1(1)绘制矩形452(2)绘制圆形45.3(3)绘制线段454(4)绘制一组线段455(5)绘制组填充颜色的多边形:456(6)文本标注5五、矩阵处理o5,11、矩阵的内存分配与释放32(3)为新矩阵分配达存释放矩阵内存514(4)复制矩阵5,15(5)初始化矩阵5.1.6(6)初始化矩阵为单位矩阵522、访回矩阵元焘52.1(1)假设需要访间一个2D浮点型矩阵的第(i,j个单元,5.2.2(2)间接访间5.23(3)直接访间(假设矩阵数据按4宰节行对齐)524(4)直接访间(当数据的行对齐可能存在间隙时 possible alignment gaps)5,25(5)对于初始化后的矩阵进行直接i°533、矩阵/向量运算5.3,1(1)矩阵之间的运算532(2)矩阵之间的元素级运算:53,3(3)向量乘积534(4)单一矩阵的运535(5)非齐次线性方程求解■536(6)特征債与特征向量(矩阵为方阵)6六、视频处理611、从视频流中捕捉一帧画面61.2(2)Y支从摄像头或视频文件(AM格式)中捕捉帧画面6,11(1)open个摄像头捕捉器6,1,3(3)初始化一个祕频文件捕捉器614(4)捕捉一帧画面61.5(5)释放视频流捕捉o622、获取/设置视频流信息6,2.1(1)获取视频流设备信息6,2,2(2)获取帧图信息6,23(3)设置丛视频文件抓取的第一帧画而的位置∵633、保存视频文件6.3,1(1)初始化视频编写器6.3,2(2)保持视频文件63)释放视频编写器[编辑]简介[编辑]1、 OpenCV的特点[编辑](1)总体描述· Opencv是一个基于CC++语言的开源图像处理函数库其代码都经过优化,可用于实时处理图像具有良好的可移植性可以进行图像/视频载入、保存和采集的常规操作具有低级和高级的应用程序接口(API·提供了面向 Intel IPP高效多媒体函数库的接口,可针对你使用的 Intel CPU优化代码,提高程序性能(译注: OpenC2.0版的代码已显著优化,无需IPP来提升性能,故2.0版不再提供IPP接口)[编辑(2)功能图像数据操作(内存分配与释放,图像复制、设定和转换)Image data manipulation (allocation, release, copying, setting, conversion·图像/视频的输入输出(支持文件或摄像头的输入,图像/视频文件的输出)Image and video I/o (file and camera based input, image/video file output).矩阵/向量数据操作炇线性代数运算(矩阵乘积、矩阵方程求解、特征值、奇异值分解)Matrix and vector manipulation and linear algebra routines(products, solvers, eigenvalues, SVD)支持多种动态数据结构(链表、队列、数据集、树、图)Various dynamic data structures(lists, queues, sets, trees, graphs)·基本图像处理(去噪、边缘检测、角点检测、采样与插值、色彩变換、形态学处理、直方图、图像金字塔结构)Basic image processing(filtering, edge detection, corner detection, sampling and interpolation, colorconversion, morphological operations, histograms, image pyramids)·结构分析(连通域/分支、轮廓处理、距离转换、图像矩、模板匹配、霍夫变换、多项式逼近、曲线拟合、椭圆拟合、狄劳尼三角化)Structural analysis(connected components, contour processing distance transform, various momentstemplate matching, Hough transform, polygonal approximation, line fitting, ellipse fitting, Delaunaytriangulation).·摄像头定标(寻找和跟踪定标模式、参数定标、基本矩阵估计、单应矩阵估计、立体视觉匹配)Camera calibration(finding and tracking calibration patterns, calibration, fundamental matrixestimation, homography estimation, stereo correspondence).·运动分析(光流、动作分割、目标跟踪)Motion analysis(optical flow, motion segmentation, tracking)目标识别(特征方法、HMM模型Object recognition(eigen-methods HMM)基本的GUI(显示图像/视频、键盘/鼠标操作、滑动条)Basic Gui (display image/ video keyboard and mouse handling, scroll-bars)图像标注(直线、曲线、多边形、文本标注)Image labeling(line, conic, polygon, text drawing[编辑](3) Opencvi模块cv-核心函数库Vaux-辅助函数库:e0机数线性代数作m|-机器学习函数库[编辑]2、有用的学习资源[编辑](1)参考手册:< opencv-root>/ docs/index. htm(译注:在你的 OpenCV安装目录< opencv-root>内)[编辑](2)网络资源:Etkmi:http:/www.intel.com/technology/computing/opencvl[编辑](3)书籍:Open Source Computer Vision Libraryby Gary R Bradski, Vadim Pisarevsky, and Jean-Yves Bouguet, Springer, 1st ed. (June, 2006)chenyusiyuan:补充以下书籍Learning OpenCV -Computer Vision with the OpenCV Libraryby Gary Bradski Adrian Kaehler, O Reilly Media, 1 st ed(September, 2008)OpenCv教程——一基础篇作者:刘瑞祯于仕琪,北京航空航天大学出版社,出版日期:200706(4)视频处理例程(在< opencv-root>/ samples/c/):·颜色跟踪: camshiftdemo点跟踪:| kemo动作分割: motel边缘检测: laplace[编辑](5)图像处理例程(在< opencv-root>/ samples/c/)边缘检测:edge图像分割: pyramid_ segmentation形态学: morphology直方图: demist距离变换: distrains椭圆拟合: fitellipse[编辑]3、 OpenCv命名规则[编辑](1)函数名CvActionTargetMod(.)Act⊥cn=核e functionality)(e.g. set, create)Targettarget image area) (e, g. contour, polygon)Modih (optional modifiers) (e.g. argument type)[编辑](2)矩阵数据类型:CV_(SIUIF)Cs=符号整型UE,q.:Cv_8UC1是指_个8位无符号整型单通道矩阵CV 32FC2是指一个32位浮点型双道道矩阵[编辑](3)图像数据类型:IPL_DEPTH_⊥nc1ude< VAux.h>include inc⊥ ude sinclude /一般不需要,cv,h内已包含该头文件[编辑]4、编译建议[编辑](1)Linux:g++ helloworld. cpp-o hello-worldI /usr/local/include/opencv -L /usr/local/liblm-Icv-highqui-Icvaux[编辑](2)Windows在Ⅵ visual studio的选项和项目牛设置好 OpenCv相关文件的路径。[编]5、C例程hello-worid. cpp/该程序从文件中读入一幅图像,将之反色,然后显示出来⊥nc1udeinclude ⊥nc1ude#include #include highgui.h>int main (int argc, char argv[IplImage* img=0int height, width, step, channelsuchar *datai. i,i,kif(argcheight iwidthimg->widthStepimg->widthstep ichannelsimg->channelsdata(uchar *)img->imageData iprint f("Processing a dx%d image with d channels", height, width, channels)create a windowcvNamedwindow("mainwin CV WINDOW AUTOSIZEcvMoveWindow ("mainwin", 100, 100)t the image相当于 caNot(img);for(i-o; isheighti 1++) for(j=; j
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