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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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基于FPGA的图像识别常用算法的设计，Sobel边缘检测，肤色识别算法，腐蚀膨胀算法，中值滤波算法，均值滤波

为matlab源码，实现了超分辨率图像重建算法。

BP神经网络分类MATLAB代码+测试数据，亲测绝对可运行，绝对业界良心

北京航空航天大学研究生数学必修课程，数值积分大作业。

熵阈值法是图像分割中的重要方法, 并在图像处理中得到了广泛的应用。针对香农熵阈值法因存在对数计算而导致计算量过大的问题,这里运用一种新的信息熵; 并用于图像分割的阈值选取，Tsallis熵及其灰度熵的分割方法不仅降低了计算复杂度，而且分割效果更好。

详细的讲解了SVPWM的过程，及其仿真，很适合初学者或(37)即磁链空间矢量可以等效为电压空间矢量的积分,如果能够控制电压空间矢量的轨迹为如式(3.4)所示的圆形矢量,那么磁链空间矢量的轨迹也为圆形。这样,电动机旋转磁场的轨迹问题就可以转化为电压空间矢量的运动轨迹问题。进一步分析,由式(3.3)(3.5)(3.7)可以得到公式(3.8)∫-+yy(38)对电压积分,利用等式两边相等的原则有(39)其中,v为电机磁链的幅值,即为理想磁链圆的半径。y当供电电源保持压频比不变时,磁链圆半径v是固定的。在 SVPWM控制技术中,是取以y为半径的磁链圆为基准圆的。32逆变器电压的输出模式图32给出了电压源型PWM逆变器—异步电动机示意图14。昇步电动机定子绕组YY图3.2PWM逆变器电路(1~6为GBT)对于180°导电型的逆变器来说,三个桥臂的六个开关器件共可以形成8种开关模式。用分别标记三个桥臂的状态,规定当上桥臂器件导通时桥臂状态为1,下桥臂导通时桥臂状态为0,这样逆变器的八种开关模式对应八个电压空间矢量,其中为直流侧电压在逆变器的八种开关模式中,有六种开关模式对应非零电压空间矢量,矢量的幅值为一;有两种开关模式对应的电压矢量幅值为零,称为零矢量。当零矢量作用于电机时不形成磁链矢量;而当非零矢量作用于电机时,会在电机中形成相应的磁链矢量。对于每一个电压空间矢量,可由图32求出各相的电压值,再将各相的电压值代入式(3.3),可以求得电压空间矢量的位置。下面以开关状态)=(、0、0)为例,即开关导通,其余关断。逆变电路的形式可以变为B相和C相并连后再和A相串连的形式,易得将其数值代入式(33),可得采用同样的方法可以得到如表31所示的逆变器空间电压矢量。表31逆变器的不同开关状态对应的空间矢量表相电压矢量表达式定子电压开关状态(Us大小为空间矢量A相B相C相0000000101001110010111100由于 SVPWM控制的是逆变器的开关状态,在实际分析逆变器一电动机系统时,可以通过分析逆变器输出的电压空间矢量来分析电机定子电压的空间矢量,下面给出证明。设逆变器输出的三相电压为、,由图3.2可求出加到电机定子上的相电压为(310)其中,为电机定子绕组星接时中点0相对于逆变器直流侧点的电位。电机定子电压空间矢量为(311)而由三角函数运算知++因此,逆变器输出的电压空间矢量为(312)由式(3.12)可知,在PWM逆变器一电动机系统中,对电机定子电压空间矢量的分析可以转化为对逆变器输出电压空间矢量的分析。这时,在求解表3.1时,可以直接利用逆变器输出的电压合成得到,即A,B,C三相输出电压值只有一和-—两个值。当逆变器输出某一电压空间矢量时,电机的磁链空间矢量可表示为y =y3.13)其中,W为初始磁链空间矢量;△为的作用时间。当为某一非零电压矢量时,磁链空间矢量y从初始位置出发,沿对应的电压空间矢量方向,以为半径进行旋转运动,当为一零电压矢量时,W=y,磁链空间矢量的运动受到抑制。因此合理地选择六个非零矢量的施加次序和作用时间,可使磁链空间矢量顺时针或逆时针旋转形成一定形状的磁链轨迹。在电机控制当中尽量使磁链轨迹逼近正多边形或圆形。同时,在两个非零矢量之间按照一定的原则,比如开关次数最少,插入一个或多个零矢量并合理选择零矢量的作用时间,就能调节ψ的运动速度。33SWPM的具体实现方法在实际应用中,应当利用 SVPWM自身的特点找到控制规律,避开复杂的数学在线运算,从而较为简单的实现开关控制,本节将给出实现 SVPWM的具体方法。根据3.2节中给出的不同开关状态组合可以得到如图33的电压空间矢量图C图3.3 SVPWM矢量、扇区图通常在矢量控制的系统当中,根据控制策略,进行适当的巫标变换,可以给出两相静止坐标系即(a,B)坐标系电压空间矢量的分量,g,这时就可以进行 SVPWM的控制,具体要做以下三部分的工作如何选择电压矢量。2.如何确定每个电压矢量作用的时间。3.确定每个电压矢量的作用顺序3.3.1电压空间矢量的空间位置这里需要引入扇区的概念,将整个平面分为六个扇区。如图3.3所示,每个扇区包含两个基本矢量,落在某个扇区的电压空间矢量将由扇区边界的两个基本电压空间矢量进行合成。在确定扇区时,引入三个决策变量A,B,C。根据给出的待合成的空间矢量的两个分量,p来决定A,B,C的取值,有以下关系式所在扇区的位置为当N取不同的值对应的扇区位置如图3.3所示,这样给定一个空间电压矢量就可以确定其所在的扇区。33.2电压空间矢量的合成扇区确定之后,就可以利用扇区边界上的两个基本矢量合成所需的矢量在合成过程中应当使得两个基本矢量的合成效果接近于期望矢量的效果。于是采用伏秒平衡的原则,以图3.3所示的第Ⅲ扇区为例,以a尸轴为基准,将两个基本矢量向aB轴上投影,应当有轴:=||+尸轴其中,为对应电压矢量作用的时间(=),为采样周期,通常为PW的调制周期。且|=||=-。求解上面两式可以得到这两个基本矢量的作用时间如式3.14(314)通过上面的方法即可以确定基本矢量的作用时间,当需要合成的矢量位于各个不同的扇区时都存在如上的运算。通过对每个扇区基本矢量动作时间的求解不难发现它们都是一些基本时间的组合。所以给出几个基本的时间变量x,Y,Z。定义√(315)通过计算可以得到在每个扇区内的基本矢量动作时间,(由于五段和七段式的实现方法不同,所以这里没有考虑矢量的动作顺序,仅按照逆时针方向)。设每个刷区的两个基本矢量动作的时间为于是可以得到矢量动作时间表3,2表3.2的对应关系表扇区ⅣV在实际的应用中当给定的电压值太大时会出现过调制的情况,即+>。此情况出现时,还要对上述计算出来的电压矢量的作用时间进行调整,具体方法如式3.16所示。(316)即为调整后的动作时间。在一个P啊M周期内除了非零电压矢量的作用,还要有零电压矢量的作用,零电压矢量包括对于这两个矢量的作用时间,以及开关的动作顺序,取决于采用的SPwM是五段式还是七段式,3.3节将对这两种PWM形式进行详细的介绍3.4 SVPWM的硬件实现和软件实现TI公司的TM320LF2407A系列的DSP内部有硬件来实现 SVPWM,由于每个PWM周期被分为五段,因此也被称为五段式的 SVPWM。在每个PWM调制周期内,开关状态有五种,且关于周期中心对称。而七段式的SvPM在每个PWM调制周期内有七种开关状态,需要运用软件进行实现,因此也被称为 SVPWM的软件实现。需要注意的是,无论哪种方法,所遵循的基本原则是开关动作次数最少,每个开关在一个周期内最多动作两次。3.4.1五段式 SVPWM对于五段式的 SVPWM,只在PMM周期的中间插入零矢量,具体采用哪一个由硬件根据旋转方向和开关动作次数最少的原则自行决定。例如在第Ⅲ扇区内,如果旋转方向为逆时针时针,则先动作,后动作以此类推,动作时间可以直接采用表3.2中的数据即可,然后选择零矢量(硬件决定)即可使开关次数最少。对于五段式PWM而言,零矢量作用的时间可以表示为:根据上述的配置原则,在每个扇区内开关动作的示意图如图34所示202ⅣV/1Ⅵ图34每个扇区内的开关动作示意图每个TMS320LF2407A的事件管理器EV模块都具有十分简化的电压空间矢量PWM波形产生的硬件电路。编程时只需进行如下的配置2●设置 ACTRX寄存器用来定义比较输出引脚的输出方式,决定高电平还是低电平有效,正反转,所在扇区等。●设置COMC0Nx寄存器来使能比较操作和空间矢量PWM方式,并且把 CMPRX的重装条件设置为下溢●将通用定时器1或2,4或5设置成连续增/诚计数模式,并启动定时器。然后给据在两相静止(a6)坐标系下输入到电机的电压空间矢量,分解为,确定如下的参数●所期望的矢量所在的扇区。根据 SVPWM的调制周期计算出两个基本的空间矢量和零矢量作用的时间

有5个电机仿真模型，包括开环V/F，永磁同步电机矢量控制、异步电动机的矢量控制、直接转矩控制等，欢迎下载、交流。

霍夫曼（Huffman）编码算法是满足前缀条件的平均二进制码长最短的编码算法。其编码思想是将较长的编码码字分配给较小概率的信源输出符号，而将较短的编码码字分配给较大概率的信源输出。文章详细描述了Huffman编解码的算法和matlab实现，程序已经过验证，可以直接使用