本书阐述了国内外关于稀疏水声信号处理与压缩感知应用的研究与实验成果，同时融入了作者研究团队近几年来在该领域取得的一些重要研究成果，着重讨论了稀疏水声信号处理和压缩感知应用两个方面的内容。全书分7 章，包括绪论、水声信道的基本物理特性、范数约束与稀疏估计、稀疏水声信道的估计算法、压缩感知的稀疏化预处理、压缩感知理论、压缩感知应用等，提供了有关算法的伪代码及一些MATLAB 程序。本书可作为高等院校和科研机构海洋物理、水声通信、水声工程等专业高年级本科生或研究生及相关行业研究人员的参考书。

前 言 声波作为目前水下无线通信的信号传输媒介，在实践过程中遇到了与陆地无线电通信不一样的约束，例如，水下声能量随载波频率的增加而严重衰减，水下声波（简称水声）传播路径具有多变性，传播速度约为1500 m/s。这些约束使得水声信道具有较为明显的时延多普勒双扩展等现象。本书以稀疏信号处理为应用背景，对水声信道的稀疏性特点、水声信道中的物理特性、传播机制等进行分析，研究了水声信道的估计方法。此外，在具体分析稀疏化表示方法和压缩感知基本原理的基础上，结合水声工程背景，阐述了水声遥测方面的研究进展和相关成果。 本书汇集了国内外先进的研究与实验成果，同时融入了作者研究团队近几年来在该领域取得的创新性研究成果。全书分7 章：第1 章介绍了水声学的一些基础知识，包括与水声相关的相关物理量及其计算、水声信道传播模式、水声信道传播损失规律、声呐系统等；第2 章主要介绍了水声信道的基本物理特性，包括水声传播和信道传输特性等；第3 章介绍了范数约束下的水声信道稀疏估计方法，在范数化向量空间引入稀疏估计代价函数；第4 章主要介绍了稀疏水声信道的估计算法，包括向量模式和矩阵与向量相结合的估计算法，对其进行了分析与讨论，并结合仿真和海试进行验证；第5 章介绍了压缩感知的稀疏化预处理的常用方法；第6 章介绍了压缩感知理论，包括基本概念、模型、性质、6 种典型的贪心算法及MATLAB 程序；第7 章介绍了压缩感知应用，包括对水声信道估计的进一步探讨、水声数据遥测中的应用、压缩感知在变电站噪声源定位中的应用。著者采用朴实易懂的语言总结了压缩感知在水声信道估计方面取得的研究成果，重点介绍了著者研究团队近几年来在压缩感知应用方面所做的工作，特别感谢西北工业大学航海学院的雷志雄、段睿博士、田天、孙权、朱云超和西安电子科技大学计算机学院的伍佳会，他们参与了本书的编排和整理工作。同时，感谢中山大学的杨智教授、谢燕江、钟旺盛、詹俦军、彭璐、刘撷捷、许清媛，以及厦门大学的许肖梅教授、周振强博士、陈维、陈楷、李芳兰、周跃海、曾堃、曹秀岭、江伟华、陈磊给予的帮助和支持；感谢美国阿拉巴马大学的宋爱军教授 提供的指导意见；感谢美国特拉华大学的王栋、廖恩惠、卢文芳、沙金、马夷、谢胜柏、颜秀利、卓著、严义豪、李承飞等提供的帮助和支持。 本书可作为高等院校和科研机构海洋物理、水声通信、水声工程等专业高年级本科生或研究生及相关行业研究人员的参考书。本书由国家自然科学基金（批准号：61701405）、中央高校基本科研业务费专项资金（批准号：3102017OQD007）、中国博士后科学基金（批准号：2017M613208）资助完成。 由于著者学识有限，书中定然存在不足之处，恳请读者批评指正。著者电子邮箱：wfy@nwpu.edu.cn。 著 者 2017 年8 月

目 录 第1 章 绪论 ··················································································································.1 1.1 与水声相关的物理量及其计算 ···········································································.2 1.1.1 水声能量及其计算 ···························································································.2 1.1.2 参考声压和分贝及其计算 ···············································································.3 1.2 水下声速变化特性 ·································································································.4 1.3 水声信道中3 种特殊传播模式 ···········································································.7 1.4 水声信道传播损失规律 ························································································.8 1.5 声呐系统 ··········································································································.11 1.5.1 声呐方程 ·········································································································.11 1.5.2 声呐方程的检测阈值 ······················································································.15 1.5.3 噪声与混响环境下检测阈值的设置 ·······························································.17 本章小结 ················································································································.19 第2 章 水声信道的基本物理特性 ····················································································.20 2.1 海面水声信号的传播特性 ···················································································.20 2.2 海底水声信号的传播特性 ···················································································.23 2.3 水声传播的多途效应 ····························································································.27 2.4 水声信道的选择性衰落 ·······················································································.28 2.5 多途信道的系统函数 ····························································································.29 2.6 水声信号的匹配滤波处理 ···················································································.31 本章小结 ·····················································································································.33 第3 章 范数约束与稀疏估计 ·····················································································.34 3.1 近似范数约束项与稀疏估计代价函数 ····························································.34 3.2 范数化的向量空间 ································································································.35 3.3 范数约束项与稀疏估计代价函数设计 ····························································.37 3.4 基于近似l0 范数约束的稀疏估计算法 ····························································.39 本章小结 ·················································································································.42 第4 章 稀疏水声信道的估计算法 ····················································································.43 4.1 稀疏水声信道的向量估计算法 ··········································································.43 4.1.1 问题描述 ·········································································································.43 4.1.2 向量估计方法与信道估计目标函数 ·······························································.45 4.1.3 数值仿真分析 ·································································································.52 4.1.4 海试验证 ·········································································································.54 4.2 稀疏水声信道的矩阵估计算法 ··········································································.58 4.2.1 问题描述 ·········································································································.59 4.2.2 基于压缩感知的矩阵估计算法 ······································································.60 4.2.3 数值仿真分析 ·································································································.64 4.2.4 海试验证 ·········································································································.68 本章小结 ·················································································································.74 第5 章 压缩感知的稀疏化预处理 ····················································································.75 5.1 离散余弦变换 ·········································································································.76 5.2 离散小波变换 ·········································································································.78 5.3 6 种多尺度几何分析 ·····························································································.94 5.3.1 脊波（Ridgelet）变换 ····················································································.94 5.3.2 曲波（Curvelet）变换 ····················································································.94 5.3.3 轮廓波（Contourlet）变换 ·············································································.95 5.3.4 条带波（Bandelet）变换 ················································································.96 5.3.5 楔波（Wedgelet）变换 ···················································································.97 5.3.6 小线（Beamlet）变换 ·····················································································.97 5.4 稀疏表示 ···············································································································.98 5.5 信号的低秩分析 ···································································································.101 本章小结 ··················································································································.104 第6 章 压缩感知理论 ··································································································.105 6.1 压缩感知简介 ·······································································································.105 6.2 基本概念 ········································································································.109 6.2.1 基和框架? ··································································································.109 6.2.2 低维信号模型 ·······························································································.109 6.2.3 可压缩信号 ···································································································.110 6.2.4 子空间的有限并集 ························································································.110 6.2.5 感知矩阵的有关概念 ····················································································.110 6.2.6 感知矩阵的构造 ····························································································.113 6.3 稀疏信号恢复算法 ······························································································.114 6.3.1 l1 范数最小化算法 ·························································································.114 6.3.2 基追踪和基追踪降噪方法 ············································································.117 6.4 信号恢复算法 ·······································································································.130 6.5 6 种典型的贪心算法 ···························································································.131 6.5.1 正则化正交匹配追踪 ····················································································.131 6.5.2 压缩采样匹配追踪 ························································································.135 6.5.3 分段正交匹配追踪 ························································································.138 6.5.4 子空间追踪 ···································································································.141 6.5.5 稀疏度自适应追踪 ························································································.142 6.5.6 广义正交匹配追踪 ························································································.146 本章小结 ···············································································································.149 第7 章 压缩感知应用 ·······························································································.152 7.1 压缩感知在稀疏水声信道估计中的应用 ······················································.152 7.2 水声信道的时延-多普勒双扩展模型探讨 ····················································.154 7.3 水声双扩展信道估计研究概述及未来工作展望 ········································.156 7.4 压缩感知在水声数据遥测中的应用 ·······························································.158 7.5 压缩感知在变电站噪声源定位中的应用 ······················································.163 7.5.1 变电站噪声源定位算法简介 ········································································.164 7.5.2 基于压缩感知的合成孔径技术 ····································································.167 参考文献 ·············································································································.174