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。

伍飞云，博士，毕业于厦门大学海洋与地球学院，2016年任职于西北工业大学航海学院声学与信息工程系和水声工程国家重点实验室，助理教授，2017年获得国家自然科学青年基金资助。

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