摘要传统的采样信号的方法包括四步：采样、压缩、传输和解压缩[1]。为了降低 传输、存储、传感器采集等等的成本，大量研究人员重点放在数据压缩和降维工 作上。但之前的研究需要用户先获得原始数据和存储，然后压缩和发送数据。这 个过程给传感器带来了巨大的负担。在实际应用中，很难满足需求实时采集数据。 相反，如果我们使用“压缩感知”技术直接获得的压缩信号，它将大大减少采集 数据的时间和存储空间需求。大部分信号具有可稀疏性，易于分析。因此 CS 已 经得到了广泛关注。83821

本文的目的是介绍和理解压缩感知理论的原理和运用，第二章将详细介绍其 数学模型，第三、四两章介绍其在雷达、声呐中的运用。压缩感知运用的核心是 设计一个基于压缩感知的信号测量矩阵，实现低成本的信号采集。基于压缩感知 的信号采样方法突破了奈奎斯特采样定理的限制。选取最佳重构效果的矩阵作为 信号测量矩阵，通过对测量矩阵信号的分析，将高维信号投影到低维空间，再对 数据进行压缩，并用较少的观测值对原始信号进行重建。根据 MATLAB 仿真实验 的结果，本文将介绍压缩感知理论对信号恢复的效果。

毕业论文关键字：稀疏表示；压缩感知；SAR 成像；声呐通信

Abstract The traditional sampling method includes four steps: sampling, compression, transmission and decompression。 In order to reduce the cost of transmission, storage, sensor acquisition and so on, a large number of researchers focus on data compression and dimension reduction work。 But before the research ,we need the user to obtain the original data and storage, and then compress and send the data。 This process brings a great burden to the sensor。 In practical application, it is difficult to meet the demand of real-time data acquisition。 Conversely, if we use the "compressed sensing" technology directly to obtain the compression signal, it will significantly reduce the time and storage space acquisition data needs。 Most of the signals are sparse and easy to analyze。 So CS has received wide attention。

The aim is to present and understand compressed sensing theory principles and application。 The second chapter will detail the mathematical model and the third, chapter four introduced its application in radar and sonar。 The core of compressed sensing application is to design a signal measurement matrix based on compressed sensing, which can realize the signal acquisition of low cost。 The signal sampling method based on compressed sensing breaks through the limitation of the Nyquist sampling theorem。 Select the best reconstruction of the effect of matrix as the signal measurement matrix, through analysis of signal measurement matrix, high-dimensional signal is projected to a low dimensional space, and compressing the data, and the use of a few observation values, to reconstruct the original signal。 According to the results of MATLAB simulation experiment, this paper will introduce the effect of compressed sensing theory on signal recovery。

Keywords: sparse representation； compressed sensing； SAR imaging,； Sonar communication

目 录

第一章 绪论 1

1。1 引言 1

1。2 研究背景及其意义 1

1。3 发展与现状 2

第二章 压缩感知理论 4

2。1 信号的稀疏分解 4

2。1。1 稀疏信号