稀疏场景雷达成像采样率的信息论分析

发布时间：2018-06-07 16:23

本文选题：信息论 + 压缩感知　；参考：《武汉大学》2015年博士论文

【摘要】：稀疏微波成像(sparse microwave imaging)是近年来提出的微波成像的新理论、新体制和新方法。其本质是将压缩感知(Compressed Sensing, CS)等稀疏信号处理理论与传统雷达成像理论相结合,以改进现有的雷达成像体制与方法,并逐步形成基于压缩采样(compressive sampling)与非线性重构的CS-Radar成像方法和技术体系。雷达压缩感知(radar compressive sensing)或压缩感知雷达成像(compressed sensing based radar imaging),是稀疏微波成像框架下、压缩感知与传统雷达成像理论的结合与应用。压缩感知(CS)对信号使用随机投影的量测方式,能以低于Nyquist率的采样率采集信号的有效信息并能通过其特殊处理方法恢复原始信号,从而实现数据压缩。作为一种新的信息采集和处理方法,压缩感知对于雷达应用而言具有重要意义：CS中所用的欠采样方式可以减少雷达原始数据的采样率,同时CS重构算法相对经典信号处理算法具备潜在的替代性。在压缩感知及其雷达成像应用的研究中,压缩采样条件是重要的研究内容。对于压缩采样的采样数条件,现有的分析方法包括基于组合几何以及基于信息论的分析方法。由于雷达成像与一般性压缩感知问题存在观测矩阵选择等方面不同,基于组合几何的采样条件分析的经典方法无法直接使用。信息论是运用概率论和数理统计的方法研究通信与信息传输、数据压缩等问题的应用数学分支；作为信息科学领域的普适性理论之一,对于评判新型成像系统的性能具有特定的指导作用。在雷达设计方面,信息论中的互信息等概念是雷达波形设计中使用的重要工具,同时也为雷达的分辨率与信息量的研究提供了理论指导；在压缩感知的研究方面,信息论是研究压缩感知的性能极限的有效工具。尽管信息论在雷达或压缩感知的研究中早已发挥重要的作用,然后对于雷达成像与压缩感知二者结合的问题,以信息论为出发点的研究并不多见。这也是本文以信息论为主要理论支撑研究雷达成像压缩采样条件的初衷与研究意义所在。本文的主要研究目标是在压缩感知和信息论的理论框架下,研究CS-Radar成像环境下的压缩采样问题；具体而言,运用信息论中的信息量与编码有关概念和原理建立雷达成像中压缩感知问题的信息论模型,并分析雷达成像在无失真重构和限失真近以重构条件下的采样数条件。具体的研究工作包括：(1)阐述经典雷达成像与基于压缩感知的雷达成像的基本概念和理论基础。对雷达信号的组成及信号处理方法进行描述,介绍经典雷达成像理论和压缩感知理论,并说明雷达成像的经典算法与压缩感知算法。(2)从经典采样定理的扩展与延伸出发引出压缩采样,介绍对于常规压缩感知问题的压缩采样条件的经典分析方法和信息论分析方法。重点梳理了常规压缩采样条件的信息论分析方法,包括从信源、信道及编码等概念；最后通过雷达成像的模拟实验分析基于压缩感知或基于信息论的现有分析方法对于CS雷达成像研究的局限性。(3)从信息论的角度分析稀疏雷达场景的无失真重构条件。聚焦到对稀疏场景实施雷达压缩采样这一过程,建立稀疏场景的雷达观测的信源-信道模型。对于稀疏场景的雷达观测,首先给出雷达场景的稀疏信源模型以及相关模型参数的估计方法；从而可以计算稀疏场景本身带有的信息量,再以信道容量为工具定量分析雷达观测矩阵的信息通过能力；最后从无失真信息重构的原理出发,分析雷达压缩采样前提下是否能实现无失真场景重构的条件。(4)利用互信息和率失真为工具研究稀疏场景近似重构的雷达降采样条件,即CS雷达的降采样比、信噪比及场景稀疏度等参数之间的关系。依照限失真信息传输条件,从信息最小冗余的原则出发给出CS-Radar成像中对降采样比等条件的最低要求,并与现有的基于计算实验的相变图等分析方法进行对比分析,以验证基于信息论的分析方法的有效性和优越性。本文依据基于信源-信道模型及其信息量条件的分析与验证方法,通过对压缩采样条件下、稀疏场景的无失真重构和限失真重构的采样条件的理论分析与实验,分析或验证了不同重构条件下的压缩采样的适用性及其采样数条件。本文的主要贡献和创新点有：(1)提出了一种基于高斯混合模型的建模方法,实验证明能有效实现稀疏场景的雷达成像建模。(2)提出了一种雷达压缩采样的信源-信道分析方法,实验证明能有效扩展现有信源熵及信道容量的无失真重构计算。(3)提出了一种限失真采样数条件分析方法,实验证明具有雷达成像最小信息冗全时塞失直条件下的右效性和优越性。
[Abstract]:Sparse microwave imaging (sparse microwave imaging) is a new theory, new system and new method of microwave imaging proposed in recent years. Its essence is to combine the sparse signal processing theory of compressed sensing (Compressed Sensing, CS) with the traditional radar imaging theory, in order to improve the existing radar imaging system and method, and gradually form a pressure based on pressure. CS-Radar imaging methods and technical systems of compressive sampling and nonlinear reconstruction. Radar compression perception (radar compressive sensing) or compressed sensing radar imaging (compressed sensing based radar imaging) are the combination and application of compression perception and traditional radar imaging theory under the framework of sparse microwave imaging. Compression sense Knowing (CS) the method of using random projection to signal the signal, can collect the effective information of the signal with the sampling rate below the Nyquist rate and can recover the original signal through its special processing method, so as to realize the data compression. As a new information acquisition and processing method, the compression sense is of great significance to the radar application: in CS Using the undersampling method can reduce the sampling rate of radar original data, while the CS reconstruction algorithm has potential alternative to the classical signal processing algorithm. In the research of compressed sensing and radar imaging application, the compression sampling condition is an important research content. Based on combinatorial geometry and analysis based on information theory, the classical method of sampling condition analysis based on combinatorial geometry cannot be used directly because of the difference in the selection of observation matrix in radar imaging and general compression perception. The theory of information is the use of probability theory and mathematical statistics to study communication and information transmission. The branch of Applied Mathematics, such as compression, as one of the universality theories in the field of information science, has a specific guiding role in evaluating the performance of the new imaging system. In radar design, the concept of mutual information in the information theory is a critical tool used in radar waveform design, and also for radar resolution and information. Quantitative research provides theoretical guidance; information theory is an effective tool to study the performance limits of compressed perception in the study of compressed perception. Although information theory has played an important role in the research of radar or compressed sensing, information theory is the starting point for the combination of radar imaging and compression perception of the two. This is also the original intention and significance of studying the compression sampling conditions of radar imaging with information theory as the main theory. The main goal of this paper is to study the problem of compressed sampling in the CS-Radar imaging environment under the theoretical framework of compressed sensing and information theory; specifically, using information in the information theory The information theory model of the compression perception in radar imaging is established by the concepts and principles of interest and coding, and the conditions for the sampling number of radar imaging under the conditions of distortion reconstruction and limited distortion near the reconstruction are analyzed. The specific research work includes: (1) the basic concepts and principles of classical radar imaging and radar imaging based on compressed sensing are described. On the basis of the description of the composition and signal processing methods of radar signals, the classical radar imaging theory and compression perception theory are introduced, and the classic algorithms and compressed sensing algorithms for radar imaging are described. (2) the compression sampling is introduced from the extension and extension of the classical sampling theorem, and the compression sampling strip for conventional compression sensing is introduced. The classical analysis method and the information theory analysis method, focusing on the information theory analysis method of conventional compression sampling conditions, including the concepts of source, channel and coding. Finally, the limitations of CS radar imaging research based on compressed sensing or information based analysis are analyzed by simulation experiments of radar imaging (3 From the point of view of information theory, this paper analyzes the undistorted reconstruction condition of sparse radar scene, focusing on the process of radar compression sampling for sparse scene, and establishing the source channel model of radar observation in sparse scene. For radar observation of sparse scene, the sparse source model of radar scene and the parameter estimation of related model are given first. It can calculate the information amount of the sparse scene itself, and then analyze the information of the radar observation matrix by the channel capacity as a tool. Finally, based on the principle of the reconstruction of the undistorted information, the condition of realizing the reconstruction of the undistorted scene under the precondition of radar compression is analyzed. (4) use the mutual information and rate. Distortion is used to study the radar drop sampling condition of sparse scene reconstruction, that is, the relation between the CS radar's drop sampling ratio, the signal to noise ratio and the scene sparsity. According to the transmission condition of the distortion information, the minimum requirement for the reduced sampling ratio in the CS-Radar imaging is given from the principle of minimum information redundancy, and the existing conditions are also given. The analysis method of phase transformation graph based on computational experiments is compared to verify the effectiveness and superiority of the information based analysis method. Based on the analysis and verification method based on the source channel model and the information quantity condition, the sampling of the sparse scene reconstruction and the reconstruction of the limited distortion under the compressed sampling condition Theoretical analysis and experiment of conditions, the applicability and sampling conditions of compressed sampling under different reconfiguration conditions are analyzed or verified. The main contributions and innovation points of this paper are as follows: (1) a modeling method based on Gauss mixed model is proposed. The experiment proves that the radar imaging modeling can be effectively implemented in sparse sparse scenes. (2) a kind of thunder is proposed. The source channel analysis method of compressed sampling is proved to be effective in expanding the undistorted reconstruction calculation of the existing source entropy and channel capacity. (3) a conditional analysis method for the limited distortion sampling number is proposed. The experiment proves that the right efficiency and superiority of the radar imaging minimum information redundancy is proved.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P225.1

【相似文献】