压缩感知方法及在探地雷达信号采集中的模拟研究

发布时间：2018-07-27 09:14

【摘要】：由于地下不同介质介电性质等存在差异,探地雷达可以通过激发和接收电磁波来反应地下的情况。在信号采集端,为了遵循奈奎斯特采样定律,以及由此导致的采集数据量过大,使得在雷达仪器设备的研发中产生很多困难。压缩感知作为一种新的信号采集与成像技术,在信号满足自身稀疏或在变换域中稀疏的条件下,能通过采集到远低于奈奎斯特的数据量恢复原始信号,这对减轻仪器设备的存储压力具有实际意义。论文研究了采样定律及传统仪器设备数字信号采集的机制。讨论了探地雷达信号的稀疏特性。研究了欠定线性系统的特征以及通过p范数来提高欠定线性系统解的稀疏性。压缩感知实际上是在信号采集的同时实现了数据压缩,是一个降维采样的过程,而不是在信源编码意义上的压缩。它主要由信号的稀疏表示,信号的采集和恢复三大部分组成。论文对压缩感知的重构算法(正交匹配追踪和基追踪)在恢复信号时的误差;支撑集正确概率;计算复杂度等方面进行了对比研究。本文建立了一个包含地下目标体的仿真模型,对地下空间离散化,同时通过创建字典将雷达信号与地下目标体相关联,用低维高斯随机矩阵采集信号。模拟试验说明了通过压缩感知可以极大地减少数据采集量并实现地下目标体的重构成像。
[Abstract]:Because of the difference in dielectric properties of different subterranean media, GPR can react underground by excitation and reception of electromagnetic waves. In order to follow the Nyquist sampling law and the large amount of data collected from it, it makes a lot of difficulties in the R & D of radar instruments. Compression perception is made. It is a new signal acquisition and imaging technique, which can recover the original signal by collecting far less than Nyquist's data in the condition that the signal is sparse or sparse in the transform domain. This is of practical significance to reduce the storage pressure of the instrument and equipment. The sparsity of the ground penetrating radar signal is discussed. The characteristics of the underdetermined linear system and the sparsity of the undetermined linear system are improved by the p norm. The compressed sensing is actually compressing the data at the same time when the signal is collected, it is a path of reducing the dimension of the sampling, not the compression of the source code. It is mainly composed of signal sparse representation, signal acquisition and recovery three parts. This paper makes a comparative study on the reconstruction algorithm of compressed sensing (orthogonal matching tracking and base tracking) in the recovery signal, the correct probability of the support set, and the computational complexity. A simulation model containing the underground target body is established in this paper. At the same time, the subsurface space is discretized and the radar signal is associated with the underground target body by creating a dictionary. The low dimensional Gauss random matrix is used to collect the signal. The simulation experiment shows that the data acquisition can be greatly reduced and the reconstruction imaging of the underground target body can be realized by compression perception.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.3

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