基于压缩传感的信号重构算法及应用研究

发布时间：2018-05-03 00:37

本文选题：压缩传感 + 信号重构　；参考：《燕山大学》2014年硕士论文

【摘要】：传统的奈奎斯特采样定理要求采样信号的频率必须大于或等于原始信号频率的两倍才能保证不失真的恢复出原始信号，这无疑给信号处理的能力提出了更高的要求，也给相应的硬件设备带来了极大的挑战。压缩传感理论突破了传统的香农采样定理，以远低于奈奎斯特采样频率的非适应性测量和优化方法高概率重构信号。本文主要针对目前压缩传感重构算法在测量值数目和重建质量上的一些不足进行了深入的研究并做出了一些改进。首先，针对目前压缩传感理论的经典重构算法进行了分析与仿真，主要包括基于l0范数最小化的贪婪系列算法和基于l1范数最小化的经典算法，并且针对现有重构算法在对图像进行处理时按列处理的缺陷，提出了一种行列均衡的改进方案，实验证明该方案提高了重构质量。其次，针对目前CS重构中l1范数优化在某些测量值很少的情况下不能精确地重构出原始信号的不足，提出采用l p(0p1)范数代替l1范数，并且将参数规则化引入到算法中，提出了一种参数规则化的IRLS算法，实验证明改进的算法提高了对稀疏信号的恢复能力。此外，针对所提算法在重构二维图像时存储量大、重构时间较长的缺点，将分块思想引入到该算法中，提高了重构速度。最后，针对目前无线传感器网络的能量有限性问题，提出将压缩传感应用于无线传感器网络中，实验证明，CS与WSN的结合，，降低了网络的能耗，延长了网络的生命周期。
[Abstract]:The traditional Nyquist sampling theorem requires that the frequency of the sampled signal must be greater than or equal to twice the frequency of the original signal in order to guarantee the recovery of the original signal without distortion, which undoubtedly puts forward higher requirements for the ability of signal processing. It also brings great challenges to the corresponding hardware equipment. The compression sensing theory breaks through the traditional Shannon sampling theorem and uses the non-adaptive measurement and optimization method to reconstruct signals with high probability which is far lower than Nyquist sampling frequency. In this paper, the shortcomings of the current compression sensor reconstruction algorithm in the number of measured values and reconstruction quality are studied and some improvements are made. Firstly, the classical reconstruction algorithms of compression sensing theory are analyzed and simulated, including greedy series algorithms based on l0 norm minimization and classical algorithms based on L1 norm minimization. Aiming at the defects of the existing reconstruction algorithms in processing images by column, an improved scheme of row and column equalization is proposed, which is proved by experiments to improve the reconstruction quality. Secondly, aiming at the deficiency of L 1 norm optimization in CS reconstruction which can not accurately reconstruct the original signal in some cases where the measurement value is very small, this paper proposes to replace l 1 norm with l 1 norm by using l p0 p 1) norm, and introduces the parameter regularization into the algorithm. A parameterized IRLS algorithm is proposed. The experimental results show that the improved algorithm improves the recovery ability of sparse signals. In addition, in view of the disadvantages of the proposed algorithm, such as large storage and long reconstruction time, the proposed algorithm is introduced into the algorithm to improve the reconstruction speed. Finally, aiming at the problem of limited energy in wireless sensor networks at present, the application of compressed sensing in wireless sensor networks is proposed. Experiments show that the combination of CS and WSN reduces the energy consumption and prolongs the lifetime of wireless sensor networks.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

【参考文献】