基于相位恢复阈值算法与内投影神经网络算法的稀疏信号重构

发布时间：2018-01-16 08:02

本文关键词：基于相位恢复阈值算法与内投影神经网络算法的稀疏信号重构　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着信息技术的发展和大数据时代的到来,人们对信息量的需求也在不断地增加,这给信号数据的采样、存储和传输带来了新的挑战.稀疏信号恢复问题越来越受到关注,并且在信号处理、压缩感知、机器学习、统计学等领域应用广泛.本文以压缩感知为基础,选取特殊的测量矩阵,对稀疏信号数据的重构进行了研究.本文主要内容如下:第一章简述了压缩感知和稀疏信号恢复的研究背景,概述了国内外对压缩感知和稀疏信号恢复的研究历史及研究现状,总结了本文的主要工作和全文的组织结构.第二章阐述了稀疏信号数据的重构理论,主要包括三大核心问题,即信号的稀疏表示、测量矩阵设计和信号的重构算法设计.第三章介绍了稀疏信号的相位恢复问题,研究了在相位信息缺乏的情况下的稀疏信号恢复,提出了一种用新的迭代硬阈值(IHT)算法来解决相位恢复问题.接下来在IHT算法中加入回溯的思想,即基于回溯的迭代硬阈值算法(BIHT),克服了IHT不稳定的缺点,并且提高了计算的速度和精度.第四章提出了稀疏信号重构问题的的内点投影神经网络(IPNN)算法.首先介绍了一个非凸的极小化问题,提出了利用高相干性的测量矩阵进行稀疏信号重构.通过引入IPNN解决非凸的极小化问题,并在一定的条件下,证明了IPNN的收敛性.最后,通过一系列的实验表明了IPNN对于极小化方法的有效性.第五章归纳总结了全文所做的工作,并对本文可以继续研究的内容作了分析与展望.
[Abstract]:With the development of information technology and the arrival of big data, the demand for information is also increasing, the data acquisition, storage and transmission has brought new challenges. The sparse signal recovery problem more and more attention, and in signal processing, compressed sensing, machine learning, statistics and other fields of application widely. Based on the compressed sensing measurement matrix, selection of special data, the reconstruction of sparse signals is studied. The main contents of this paper are as follows: the first chapter introduces the research background of compressed sensing and sparse signal recovery, both at home and abroad are summarized on compressed sensing and sparse signal recovery the research history and present research, summary the organization structure and the main work of this paper. The second chapter expounds the theory of sparse signal reconstruction data, including the three core issues, namely signal sparse representation, measurement matrix The design of array design and signal reconstruction algorithm. The third chapter introduces the phase retrieval problem of sparse signal, sparse signal phase information in the absence of recovery, and presents a new iterative hard thresholding (IHT) algorithm to solve the problem of phase retrieval. Then add the idea back in the IHT algorithm. Based on the iterative hard thresholding of backtracking algorithm (BIHT), IHT overcomes the shortcomings of instability and improve the speed and accuracy of calculation. The fourth chapter puts forward the projection neural network point sparse signal reconstruction problem in (IPNN) algorithm. First introduced a non convex minimization problem, put forward sparse signal reconstruction using the measurement matrix with high coherence. To solve non convex minimization problem by introducing IPNN, and under certain conditions, convergence of the IPNN. Finally, through a series of experiments show that the IPNN for the minimum The fifth chapter summarizes the work done in the full text, and makes an analysis and Prospect of the content that can continue to be studied in this article.

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183;TN911.7

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