压缩感知中正交匹配追踪算法的理论研究

项目名称： 压缩感知中正交匹配追踪算法的理论研究

项目编号： No.11526081

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 李海锋

作者单位： 河南师范大学

项目金额： 3万元

中文摘要： 压缩感知促进了信号处理理论以及工程应用的发展，已经成为信号处理领域研究热点之一。重建算法是压缩感知理论的重要组成部分。本项目针对复杂度较低的正交匹配追踪算法（Orthogonal matching pursuit, OMP）展开研究，其内容如下：① 无噪的情形下，改进保证OMP算法精确重建稀疏信号的充分条件的上界，得到宽松的上界，进而减少采样数目，降低成本；② 加性噪声与乘性噪声干扰的情况下，针对OMP算法的重建性能展开分析，得到与未知稀疏信号无关的充分条件，进而对工程实践起到一定的指导作用。为了同时达到抗干扰，准确重建原信号及降低采样数目的目标，在研究中将采用线性与非线性泛函分析、空间相关理论、数值分析、随机分析、概率统计等数学理论方法和机器学习方法，以期在基本理论以及高性能关键技术方面取得较好的成果。

中文关键词： 压缩感知；稀疏优化；贪婪算法；；

英文摘要： Compressed sensing promotes the development of the theory and engineering application and has been one of the hottest topics in the field of signal processing. The reconstruction algorithm is an important part of compressed sensing. The project analyzes orthogonal matching pursuit (OMP) algorithm that has low complexity, the contents are as follows: ① under the case of noiseless, we improve the upper bound of the sufficient condition, which guarantees that OMP algorithm accurately reconstructs sparse signals, and get relaxed bound. Thus, reducing the number of sampling and the cost. ② under the perturbations of additive noise and multiplicative noise, this project researches the performance of OMP algorithm and obtains sufficient condition that has nothing to do with the unknown sparse signal. The condition will guide the engineering practice. In order to suppress the corruptions and noises, to ensure the recovery reliably and to reduce the number of the observed measurements at the same time, in the research, some mathematical methods and machine learning methods will be used, such as linear and nonlinear functional analysis, the space correlation analysis, numerical analysis, stochastic analysis, probability and statistics and sub-supervised or unsupervised learning methods. The proposal intends some influenti

英文关键词： compressed sensing；sparse optimization；greedy algorithm；；