基于树形结构回溯正交匹配追踪算法的压缩感知信号重建.docVIP

 基于树形结构回溯正交匹配追踪算法的压 缩感知信号重建# 王方非1，岑翼刚1，雷蕾1，岑丽辉2** 5 10 15 20 25 30 （1. 北京交通大学信息科学研究所，北京 100044； 2. 中南大学信息工程与技术学院，湖南 长沙 410083） 摘要：压缩感知理论作为一种利用信号稀疏性的信号采样、编解码理论，通过求解最优化问 题精确重构原始信号。本文基于信号小波变换系数树形结构的特点，提出一种基于小波域树 形 结 构 的 回 溯 正 交 匹 配 追 踪 算 算 法 (Tree-based Backtracking Orthogonal Matching Pursuit, TBOMP)。该算法可在信号稀疏度未知的情况下，将小波树结构转化为备选原子间 的对应关系，使得原子的选取更加结构化，缩小有哪些信誉好的足球投注网站空间，并通过回溯过程选择候选原子以 及删除错选原子，最终实现信号的精确重建。仿真结果表明，该算法信号重建的质量较同 类压缩感知算法大大提高。 关键词：压缩感知；小波树；正交匹配追踪；稀疏恢复 中图分类号：TN911.7 Tree-based Backtracking Orthogonal Matching Pursuit for Signal Reconstruction Based on Compressive Sensing WANG Fangfei1, CEN Yigang1, LEI Lei1, CEN Lihui2 (1. Institute of Information Science, Beijing Jiaotong University, Beijing 100044; 2. Institute of Information Science and Engineering, Central South University, Changsha 410083) Abstract: Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of tree model in wavelet domain. Thus, the algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without the prior information of signal sparsity. The atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which achieves an accurate reconstruction of the signal ultimately. Compared with the other compressed sensing algorithm, simulation results show that our proposed algorithm improved the quality of the reconstructed signal significantly. Key words: Compressed sensing;Wavelet tree; Orthogonal matching pursuit; Sparse recovery 35 0 引言 压缩感知理论(Compressed Sensing, CS)[1-4]旨在以低信息量，高概率恢复出稀疏的或可 压缩的信号，其突破