基于二次筛选的回溯广义正交匹配追踪算法的稀疏信号重构

Sparse Signal Reconstruction of Backtracking Generalized Orthogonal Matching Pursuit Algorithm Based on Secondary Screening

压缩感知是一种新型的信号采样及重构理论,高效的信号重构算法是压缩感知由理论转向实际应用的枢纽。为了更精确地重构出原始稀疏信号,本文提出一种基于二次筛选的回溯广义正交匹配追踪算法。首先采用内积匹配准则选出较大数目的相关原子,提高原子的利用率。其次利用广义Jaccard系数准则对已选出的原子进行二次筛选,得到最匹配的原子,优化原子选取方式。实验结果表明,在不同稀疏度和观测值下进行信号重构,相比于回溯广义正交匹配追踪算法、正交匹配追踪算法及子空间追踪算法,本文算法在重构误差及重构成功率方面有较大的优越性。

Compressed sensing is a new theory of signal sampling and reconstruction.Efficient signal reconstruction algorithm is the pivot of compressed sensing from theory to practical application.To reconstruct the original sparse signal more accurately,a backtracking generalized orthogonal matching pursuit algorithm based on secondary screening is proposed.Firstly,a large number of related atoms are selected to improve their utilization rate by using inner product matching criterion.Secondly,the generalized Jaccard coefficient criterion is used for the selected atoms to obtain the most matched atoms and optimize the atom selection method.The experimental results show that when the signal is reconstructed under different sparseness and observed values,the proposed algorithm has greater advantages in terms of reconstruction error and success rate compared with backtracking generalized orthogonal matching pursuit algorithm,orthogonal matching pursuit algorithm and subspace pursuit algorithm.