基于子空间匹配追踪的信号稀疏逼近

Signal Sparse Approximation via Subspace Matching Pursuit

信号的稀疏表示或最佳N项逼近在数据压缩、特征提取和模型降阶等领域得到了广泛的应用．最佳N项逼近是一个典型的NP难的问题．次最优的匹配追踪、正交匹配追踪和基匹配追踪是目前流行的算法．本文提出了一种新的算法——子空间匹配追踪．该算法可以克服匹配追踪算法中的过匹配现象,加速了算法收敛速度,同时计算量比正交匹配追踪小得多．最后,比较了匹配追踪、正交匹配追踪和子空间匹配追踪对仿真信号和语音信号的表示性能．表明了我们的方法有效均衡了计算量和收敛速度两方面的要求．

Signal sparse representations or the optimal N-term approximations have been widely applied to many areas such as the data compression, feature extraction, and model reduction. The optimal N-term approximation is a NP difficult problem. The sub-optimal matching pursuit （MP）, orthogonal matching pursuit （OMP）, and basis matching pursuit （BMP） are existing popular algorithms. This paper proposes a novel matching pursuit algorithm, namely the subspace matching pursuit （SSMP）. This algorithm can effectively overcome the over-matching phenomenon in the matching pursuit, improves the convergence rate, and has much less computation than the OMP. Finally, three algorithms are applied to simulation signals and speech signals, and the results show that the SSMP is a good trade-off between computation burden and convergence rate.