Signal Sparse Approximation Via Subspace Matching Pursuit

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 is advanced on the basis of MP and OMP.Firstly, we introduce the MP and OMP. We propose these two sutra algorithms have limitation which they can't overcome by themselves: the over-matching phenomenon in the MP and large computation in the OMP. SSMP can effectively overcome the over-matching phenomenon in the MP, 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.