Four-Parameter Subspace Matching Pursuit Algorithm With The Help Of Time-frequency Distribution

Signal sparse representation or the optimal N-term approximation is one of the important problems, which is applied to many areas such as the data compression, denoising. The redundant dictionary and matching pursuit algorithm are one of the main approaches to capturing signal sparse representation. The representation capabilities of dictionary and computation cost of matching pursuit algorithm are two main factors in this approach. The former is related to the size and the parameters' form of dictionary, the latter is done to the size of dictionary and algorithms' design. Chirp atoms are one of the most fundamental forms of signals, which are encountered in the many applied areas such as radar systems, sonar, seismic signals and speech signals.This paper proposes a novel matching pursuit algorithm, namely four-parameter subspace matching pursuit algorithm with the help of the time-frequency distribution. This algorithm is advanced on the basis of matching pursuit (MP) and the subspace matching pursuit (SSMP).Firstly, we introduce the MP and SSMP. We propose MP algorithm has limitation that it can't overcome by itself: the over-matching phenomenon in the MP. But SSMP can effectively overcome the over-matching phenomenon in the MP, improves the convergence rate. In this paper, we propose a novel matching pursuit algorithm, namely four-parameter subspace matching pursuit algorithm with the help of the time-frequency distribution, in order to effectively overcome the great cost of computation in the four parameter matching pursuit. In the algorithm, the time-frequency centers of the Chirp atoms are determined from the pilot TF distribution and then the scale factor and Chirp rate is estimated by the stencil matching method. In this way, a four-parameter search of high computational complexity is simplified into the two two-parameter searches with low computational complexity. In order to take full advantage of the pilot TF distribution, we search multiple matching Chirp atoms in each iteration and these atoms are not orthogonal with each other any more. Therefore, the LSM algorithm is used to compute the orthogonal projection of the signal or residual signal onto the corresponding subspace spanned by these atoms. Comparing with the three-parameter matching pursuit and subspace matching pursuit, the proposed algorithm requires much less TF atoms to approximate a signal, which is verified by the numerical results to speech signals.