The Research On Fast Algorithm Of Seismic Signal Sparse Decomposition And Atomic Dictionary Selection

In recent years, with the development of signal sparse decomposition, the technology has been widely used in seismic signal interpretation, such as the separation of seismic signal and noise,de-noising, etc. But even as the lowest algorithm complexity in sparse decomposition, the calculation of the MP algorithm is very large. The problem has hindered its further application in seismic data interpretation. In order to improve the speed of sparse decomposition of seismic signal, scholars have proposed some fast algorithm, and the Ant Colony Algorithm is one of them. However, the quality of the reconstructed signal based on ACO is poor, so this paper will research on the Ant Colony Algorithm and Monte Carlo Algorithm. We will improve the speed of seismic signal sparse decomposition in the case of that the quality of the reconstructed signal is ensured. In addition, this paper research on six mathematical models that has been applied in seismic signal processing and use the non-uniform discretization of frequency parameters to complete over-complete dictionary of atoms and select the best match the structure of seismic signal by the experimental method.Firstly, this paper improves the MP algorithm based on Ant Colony Optimization (ACO) algorithm. By adjusting the parameters,saving the inner product value in the process of calculation,dividing the ants into two kinds and changing the selecting strategy, the results of simulation prove that the speed of the signal sparse decomposition is lower than the Genetic algorithm. Moreover, the quality of reconstructed signal after sparse decomposition is better than the Genetic algorithm.Secondly, in this paper Monte Carlo Method is applied in seismic signal sparse decomposition. The results of the simulation confirm that the speed of the MP algorithm based on the Monte Carlo Method is 136 times as fast as the speed of the base MP algorithm. But its quality of decomposition is close to the Genetic algorithm. So in order to improve its quality, this paper continues to improve this algorithm. The results of simulation prove that the decomposition quality gained from the MP algorithm based on the improved Monte Carlo Method is better than that from the Genetic Algorithm and the improved ACO algorithm.Thirdly, over-complete dictionary of atoms is created by the non-uniform discretization of frequency parameters in this paper. Firstly, seismic signal is spectrum analyzed. After that, when the over-complete dictionary of atoms is being created, the selection of the frequency parameters refers to the spectrum analysis. The frequency parameters are set in highly denseness in high energy frequency band, but in sparse denseness in low energy frequency band. The results of simulation prove that the decomposition quality using non-uniform discretization of the frequency parameters to create over-complete dictionary of atoms is better than that using uniform discretization of the frequency parameters to create over-complete dictionary of atoms, if the dictionaries of atoms have the same size.Finally, the sparse decomposition is operated in the six dictionaries of atoms for pre-stack seismic signal without noise and post-stack with noise with the MP algorithm based on improved ACO and BP algorithm. And then we will compare the speed of decomposition and the quality of the reconstructed signal and select one over-complete dictionary of atoms that best match the structure of seismic signal.