Compressive sensing (CS) aims to recover sparse or compressible signal with low amount of information and high probability. It breaks the traditional rule of Nyquist sampling theorem, which states that a signalâ€™s information is preserved if it is uniformly sampled at a rate at least two times faster than its Fourier bandwidth. By this state-of-the-art signal compressive and processing theory, the signal sampling frequency, the cost of processing time and the data storage and transmission can be greatly reduced.Signal sparse representation, measurement matrix construction and reconstruction algorithm are three core issues of CS. Reconstruction algorithm, as an important part of the compressive sensing theory, is directly related to the actual signal reconstruction accuracy and computational complexity. Therefore, the studying of reconstruction algorithm is particularly important for CS. The main contributions of this paper are as follows:Based on the comparison and analysis of the common reconstruction algorithms and the introduction of the detailed implementation steps of several algorithms, we propose a new improvable and innovative idea for the future research, according to the different characteristics of reconstruction algorithms.In order to propose a new signal reconstruction algorithm, which on the basis of an in-depth study of the matching pursuit series algorithms, we introduce the sparse representation of CS into this research. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without the prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atomsâ€™reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show that our proposed algorithm improves the quality of the reconstructed signals significantly.Based on the above research on reconstruction algorithm, we apply the TBOMP algorithm on the actual seismic signal reconstruction. Compared with the other reconstruction algorithm, experiment results show that this new algorithm achieves better recognition performance. |