Research On Seismic Signal Compression Based On Sparse Representation

Seismic data compression based on sparse representation is studied in this paper. To the scientist, the records of seismic data are very valuable information, the knowledge of seismology can be learned through these records. The records saved a huge amount of seismic data which history is more than 100 years. The compression is a problem. Seismic data have the characteristics of the self-similarity. According to the self-similarity, the method of dictionary learning can obtain the over complete dictionary, and the sparse representation can be used to solve the compression problem. The methods of dictionary learning are studied in two ways, one is the coherence of dictionary atoms and the other is the similarity among samples. The main contents are as follows.The first method is improving the dictionary by reducing the self-coherence of atoms, which can avoid similar pairs of atoms appearing. The dictionary can be improved in limited size. In the dictionary updating, penalty items that contain r tight frame ? is added to the optimization problem, to control the trade-off between minimizing the self-coherence and minimizing the approximation error.Second method takes into account the similarity of samples. Through the combination of the clustering and the dictionary learning, the method of training over complete dictionary is proposed. There are a lot of similarities among the samples. The similar samples are clustered by the clustering algorithm, and the weight coefficient of each cluster is calculated. In the objective function, the weight coefficients are given to each cluster. By the transformation of the objective function, the original cost function can be solved by the K-SVD algorithm.The experiments prove that the dictionary obtained by the two methods above is effective in signal reconstruction. Two factors, such as the coherence of dictionary atoms and the similarity among samples, are considered. Based on the traditional dictionary learning model, the dictionary learning model is improved in two directions. The effect of signal reconstruction is improved under the condition of same compression ratio.