MCA框架下Shearlet和DCT字典组合地震数据重建

Seismic data reconstruction with the discrete cosine transform and Shearlet dictionaries under the morphological component analysis framework

相比于单一变换,形态分量分析(MCA)是信号稀疏表示的一种更有效的手段。在MCA框架下,提出了一种Shearlet字典和DCT字典组合的地震数据重建方法。首先,基于MCA框架,分别选取DCT字典和Shearlet字典稀疏表示地震数据中的局部奇异分量与平滑线状分量;随后,通过加入指数阈值模型和指数阈值函数的块坐标松弛(BCR)算法重建各个分量;最后,合并各个分量得到重建结果。合成数据实验和真实数据实验均表明,该方法能够有效地重建缺失地震数据,且重建精度高于单一Shearlet字典、Curvelet+DCT字典组合和Shearlet+Curvelet字典组合。

Compared to a single transformation,the morphological component analysis(MCA)is a more efficient method of sparse representation of signals.In this paper,we propose a seismic data reconstruction method with the discrete cosine transform(DCT)and Shearlet dictionaries under the MCA framework.Firstly,we select the DCT dictionary and the Shearlet dictionary to represent local singular components and smooth linear components of seismic data respectively.Then we reconstruct all the components by the block coordinate relaxation(BCR)algorithm with an exponential threshold model and exponential threshold function.Finally,we merge the components to get a reconstructed result.Experiments on synthetic and real data show that the proposed method can effectively reconstruct missing seismic data and the accuracy of reconstruction is higher than the single Shearlet dictionary,the Curvelet + the DCT dictionaries,the Shearlet+the Curvelet dictionaries.