压缩感知地震数据重建中的三个关键因素分析

地震数据重建对地震资料处理和成像具有重要意义。基于压缩感知的地震数据重建方法是应用较广泛的一类方法，其中的稀疏变换、迭代算法和阈值模型等的选取将影响最终地震数据重建的效果和计算效率。本文着重分析了Fourier、Curvelet和Seislet这三种稀疏变换对地震数据重建的影响，比较了POCS（Projection onto Convex Sets）、IHT（Iterative Hard Thresholding）、Bregman和JRSI（Joint Reconstruction by Sparsity-promoting Inversion）四种迭代算法各自的优缺点，研究了线性、指数和数据驱动三种不同阈值模型的特性。通过模拟和实际算例对比分析了压缩感知地震数据重建过程中上述三个关键因素的影响，得到了三方面的重要认识和结论，为在实际地震数据重建中选择上述因素提供了可靠依据和现实建议。

Three key factors in seismic data reconstruction based on compressive sensing

Seismic data reconstruction is significant for seismic data processing and imaging.Reconstruction methods based on compressive sensing are widely used.In these methods,the sparsity transform,the iterative algorithm,and the threshold model affect the final reconstruction performance and computation efficiency.For the sparsity transform,we analyze the influence of Fourier transform,Curvelet transform and Seislet transform in seismic data reconstruction.For the iterative algorithm,we discuss the projection onto convex sets (POCS),the iterative hard thresholding (IHT),Bregman,and the joint reconstruction by sparsity-promoting inversion (JRSI) reconstruction methods and analyze the advantages and disadvantages of these four methods.For the threshold model,we work on the linear threshold model,the exponential threshold model,and the data-driven threshold model.We analyze how these three key factors affect the reconstruction results through synthetic and real data examples.At the end we draw some conclusions and propose suggestions for practical seismic data reconstruction.