压缩感知理论下基于快速不动点连续算法的地震数据重建

Seismic data reconstruction using FFPC algorithm based on compressive sensing

地震勘探中由于采集成本和采集条件等因素导致的地震数据不完整性极大地影响了地震数据的后续处理。为此,引入了一种压缩感知理论下的快速不动点连续(fast fixed point continuation,FFPC)算法对缺失的地震数据进行重建。首先对地震数据进行小波变换,然后根据要求选择合适的测量矩阵对地震数据进行缺失处理,最后采用FFPC算法重建缺失后的稀疏地震数据。模型数据及实际地震数据测试结果表明,该算法能够很好地完成地震数据重建,重建后的地震数据具有较高的信噪比。相对于不动点连续(fixed point continuation,FPC)算法,FFPC算法耗时更短、重建效率更高;相对于传统的正交匹配追踪(orthogonal matching pursuit,OMP)以及最小化L1范数的谱投影梯度(spectral projected-gradient for L1minimization,SPGL1)等算法,FFPC算法的重建精度更高。

Due to the limitations in acquisition conditions,seismic exploration data is usually incomplete and thus influences subsequent seismic data processing.In this paper,a Fast Fixed Point Continuation(FFPC)algorithm based on compressive sensing theory is used to reconstruct missing seismic data.First,wavelet transform is applied to seismic data.Then,the appropriate measurement matrix is selected through analysis of missing signal.Finally,an FFPC algorithm is used to reconstruct the missing seismic data.Tests on both synthetic data and field data show that the method could reconstruct missing seismic data with a high SNR.The FFPC algorithm is less time consuming and more efficient compared to the Fixed Point Continuation(FPC)algorithm.The FFPC algorithm also has a higher reconstruction precision compared to the traditional Orthogonal Matching Pursuit(OMP)and Spectral Projected gradient for L1 minimization(SPGL1)algorithms.