基于字典学习和ADMM的地震数据重建

Seismic data reconstruction using dictionary learning and the alternating direction method of multipliers

针对压缩感知下与字典学习和交替方向乘子算法(alternating direction method of multipliers,ADMM)密切相关方法存在的问题,研究并提出了一种在压缩感知理论下采用字典学习和ADMM重建地震数据的方法。首先对不完整地震数据进行字典学习,使其稀疏地表示,再根据地震道的缺失情况设计合理的采样矩阵,最后对建立的L1范数约束模型采用ADMM进行求解得到重建后的地震数据。建立了压缩感知下基于字典学习和ADMM的地震数据插值技术流程。正演模拟数据和实际数据的重建实验结果表明:与压缩感知理论下采用固定基的重建方法相比,字典学习能够自适应地对地震数据进行更优的稀疏表示。与常用的curvelet等重建算法相比,采用ADMM能够更加精确地重建地震数据。与固定基和正交匹配追踪(orthogonal matching pursuit,OMP)相比,在压缩感知理论下采用字典学习和ADMM重建的地震数据有更高的信噪比。

This paper proposes a seismic data reconstruction method using dictionary learning and the alternating direction method of multipliers (ADMM) based on compressed sensing.Firstly,a learned dictionary is used to sparsely represent the incomplete seismic data.Then,a reasonable measurement matrix is designed.Finally,the L1-norm constrained model is solved by the ADMM to obtain the reconstructed seismic data.In addition,a seismic data interpolation flow is established,which uses dictionary learning and the ADMM based on compressed sensing.Compared to reconstruction methods using a fixed basis,the dictionary learning is able to sparsely represent seismic data adaptively.Compared to conventional reconstruction algorithms,such as the curvelet,the ADMM can reconstruct seismic data more accurately.Tests on both synthetic and real data indicated that the results of the reconstruction obtained with the proposed method have a higher signal-to-noise ratio (SNR) than those obtained using fixed base and orthogonal matching pursuit (OMP) methods.