Recovery of Seismic Wavefields Based on Compressive Sensing by an l1-Norm Constrained Trust Region Method and the Piecewise Random Sub-sampling

SUMMARY Due to the influence of variations in landform, geophysical data acquisition is usually sub-sampled. Reconstruction of the seismic wavefield from sub-sampled data is an ill-posed inverse problem. Compressive sensing can be used to recover the original geophysical data from the sub-sampled data. In this paper, we consider the wavefield reconstruction problem as a com-pressive sensing and propose a piecewise random sub-sampling scheme based on the wavelet transform. The proposed sampling scheme overcomes the disadvantages of uncontrolled random sampling. In computation, an l 1-norm constrained trust region method is developed to solve the compressive sensing problem. Numerical results demonstrate that the proposed sampling technique and the trust region approach are robust in solving the ill-posed compressive sensing problem and can greatly improve the quality of wavefield recovery. 2 Y. Wang et al. Key words: Computational seismology – inverse theory – wavefield reconstruction – com-pressive sensing – regularization – sparse optimization