A review on restoration of seismic wavefields based on regularization and compressive sensing

Restoration of seismic data as an ill-posed inverse problem means to recover the complete wavefields from sub-sampled data. Since seismic data are typically sparse in the curvelet domain, this problem can be solved based on the compressive sensing theory. Meanwhile three major problems are modelling, sampling and solving methods. We first construct l(0) and l(1) minimization models and then develop fast projected gradient methods to solve the restoration problem. For seismic data interpolation/restoration, the regular sub-sampled data will generate coherence aliasing in the frequency domain, while the random sub-sampling cannot control the largest sampling gap. Therefore, we consider a new sampling technique in this article which is based on the controlled piecewise random sub-sampling scheme. Numerical simulations are made and compared with the iterative soft thresholding method and the spectral gradient-projection method. It reveals that the proposed algorithms have the advantages of high precision, robustness and fast calculation.