Seismic Data Restoration Based on Compressive Sensing Using Regularization and Zero‐Norm Sparse Optimization

Seismic data restoration is an ill‐posed inverse problem. Based on the sparseness of seismic data in the curvelet domain, this problem can be transformed into a sparse optimization problem. This paper proposes to use the approximation of zero‐norm as the objective function and develop a projected gradient method to solve the corresponding minimization problem. We also employ a recently proposed piecewise random sampling method which can control the sampling gap and keep the randomness of sampling. Numerical results show that the projected gradient method can reduce the amount of computation greatly, and the restoration based on the piecewise random sampling is better than that of random sub‐sampling.