中文摘要：

地震数据重构问题是一个病态的反演问题．本文基于地震数据在curvelet域的稀疏性，将地震数据重构变为一个稀疏优化问题，构造0范数的逼近函数作为目标函数，提出了一种投影梯度求解算法．本文还运用最近提出的分段随机采样方式进行采样，该采样方式能够有效地控制采样间隔并且保持采样的随机性．地震数值模拟表明，基于0范数逼近的投影梯度法计算效率有明显的提高；分段随机采样方式比随机欠采样有更加稳定的重构结果．

英文摘要：

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 both control the sampling gap and keep the randomness of sampling. Numerical results show that the projectedgradient method can reduce the amount of computation greatly, and the restoration based on the piecewise random sampling are better than that of random sub-sampling.