应用快速POCS算法的非均匀地震数据重建

凸集投影(Projection on Convex Sets, POCS)算法已经成功地应用于地震数据重建，灵活且简单。然而该算法要求重构数据必须是在规则网格上进行，由于障碍物等因素导致实际采集数据偏离预设网格点，重构效果不佳，且该算法的收敛速度仅为O(1/k),其中k为迭代次数。针对以上问题，首先构建了非均匀网格地震数据正演模型；然后从快速迭代收缩阈值算法(Fast Iterative Shrinkage Thresholding Algorithm, FISTA)出发，推导并提出了基于曲波变换的快速凸集投影算法(Fast POCS,FPOCS),该算法保留了迭代收缩阈值算法(ISTA)的计算简单性，具有全局收敛速度O(1/k²);是一种快速的地震数据重构方法；最后通过模拟和实际数据处理验证了本文方法的有效性。

Reconstruction of non-uniformly sampled seismic data based on fast POCS algorithm

The projection on convex set (POCS) algorithm has been successfully applied to seismic data reconstruction, and it is flexible and simple.However, this algorithm must reconstruct data on a regular grid, and the actual collected data deviate from preset grid points due to obstacles and other factors, which results in poor reconstruction effects.Moreover, the convergence speed of the algorithm is only O(1/k).In order to solve these challenges, this paper builds a forward model of seismic data with non-uniform grids and derives a fast POCS (FPOCS) algorithm based on curvelet transform from the fast iterative shrinkage thresholding algorithm (FISTA).The FPOCS is a fast seismic data reconstruction method, which retains the computational simplicity of ite-rative shrinkage thresholding algorithm (ISTA) and has a global convergence speed of O(1/k²). Finally, the paper demonstrates the effectiveness of the proposed method through simulation and actual data.