Curvelet-based POCS interpolation of nonuniformly sampled seismic records

An exceedingly important inverse problem in the geophysical community is the interpolation of the seismic data, which are usually nonuniformly recorded from the wave field by the receivers. Researchers have proposed many useful methods to regularize the seismic data. Recently, sparseness-constrained seismic data interpolation has attracted much interest of geophysicists due to the surprisingly convincing results obtained. In this article, a new derivation of the projection onto convex sets (POCS) interpolation algorithm is presented from the well known iterative shrinkage-thresholding (IST) algorithm, following the line of sparsity. The curvelet transform is introduced into the POCS method to characterize the local features of seismic data. In contrast to soft thresholding in IST, hard thresholding is advocated in this curvelet-based POCS interpolation to enhance the sparse representation of seismic data. The effectiveness and the validity of our method are demonstrated by the example studies on the synthetic and real marine seismic data.