Seismic data reconstruction via fast projection onto convex sets in the seislet transform domain

Abstract

According to the compressive sensing (CS) theory in the signal-processing field, we proposed a new seismic data reconstruction approach based on a fast projection onto convex sets (POCS) algorithm with sparsity constraint in the seislet transform domain. The FPOCS can obtain much faster convergence than conventional POCS (about two thirds of conventional iterations can be saved) . The seislet transform based reconstruction approach can achieve obviously better data recovery results than f − k transform based scenarios, considering both signal-to-noise ratio (SNR) and visual observation, because of a much sparser structure in the seislet transform domain. Both synthetic and field data examples demonstrate the performance of the proposed approach.