Seismic Data Interpolation by the Projected Iterative Soft-threshold Algorithm for Tight Frame

Seismic data recovery from missing traces is a crucial step in seismic data pre-processing. Recently researches have proposed many useful methods to reconstruct the seismic data based on compressed sensing. Curvelet frames can be used to sparsely represent the seismic data volume, analysis model has been proposed to reconstruct the seismic data, however, the latest kind of discrete curvelet transform has tight frame property, the recent insights show synthetically model is more suitable for a tight frame. A synthetically model is introduced to seismic data reconstruction; projected iterative soft-threshold algorithm (pFISTA) is used to solve the model. The recovery performs well on synthetic as well as real data by the proposed method. Comparing with the analysis model solved by an iterative soft-threshold algorithm (FISTA) in the curvelet domain, the new method has improved reconstruction efficiency and reduced the computation time.