Method for reconstructing seismic data using a projection onto a convex set and a complicated curvelet transform

The Nyquist sampling theorem must be followed in conventional seismic data acquisition; however, due to missing traces or exploration cost constraints, field data acquisition cannot meet the sampling theorem, so prestack data must be reconstructed to meet the requirements. 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, based on compressive sensing (CS) theory in the signal-processing field. In comparison to traditional projection onto convex sets (POCS), the faster projection onto convex sets (FPOCS) can achieve much faster convergence (about two-thirds of conventional iterations can be saved). To address the slow convergence of typical threshold parameters during reconstruction, an exponential square root lowered threshold and process 2-D seismic data reconstruction with hard thresholding has been purposed. Because of the much sparser structure in the seislet transform domain, the seislet transform-based reconstruction approach can clearly achieve better data recoveryresults than f-k transform-based scenarios, in terms of both signal-to-noise ratio (SNR) and visual observation. The proposed approach’s performance is demonstrated using both synthetic and field data examples.