Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing

Because of limited acquisition conditions in the field, seismic data is usually incomplete which would affect following data processing. To solve this problem, data reconstruction has been widely studied. Some methods based on compressed sensing has been developed in recent years, such as Curvelet Recovery by Sparsity-promoting Inversion method (CRSI), and the linearized Bregmen iterative threshold method. CRSI reconstructs randomly lacked seismic data to get a high-SNR data, taking advantage of seismic waveform's sparse representation in the Curvelet domain based on the steepest descent algorithm that ensures accuracy and stability of the iteration, but its convergence speed is slow. The linearized Bregman threshold method converges fast, but becomes unstable in later iterations because it adds back, residuals to the result, which leads to comparatively lower SNR of the final recovered data. Combining advantages of the two methods, we propose a new joint Curvelet-domain iterative threshold algorithm that combines the recovery quantities from both the CRSI and the Bregman method with respective weights of two items, which are adjusted exponentially during each iteration. The test results of the model and real seismic data demonstrate that this method is fast and stable in iteration and yields high-SNR reconstructed data.