Curvelet-TV regularized Bregman iteration for seismic random noise attenuation

• A method for seismic random noise attenuation was proposed.
• The method is a combination of the SOTV with curvelets.
• The algorithm is solved efficiently based on split Bregman iterations.
• The combined method uses the advantages of both SOTV and curvelets.
• Numerical results show superior performance of the combined method.

We propose a powerful denoising method to attenuate random noises in seismic images. The method is a combination of recently developed tools of multiscale, multidirectional curvelets and second-order total-variation (SOTV) regularization. Directional derivative characteristic of SOTV helps an improvement in the quality of final image by suppressing fine-scale artifacts due to curvelets. We formulate the problem in a convex constrained optimization setting to be tackled efficiently by split Bregman iterations. Then the discrepancy principle and Steins unbiased risk estimate (SURE) are used as two stopping criteria to determine the optimum number of Bregman iterations. The SURE score is evaluated at each iteration via stochastic Monte Carlo (MC) technique. Numerical experiments with different synthetic and real seismic images show that the algorithm converges in a few iterations. Furthermore, the obtained results confirm an improvement in signal-to-noise-ratio (SNR) and structural similarity (SSIM) when using the combined method compared to the cases using curvelets or SOTV.