Robust reconstruction via Group Sparsity with Radon Operators
Ji Li, Daniel O. Trad
Sparse solutions of linear systems play an important role in seismic data processing,including denoising and interpolation. An additional structure called group sparsity can be used to improve the performance of the sparse inversion. We propose a robust group sparse inversion algorithm based on Orthogonal Matching Pursuit with the Radon operators in the frequency slowness (w-p) domain. The proposed algorithm is used to interpolate seismic data and attenuate erratic noise simultaneously. During each iteration, The proposed algorithm first picks the dominant slowness group. Then, all the Radon coefficients located within the currently selected slowness groups are fit to the data in the time-space (t-x) domain via a robust solver, which is a 1−1 ADMM solver. In other words, we adopt a cost function that directly utilizes the selected coefficients to fit synthesized signals via 1−1 norm in the time-space domain. We prove that the proposed algorithm is resistant to erratic noise, making it attractive to applications such as simultaneous source deblending and reconstruction of noisy onshore datasets. We compare the performance of the same method with and without the group sparsity constraint and also with other Radon-based inversion methods. The result shows that the strong group sparsity inversion performs better than the traditional sparsity inversion. Both synthetic and real seismic data are being tested to examine the performance of the proposed algorithm.