Robust reconstruction of non-uniformly sampled 3D seismic data with outliers

Compressive sensing acquisition utilizes non-uniform sampling along spatial directions, allowing for the reconstruction of seismic data without satisfying the requirements of Nyquist sampling theory. However, the reconstruction of compressive sensing data may fail in the case of measurement outliers. Moreover, realistic environmental conditions often alter the sampling geometry, resulting in both missing samples and non-uniform samples relative to the designed grid. To reconstruct non-uniformly sampled data with outlier noise, we propose a reconstruction model that incorporates an interpolation operator and a robust measurement term within the data misfit. The robust measurement term utilizes the Huber norm to align the reconstructed data and sampled data with outliers, thereby enhancing robustness to realistic noise. The interpolation operator maps data from a uniform grid to a non-uniform grid using a barycentric Lagrangian interpolator. We apply the robust projection onto convex sets algorithm to solve this optimization problem. Numerical tests demonstrate the effectiveness of the proposed approach. Superior reconstruction results are achieved compared to methods that do not incorporate robust measurements or consider true coordinates.