Robust Sparse Deconvolution in the Presence of Outliers

In this paper, two approaches are presented for sparsity-based deconvolution of seismic data in the presence of non-Gaussian noise. First, we perform sparse deconvolution in the time domain using a robust measure of data misfit. Second, it is shown that performing conventional sparse deconvolution in the frequency domain significantly increases its stability against outliers and that decreases the computational CPU time. Numerical experiments show that the proposed methods perform much better than conventional sparse deconvolution and the Wiener deconvolution in the sense of reconstruction error.