Algorithms for Sparse Multichannel Blind Deconvolution

In this article, we present two algorithms for sparse multichannel blind deconvolution (SMBD). The first algorithm is based on a cascade of a forward and a backward prediction error filter (C-PEF). The second consists in an alternating minimization algorithm for estimating both the reflectivity series and the seismic wavelet (AM-SMBD). We also compare the algorithms with other state-of-the-art sparse blind deconvolution algorithms. Simulation results with synthetic data for different signal-to-noise ratio (SNR) levels showed that the AM-SMBD outperformed [in terms of the Pearson correlation coefficient (PCC) and the Gini correlation coefficient (GCC)] other estimation methods, such as the reduced SMBD, the Toeplitz-structured sparse total least square (TS-sparseTLS), and the SMBD via spectral projected gradient (SMBD-SPG). For the same data, the C-PEF was able to provide better results (in terms of the GCC, visual inspection, and frequency gain) when compared with the fast SMBD (F-SMBD). In a simulation considering reflectivities with different levels of sparsity, the C-PEF seems to be more robust for less sparse data when compared with AM-SMBD and SMBD-SPG (up to a certain degree of sparsity). Finally, simulations considering a real land acquisition show that both algorithms were able to greatly improve the resolution of the seismic data.