Adaptive Overcomplete Dictionary Learning-Based Sparsity-Promoting Regularization for Full-Waveform Inversion

Full-waveform inversion (FWI) is a highly nonlinear and ill-posed inverse problem, which needs proper regularization to produce reliable results. Recently, sparsity and overcompleteness have been successfully applied to seismic data processing. In this study, we propose a novel adaptive sparsity-promoting regularization for FWI which combines the L-BFGS algorithm with an adaptive overcomplete dictionary learning method. The dictionary is learned from many small imaging patches taken from the optimal velocity model that is obtained by previous L-BFGS iterations. Our dictionary learning method tries to exploit the 2D geometric structure of the training patches in a more direct way and is simple to implement. We test our proposed method on a smoothed Marmousi model, a BG Compass model, and a SEG/EAGE salt model. Since total variation (TV) regularization plays an important role in FWI, the inversion results using the TV regularization method are also presented for comparison purposes. From these experiments, we conclude that the proposed method can achieve better performance than the FWI with the TV regularization method.