Combining adaptive dictionary learning with nonlocal similarity for full-waveform inversion

Abstract

ABSTRACT We study the full-waveform inversion (FWI) problem for the recovery of velocity model/image in acoustic media. FWI is formulated as a typical nonlinear optimization problem, many regularization techniques are used to guide the optimization process because the FWI problem is strongly ill-posed. Recently, sparsity regularization has attracted considerable attention in the field of inverse problems. In addition, the nonlocal similarity is also an inherent property of many subsurface images themselves. In this paper, we present a novel computational framework for FWI based on joint local sparsity and nonlocal self-similarity. First, principal component analysis (PCA)-based dictionary learns from noisy approximation images (the estimated results from certain local optimization method) and the learned dictionary is used to guide similar patch grouping. Second, the sparse representation and the nonlocal similarity are introduced as the regularization term. At last, the relative total variation (RTV) algorithm is used to further eliminate the residual artefacts in the reconstructed model more thoroughly. In our inversion strategy, the external optimization knowledge, and the intrinsic local sparsity and nonlocal self-similarity prior of model are used jointly for FWI. Computational results demonstrate the proposed method is obviously superior to existing inversion methods both qualitatively and quantitatively, including total variation FWI method in model-derivative domain and sparsity promoting FWI method in the curvelet domain.