Edge-preserving seismic imaging using the total variation method

Inverse problems are generally mathematically ill-posed and, therefore, regularization methods are required to obtain stable and unique solutions. The total variation (TV) regularization method is used to resolve sharp interfaces and obtain solutions where edges and discontinuities are preserved. TV regularization accomplishes these goals by imposing sparsity on the gradient of the model parameters. In this paper, the TV method is applied to invert acoustic perturbations using the single-scattering Born modelling operator. The TV regularization leads to images of model parameters with preserved discontinuities and edges. Synthetic data examples are used to test the proposed seismic imaging algorithm.