3-Component Sparse S Transform

In this paper, the sparse S transform is extended to 3-component data and considered in the framework of the sparse inverse theory. The 3-component sparse S transform is formulated as a constrained optimization where the group sparsity constraint is minimized subject to a data fidelity constraint. Then a fast and efficient algorithm based on the alternative split Bregman technique is employed to solve the optimization. Numerical experiments using synthetic and real seismic data show that the proposed 3-component sparse S transform automatically generates higher resolution TF maps compared to single-component sparse decompositions, which has application in phase splitting and earthquake analysis.