Acceleration on sparse promoting seismic applications

Sparse promoting oriented problems are never new in seismic applications. Back in 1970s, geophysicists had well exploited the robustness of sparse solutions. Moreover, with the emerging usage of compressed sensing in recent years, sparse recovery have been favored in dealing with 'curse of dimensionality' in various seismic field acquisition, data processing, and imaging applications. Although sparsity has provided a promising approach, solving for it presents a big challenge. How to work efficiently with the extremely large-scale seismic problem, and how to improve the convergence rate reducing computation time are most frequently asked questions in this content. In this abstract, the author proposed a new algorithm – PQN$\ell_1$, trying to address those questions. One example on seismic data processing is included.