Iterative algorithms for total variation-like reconstructions in seismic tomography

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, . . .) is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.