  This work studies the usage of well-known smoothed total variation
regularization for solving an atmospheric tomography problem named as {\em
GPS-tomography} in some quasi-Newton methods. That is we solve an
unconstrained, convex, smooth minimization problem associated with a general
type Tikhonov functional containing smoothed type total variation penalty term
by quasi-Newton methods. As a result of the conducted experiments, it is
concluded that limited memory BFGS algorithm with trust region is the effective
algorithm in terms obtaining a reasonably optimum solution.
