An accelerated primal-dual iterative scheme for the L2-TV regularized model of linear inverse problems

A model with the L-2 and total variational (TV) regularization terms for linear inverse problems is considered. The regularized model is reformulated as a saddle-point problem, and the primal and dual variables are discretized in the piecewise affine and piecewise constant finite element spaces, respectively. An accelerated primal-dual iterative scheme with an O(1/N-2) convergence rate is proposed for the discretized problem, where N is the iteration counter. Both the regularization and perturbation errors of the regularized model, and the finite element discretization and iteration errors of the accelerated primal-dual scheme, are estimated. Preliminary numerical results are reported to show the efficiency of the proposed iterative scheme.