Abstract
A model with the 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 convergence rate is proposed for the discretized problem, where 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.
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