An Iterative $L_{1}$ -Based Image Restoration Algorithm With an Adaptive Parameter Estimation

Regularization methods for the solution of ill-posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known. In this paper, we consider the L₁-regularized image deblurring problem and evaluate its solution using the iterative forward-backward splitting method. Based on this approach, we propose a new adaptive rule for the estimation of the regularization parameter that, at each iteration, dynamically updates the parameter value, following the evolution of the objective functional. The iterative algorithm automatically stops, without requiring any assumption about the perturbation process, when the parameter has reached a seemingly near optimal value. In spite of the fact that the optimality of this value has not yet been theoretically proved, a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state-of-the-art algorithms.