Title Fast image reconstruction algorithms combining half-quadraticregularization and preconditioning

In this paper, we focus on image deconvolution and image reconstruction problems where a sought image is recovered from degraded observed data. The solution is defined to be the minimizer of an objective function combining a data-fidelity term and a edge-preserving, convex regularization term. Our objective is to speed up the calculation of the solution in a wide range of situations. To this end, we propose a method applying pertinent preconditioning to an adapted half-quadratic equivalent form of the objective function. The optimal solution is then found using an alternating minimization (AM) scheme. We focus specifically on Huber regularization. We exhibit the possibility get very fast calculations while preserving the edges in the solution. Preliminary numerical results are reported to illustrate the effectiveness of our method.