Talk by Marco Donatelli, University of Insubria, Italy.
Regularization techniques for image reconstruction problems typically involve a smooth term and a potentially non-smooth convex term. A common approach to solving these problems is the use of proximal gradient methods. To accelerate the convergence of these first-order iterative algorithms, extrapolation strategies have been introduced in the literature. We propose a variable metric strategy that can be reinterpreted as a right-preconditioning method. Consequently, we also investigate a left-preconditioned version of the same proximal gradient method, together with possible approximation techniques. We prove the convergence of the preconditioned iterations under a suitable choice of the sequence of preconditioners. Numerical results show that preconditioning accelerates convergence while reducing the overall CPU time.
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