Simulated annealing, acceleration techniques, and image restoration

Typically, the linear image restoration problem is an ill-conditioned, underdetermined inverse problem. Here, stabilization is achieved via the introduction of a first-order smoothness constraint which allows the preservation of edges and leads to the minimization of a nonconvex functional. In order to carry through this optimization task, we use stochastic relaxation with annealing. We prefer the Metropolis dynamics to the popular, but computationally much more expensive, Gibbs sampler. Still, Metropolis-type annealing algorithms are also widely reported to exhibit a low convergence rate. Their finite-time behavior is outlined and we investigate some inexpensive acceleration techniques that do not alter their theoretical convergence properties; namely, restriction of the state space to a locally bounded image space and increasing concave transform of the cost functional. Successful experiments about space-variant restoration of simulated synthetic aperture imaging data illustrate the performance of the resulting class of algorithms and show significant benefits in terms of convergence speed.