Simulated annealing, acceleration techniques, and image restoration

Typically, the linear image restoration problem is an ill-conditioned, unde rdetermined inverse problem. Here, stabilization is achieved via the introd uction 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 computati onally much more expensive, Gibbs sampler, Still, Metropolis-type annealing algorithms are also widely reported to exhibit a low convergence rate. The ir finite-time behavior is outlined and we investigate some inexpensive acc eleration techniques that do not alter their theoretical convergence proper ties; namely, restriction of the state space to a locally bounded image spa ce and increasing concave transform of the cost functional. Successful expe riments about space-variant restoration of simulated synthetic aperture ima ging data illustrate the performance of the resulting class of algorithms a nd show significant benefits in terms of convergence speed.