ON THE CONVERGENCE OF METROPOLIS-TYPE RELAXATION AND ANNEALING WITH CONSTRAINTS
Probability in the Engineering and Informational Sciences
Edge-Preserving Image Reconstruction with Wavelet-Domain Edge Continuation
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Improved global cardiac tractography with simulated annealing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
Optimization by Stochastic Continuation
SIAM Journal on Imaging Sciences
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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