Fixed point strategies provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems in image processing. They constitute a natural environment to explain the behavior of advanced convex optimization methods. In addition, an increasing number of problems go beyond optimization since their solutions are not optimal in the classical sense of minimizing a function but, rather, satisfy more general notions of equilibria. Among the formulations that fall outside of the realm of standard minimization methods, we can mention variational inequality and monotone inclusion models, game-theoretic approaches, neural network structures, and plug-and-play methods. This talk will provide an overview of the main tools of fixed point theory and discuss some of their applications to image processing problems. The prominent role played by the forward-backward algorithm will be emphasized.
Fixed point methods in image processing
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