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Bayesian reconstruction in emission tomography: new bilevel optimization methods and a new approach to the parameter selection problem

Abstract

We have recently designed suitable algorithms to solve several convex optimization problems whose solutions are used in tomographic image reconstruction. Such results were later specialized for bilevel convex problems aiming at the efficient solution of the task of finding a regularization parameter applicable to the objective of tomographic reconstruction. The present project is about the development of more general optimization methods than those we have so far obtained and a new criterion for parameters choice, which is more specific to models involving an optimization problem.In particular, it is of our interest to study the application of these algorithms to the solution of regularized models in a way such that the ideal parameter for reconstruction is found during the processing of the iterations, which would avoid the nedd of executing a computationally expensive numerical method several times to obtain a reconstruction. Another point to be studied is a parallel implementation of the algorithms in order to make use of the recent developing of low-cost parallel hardware to enable high quality reconstructions within very little computational time. (AU)

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