IEEE Trans Image Process - Sparse stochastic processes and discretization of linear inverse problems.

Tópicos

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{ framework(1458) process(801) describ(734) }
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{ cost(1906) reduc(1198) effect(832) }
{ group(2977) signific(1463) compar(1072) }
{ gene(2352) biolog(1181) express(1162) }
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Resumo

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies continuous-domain signals as solutions of linear stochastic differential equations. Accordingly, we show that the class of admissible priors for the discretized version of the signal is confined to the family of infinitely divisible distributions. Our estimators not only cover the well-studied methods of Tikhonov and l1-type regularizations as particular cases, but also open the door to a broader class of sparsity-promoting regularization schemes that are typically nonconvex. We provide an algorithm that handles the corresponding nonconvex problems and illustrate the use of our formalism by applying it to deconvolution, magnetic resonance imaging, and X-ray tomographic reconstruction problems. Finally, we compare the performance of estimators associated with models of increasing sparsity.

Resumo Limpo

present novel statisticallybas discret paradigm deriv class maximum posteriori map estim solv illcondit linear invers problem guid theori spars stochast process specifi continuousdomain signal solut linear stochast differenti equat accord show class admiss prior discret version signal confin famili infinit divis distribut estim cover wellstudi method tikhonov ltype regular particular case also open door broader class sparsitypromot regular scheme typic nonconvex provid algorithm handl correspond nonconvex problem illustr use formal appli deconvolut magnet reson imag xray tomograph reconstruct problem final compar perform estim associ model increas sparsiti

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