IEEE Trans Image Process - Nonlocal regularization of inverse problems: a unified variational framework.

Tópicos

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Resumo

We introduce a unifying energy minimization framework for nonlocal regularization of inverse problems. In contrast to the weighted sum of square differences between image pixels used by current schemes, the proposed functional is an unweighted sum of inter-patch distances. We use robust distance metrics that promote the averaging of similar patches, while discouraging the averaging of dissimilar patches. We show that the first iteration of a majorize-minimize algorithm to minimize the proposed cost function is similar to current nonlocal methods. The reformulation thus provides a theoretical justification for the heuristic approach of iterating nonlocal schemes, which re-estimate the weights from the current image estimate. Thanks to the reformulation, we now understand that the widely reported alias amplification associated with iterative nonlocal methods are caused by the convergence to local minimum of the nonconvex penalty. We introduce an efficient continuation strategy to overcome this problem. The similarity of the proposed criterion to widely used nonquadratic penalties (e.g., total variation and lp semi-norms) opens the door to the adaptation of fast algorithms developed in the context of compressive sensing; we introduce several novel algorithms to solve the proposed nonlocal optimization problem. Thanks to the unifying framework, these fast algorithms are readily applicable for a large class of distance metrics.

Resumo Limpo

introduc unifi energi minim framework nonloc regular invers problem contrast weight sum squar differ imag pixel use current scheme propos function unweight sum interpatch distanc use robust distanc metric promot averag similar patch discourag averag dissimilar patch show first iter majorizeminim algorithm minim propos cost function similar current nonloc method reformul thus provid theoret justif heurist approach iter nonloc scheme reestim weight current imag estim thank reformul now understand wide report alia amplif associ iter nonloc method caus converg local minimum nonconvex penalti introduc effici continu strategi overcom problem similar propos criterion wide use nonquadrat penalti eg total variat lp seminorm open door adapt fast algorithm develop context compress sens introduc sever novel algorithm solv propos nonloc optim problem thank unifi framework fast algorithm readili applic larg class distanc metric

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