IEEE Trans Image Process - Restoration of Poissonian images using alternating direction optimization.

Tópicos

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Resumo

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based upon multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based upon an alternating direction optimization method. The standard regularization [or maximum a posteriori (MAP)] restoration criterion, which combines the Poisson log-likelihood with a (nonsmooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is nonquadratic and nonseparable, the regularizer is nonsmooth, and there is a nonnegativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for several types of regularizers: total-variation, frame-based analysis, and frame-based synthesis. We attack these problems with an instance of the alternating direction method of multipliers (ADMM), which belongs to the family of augmented Lagrangian algorithms. We study sufficient conditions for convergence and show that these are satisfied, either under total-variation or frame-based (analysis and synthesis) regularization. The resulting algorithms are shown to outperform alternative state-of-the-art methods, both in terms of speed and restoration accuracy.

Resumo Limpo

much research devot problem restor poissonian imag name medic astronom applic howev restor imag use stateoftheart regular base upon multiscal represent total variat still activ research area sinc associ optim problem quit challeng paper propos approach deconvolv poissonian imag base upon altern direct optim method standard regular maximum posteriori map restor criterion combin poisson loglikelihood nonsmooth convex regular logprior lead hard optim problem loglikelihood nonquadrat nonsepar regular nonsmooth nonneg constraint use standard convex analysi tool present suffici condit exist uniqu solut optim problem sever type regular totalvari framebas analysi framebas synthesi attack problem instanc altern direct method multipli admm belong famili augment lagrangian algorithm studi suffici condit converg show satisfi either totalvari framebas analysi synthesi regular result algorithm shown outperform altern stateoftheart method term speed restor accuraci

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