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Restoration of Poissonian Images Using Alternating Direction Optimization | IEEE Journals & Magazine | IEEE Xplore

Restoration of Poissonian Images Using Alternating Direction Optimization


Abstract:

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images u...Show More

Abstract:

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.
Published in: IEEE Transactions on Image Processing ( Volume: 19, Issue: 12, December 2010)
Page(s): 3133 - 3145
Date of Publication: 28 June 2010

ISSN Information:

PubMed ID: 20833604

References

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