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Restoration of Poissonian Images Using Alternating Direction Optimization

Figueiredo, M A T ; Bioucas-Dias, J M

IEEE transactions on image processing, 2010-12, Vol.19 (12), p.3133-3145 [Periódico revisado por pares]

New York, NY: IEEE

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Título:
Restoration of Poissonian Images Using Alternating Direction Optimization
Autor: Figueiredo, M A T ; Bioucas-Dias, J M
Assuntos: Additive noise ; Algorithms ; Alternating direction methods ; Applied sciences ; augmented Lagrangian ; Biomedical imaging ; convex optimization ; Deconvolution ; Exact sciences and technology ; Gaussian noise ; image deconvolution ; Image Enhancement - methods ; Image processing ; Image reconstruction ; Image restoration ; Information, signal and communications theory ; Lagrangian functions ; Optimization ; Optimization methods ; Pattern Recognition, Automated - methods ; Permission ; Poisson images ; Regularization ; Restoration ; Signal processing ; State of the art ; Studies ; Sufficient conditions ; Synthesis ; Telecommunications and information theory
É parte de: IEEE transactions on image processing, 2010-12, Vol.19 (12), p.3133-3145
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Descrição: 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.
Editor: New York, NY: IEEE
Idioma: Inglês

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Restoration of Poissonian Images Using Alternating Direction Optimization

Figueiredo, M A T ; Bioucas-Dias, J M

New York, NY: IEEE

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