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2010

Restoration of Poissonian Images Using Alternating Direction Optimization

8 years 5 months ago
Restoration of Poissonian Images Using Alternating Direction Optimization
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 on multi-scale 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 on an alternating direction optimization method. The standard regularization (or maximum a posteriori) restoration criterion, which combines the Poisson log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is non-quadratic and non-separable, the regularizer is non-smooth, and there is a non-negativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for s...
Mário A. T. Figueiredo, José M. Biou
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TIP
Authors Mário A. T. Figueiredo, José M. Bioucas-Dias
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