Deconvolution of Poissonian Images Using Variable Splitting and Augmented Lagrangian Optimization

Details Deconvolution of Poissonian Images Using Variable Splitting and Augmented Lagrangian Optimization Deconvolution of Poissonian Images Using Variable Splitting and Augmented Lagrangian Optimization

2009-04-30

arxiv.org/abs/0904.4868v1

Mathematics

Optimization and Control

Submitted to the 2009 IEEE Workshop on Statistical Signal Processing

Scientific paper

Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation) to this class of images is still an open research front. This paper proposes a new image deconvolution approach for images with Poisson statistical models, with the following building blocks: (a) a standard regularization/MAP criterion, combining the Poisson log-likelihood with a regularizer (log-prior) is adopted; (b) the resulting optimization problem (which is difficult, since it involves a non-quadratic and non-separable term plus a non-smooth term) is transformed into an equivalent constrained problem, via a variable splitting procedure; (c) this constrained problem is addressed using an augmented Lagrangian framework. The effectiveness of the resulting algorithm is illustrated in comparison with current state-of-the-art methods.

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