Scaling techniques for gradient projection-type methods in astronomical image deblurring

Abstract

The aim of this paper is to present a computational study on scaling techniques in gradient projection-type (GP-type) methods for deblurring of astronomical images corrupted by Poisson noise. In this case, the imaging problem is formulated as a non-negatively constrained minimization problem in which the objective function is the sum of a fit-to-data term, the Kullback–Leibler divergence, and a Tikhonov regularization term. The considered GP-type methods are formulated by a common iteration formula, where the scaling matrix and the step-length parameter characterize the different algorithms. Within this formulation, both first-order and Newton-like methods are analysed, with particular attention to those implementation features and behaviours relevant for the image restoration problem. The numerical experiments show that suited scaling strategies can enable the GP methods to quickly approximate accurate reconstructions and then are useful for designing effective image deblurring algorithms.

2010 AMS Subject Classifications:

• 68U10
• 65K05
• 65F22

Keywords:

• image deblurring
• gradient projection methods
• Newton projection methods
• regularization algorithms

Acknowledgements

This research is supported by the PRIN2008 project of the Italian Ministry of University and Research Optimization Methods and Software for Inverse Problems, grant 2008T5KA4L. The authors are thankful to the anonymous referees for their useful comments and suggestions.