Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy

Gradient projection methods have given rise to effective tools for image deconvolution in
several relevant areas, such as microscopy, medical imaging and astronomy. Due to the
large scale of the optimization problems arising in nowadays imaging applications and
to the growing request of real-time reconstructions, an interesting challenge to be faced
consists in designing new acceleration techniques for the gradient schemes, able to
preserve their simplicity and low computational cost of each iteration. In this work we propose
an acceleration strategy for a state-of-the-art scaled gradient projection method for
image deconvolution in microscopy. The acceleration idea is derived by adapting a steplength
selection rule, recently introduced for limited-memory steepest descent methods
in unconstrained optimization, to the special constrained optimization framework arising
in image reconstruction. We describe how important issues related to the generalization of
the step-length rule to the imaging optimization problem have been faced and we evaluate
the improvements due to the acceleration strategy by numerical experiments on
large-scale image deconvolution problems.