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

• We propose an acceleration strategy for a scaled gradient projection method.
• A recent idea, based on Ritz values, is generalized to the constrained optimization framework.
• The method is applied to solve image deconvolution problems in microscopy.
• The new approach is able to exploit a clever limited-memory implementation, very effective for large-scale problems.
• Numerical results show lower computational time compared to state-of-the-art Barzilai–Borwein-based approaches.

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 step-length 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.