A new family of Polak–Ribière–Polyak conjugate gradient method for impulse noise removal

Abstract

In this paper, impulse noise removal problem is formulated as an unconstrained optimization problem with smooth objective function. It can be solved by conjugate gradient methods with desired properties (low memory and strong global convergence) in high dimensions. Accordingly, a family of the Polak-Ribière-Polyak (PRP) conjugate gradient directions is constructed for which the descent condition holds. In other words, we introduce four improved versions of PRP method three of which are based on a regularization and one of which is the combination of Fletcher-Reeves and PRP conjugate gradient parameters. Using several images, it is shown that the new methods are very robust and efficient in comparison with other competitive methods for impulse noise removal, especially in terms of the peak signal to noise ratio (PSNR).