Two efficient three-term conjugate gradient methods for impulse noise removal from medical images

In this paper, we discuss two efficient three-term conjugate gradient methods (ECG) for impulse noise removal. The directions of ECG are first the direction of steepest descent and then spanned by the three terms: The steepest descent direction, the previous direction, and the gradient differences at the previous and current points. The second and third terms are scaled by two different step sizes called conjugate gradient parameters. Our goal is to generate and control these parameters such that they do not jointly dominate while preserving the effect of all terms, except near the optimizer where the first term dominates the other two terms. They are independent of the line search method and useful for finite precision arithmetic. The global convergence of ECG is proved. The efficiency (the lowest relative cost of function evaluations) and robustness (highest number of solved problems ) of ECG compared to known conjugate gradient methods are shown in terms of PSNR (peak signal noise ratio) and time in seconds.