Image and signal recovery via a novel alternating golden ratio two-subgradient extragradient method

We introduce and analyze a novel two-subgradient extragradient method (TSEGM) for solving monotone variational inequality problems (VIPs) in real Hilbert spaces. Building on recent advances in extragradient-based schemes, the proposed algorithm enhances the classical TSEGM by integrating an alternating golden ratio mechanism, thereby eliminating reliance on computationally intensive linesearch procedures. A central feature of our method is a self-adaptive step-size rule that dynamically adjusts and may increase the step size during the iterations, improving both convergence efficiency and numerical stability. Under standard assumptions, we establish weak convergence and an R -linear convergence rate to a solution of the VIP governed by a monotone operator. Extensive numerical experiments demonstrate that the proposed algorithm outperforms several state-of-the-art methods in terms of speed and computational efficiency. Applications to image restoration and signal recovery further illustrate the practicality and robustness of the approach.