An inertial viscosity algorithm for equilibrium problems with application to signal restoration

In this article, we propose an improved viscosity algorithm for solving pseudomonotone equilibrium problems. A strong convergence theorem is established under certain conditions on the bifunction, along with suitable assumptions on the initial parameters and control sequences. We present two numerical examples, one in the finite-dimensional space $\mathbb{R}^{n}$ and the other in the infinite-dimensional space $\ell ^{2}$, which demonstrate that the proposed algorithm exhibits superior computational performance compared to existing algorithms. Also, to validate the applicability of the proposed method, we applied it to a signal processing problem, confirming its effectiveness in practical scenarios.