Electrical Impedance Tomography (EIT) is a non-invasive method for imaging conductivity distributions within a target area. The inverse problem associated with EIT is nonlinear and ill-posed, leading to low spatial resolution reconstructions. Iterative algorithms are widely employed to address complex inverse problems. However, current iterative methods have notable limitations, such as the arbitrary and subjective selection of initial parameters, lengthy computational times due to numerous iterations, and the generation of reconstructions that suffer from shape blurring and a lack of higher-order detail. To address these issues, this study investigates the impact of using ISTA and FISTA iterative algorithms on the image reconstruction process in EIT. It focuses on enhancing the convergence and accuracy of EIT image reconstruction by evaluating the effectiveness of these optimization algorithms when applied to regularized inverse problems, using standard regularization techniques. ISTA and FISTA were compared to the NOSER and Newton-Raphson methods and validated through simulation and experimental results. The results show that ISTA and FISTA achieve better visualization and faster convergence than conventional methods in terms of computational efficiency when solving regularized problems, achieving conductivity reconstructions with an accuracy of above 80%. The paper concludes that while ISTA and FISTA significantly enhance EIT image reconstruction performance, the quality of the reconstructed images heavily depends on the choice of regularization methods and parameters, which are crucial to the reconstruction process.