Saeed Karimi

In this thesis, we have done image denoising via Partial Differential Equations (PDEs) models, which is known as the Bazan equation (Bilateral-filter-based model). For this purpose, first we have discretized the equations with the Crank-Nicholson finite difference method and then compared the results of using several iterative solvers. The iterative methods used in this research were; Successive Over-Relaxation(SOR), Jacobi, Gauss-Seidel, Steepest Descent, Least Squares method and an advanced iterative method called Hybrid BiCGSTAB(l) method, which is the result of combining two iterative methods. Then, using the Particle Swarm meta-heuristic Optimization(PSO) algorithm, we optimized the solutions obtained from the BiCGSTAB(l) method as well as combination of the two BiCGSTAB(l) and the Successive Over-relaxation methods in image denoising. The obtained PSNR and SSIM values show better and more effective results in denoising and image improvement.