Modeling, Analysis, and Implementation of Finite Difference Schemes for Nonlinear Diffusion with Applications to Image Processing




Franklin, Armelle S.

Journal Title

Journal ISSN

Volume Title



This thesis proposes to model, analyze and implement a nonlinear diffusion model problem for reduction in noise and speckle in image processing applications. Specifically, the Perona-Malik model equation that is widely studied in the image processing community is implemented via explicit and implicit finite difference algorithms. The solution methodology converts discrete image data onto a finer non-uniform grid space via interpolation techniques and applies the proposed numerical algorithms to reduce noise. These numerical algorithms are investigated analytically and computationally for appropriate choices of nonlinear diffusion coefficient functions. We derived conditions for stability and convergence of the proposed numerical algorithms. Numerical experiments are presented on benchmark problems that show the robustness and reliability of the proposed numerical schemes.



Finite difference, Image processing, Perona-Malik, Nonlinear diffusion, Noise reduction, Speckle