Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science
MSU Affiliation
College of Arts and Sciences; Department of Mathematics and Statistics; Center for Computational Sciences
Research Mentor
Amanda Diegel
Creation Date
7-25-2025
Abstract
Image denoising is an important computational tool with applications in the medical, material science, and defense fields where CT-scans have a lot of noise that degrades quality and clearness. While there are several methods of solving image denoising problems, the one we focused on is total variation where we solve a difficult nonlinear partial differential equation that minimizes noise. There are also many numerical methods to find an approximate solution to this nonlinear partial differential equation, but the one we focus on is the finite element method. In addition, we used a fixed-point iteration method to handle the nonlinearity and obtain convergence. But the main problem arises in the number of iterations needed to achieve convergence due to the complexity of the nonlinear equations. So, we propose implementing Anderson Acceleration to speed up the fixed-point iteration method. In addition, we propose adding length and angle filtering to Anderson Acceleration to reduce redundant data and get convergence quicker. We used MATLAB along with FELICTY: Finite Element Implementation and Computational Interface Tool for You toolbox to execute the computations.
Presentation Date
Summer 7-31-2025
Keywords
image processing, Anderson acceleration, applied mathematics, finite element methods
Recommended Citation
Diegel, Amanda E.; Hanegan, Spence; Lim, Hyeona; and Tran, Hoang, "Finite Element Methods with Anderson Acceleration and its Application to Image Denoising" (2025). Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science. 18.
https://scholarsjunction.msstate.edu/ccs-reu/18
