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
Hyeona Lim
Creation Date
7-25-2025
Abstract
Current image denoising algorithms based on variational methods can suffer from slow convergence or no convergence due to high nonlinearity of the images. To speed up the convergence of denoising, we apply Anderson acceleration to the fixed-point image denoising problem. Anderson acceleration is an algorithmic method for reducing the number of fixed-point iterations necessary for convergence. It involves using weighted updates to each iteration based on the weighted residuals from past iterations, or history. By using finite difference methods, we can approximate the gradient and higher-order partial derivatives at points on the image. We then use these approximations to create matrix equations to solve for a denoised image. By iterating and applying Anderson Acceleration, we achieve a faster convergence of image denoising. This method is tested and compared to the fixed-point method and other conventional denoising methods using peak signal to noise ratio (PSNR).
Presentation Date
Summer 7-31-2025
Keywords
image denoising, Anderson Acceleration, applied mathematics, finite difference methods
Recommended Citation
Diegel, Amanda E.; Hanegan, Spence; Lim, Hyeona; and Tran, Hoang, "Efficient Image Denoising Models with Anderson Acceleration using Finite Difference Methods" (2025). Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science. 17.
https://scholarsjunction.msstate.edu/ccs-reu/17
