Applications in Image Processing

Abstract

In this chapter, we illustrate the usefulness of matrix-based multigrid in the field of image processing. This field is particularly suitable for uniform, rectangular grids because images are often stored in 2-d uniform arrays of pixels. We introduce algorithms for denoising noisy grayscale (noncolor) as well as color images. These algorithms are based on nonlinear elliptic PDEs. These PDEs are linearized by the fixed point iteration, and the linear elliptic PDE is discretized by the finite volume discretization method. The linear system obtained is solved by the AutoMUG(0) method. The numerical results are illustrated in images.