ROF denoising model and FETI-DP methods

Abstract

In this thesis, we discuss an image denoising problem and a parallel algorithm solving elliptic partial differential equations. Image denoising problem can be formulated as a minimization problem. As an admissible space of the minimization problem, we consider the space of functions of bounded variation, BV (Ω) which contains discontinuous functions. The proof of the existence and uniqueness of the minimizer in BV (Ω) is presented in this thesis. To get an approximate solution numerically, we present the half quadratic algorithm, which includes solving an elliptic partial differential equation. Then we propose the FETI-DP (dual-primal finite element tearing and interconnecting) method to implement the algorithm parallelly. The FETI-DP method is a non-overlapping domain decomposition method which is known to be the most scalable dual iterative substructuring method.