Algoritmo forward-backward multimalla con aplicación al problema de supresión de ruido en una imagen.

Abstract

Throughout history, optimization problems have generated great interest in the scientific community, leading to the development of theories and algorithms that determine the solution, or approximation of it, of this branch of mathematics. Image processing is a field that involves optimization. This branch of research has been studied, with greater intensity in recent decades, for the diversity of applications such as: satellite images, X -ray images, computerized tomography, etc. Within this diverse set of applications associated with optimization problems, those that due to their extensive number of variables are called large -scale optimization problems arise. Multigrid methods were developed to address large -scale problems. Then a natural question emerges, is it possible to design a multigrid algorithm from the Forward-Backward Splitting Method method in such a way that they approach the solution of a large scale optimization problem? With the aim of answering the question asked, we are preparing to develop a multigrid algorithm derived from the Forward-backward Splitting Method method. To do this, we will first design the problem of lower dimension and a certain condition that relates both the original problem and the problem of lower dimension. Then, we will build a decrease address for the directional derivative of the original problem. Finally, we will indicate the best way to perform a linear search that provides a quasi-Fejér-monotonicity in the line search iteration, inherent property of the Forward-backward method.