Developments on Finite Element Methods for Medical Image Supported Diagnostics

Variational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. For this work we consider a second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a regularized functional and to locally analyse the obtained solution. Some parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.