Fabio Marcuzzi

Giulia Deolmi, Fabio Marcuzzi

This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a projected damped Gauss-Newton, in the second one it is ill-posed and an adaptive parametrization with time localization will be adopted to regularize it. To solve the optimization loop a model reduction technique (Proper Orthogonal Decomposition) is used.

Marco Virgulin, Marco Castellaro, Enrico Grisan et al.

In this paper we propose a deterministic approach for the reconstruction of Dynamic Susceptibility Contrast magnetic resonance imaging data and compare it with the compressed sensing solution existing in the literature for the same problem. Our study is based on the mathematical analysis of the problem, which is computationally intractable because of its non polynomial complexity, but suggests simple heuristics that perform quite well. We give results on real images and on artificial phantoms with added noise.