Tomography: mathematical aspects and applications

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford-Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.Comment: 11 pages, 5 figure

Segmentation of image: by variational methods: A constructive approach

Sin resume

A note on elliptic BVP with jumping nonlinearities

Viene studiato il problema al contorno con jumping nonlinearities su un dominio limitato regolare $\Omega\subset\mathbf{R^{\textrm{n}}}$; $$-\Delta u=\lambda+u^{+}-\lambda\_u+g(u)+h\qquad\qquad in\quad\Omega$$ u=0\qquad\qquad\qquad\qquad\qquad\qquad su\quad\text{\ensuremath{\partial}}\Omega con g sublineareWe consider the boundary value problem with jumping nonlinearities on a bouded regular domain $\Omega\subset\mathbf{R^{\textrm{n}}}$; $$-\Delta u=\lambda+u^{+}-\lambda\_u+g(u)+h\qquad\qquad in\quad\Omega$$ u=0\qquad\qquad\qquad\qquad\qquad\qquad su\quad\text{\ensuremath{\partial}}\Omega with g sublinear

Min-max levels on the double natural constraint

A question about the possibility of using min-max methods on the double natural constraint, in spite of its lack of regularity, has been raised in some recent papers. In this note we give an answer by topological arguments which show the equivalence between constrained and unconstrained min-max classes, avoiding in this way any regularity problem