Noticias en español
Simultaneous identification of piecewise constant sound speed and initial data for the photoacoustic tomography problem
RESUMEN: Photoacoustic tomography is a biomedical imaging modality whose goal is to reconstruct a map of absorption in biological tissue in order to identify different structures, and in particular to determine whether they are healthy or not. This modality has multiple applications, including tumor detection, breast cancer diagnosis, imaging of blood vessel networks, and measuring blood oxygenation. In this talk, we will focus on acoustic inversion—one of the steps of photoacoustic tomography—in the case where the speed of sound is an unknown piecewise constant function....
Read MoreThe Fractional Anisotropic Calderón Problem
RESUMEN: We will discuss some recent progress on the anisotropic Calderón problem for the fractional Laplacian.
Read MoreInverse scattering for asymptotically hyperbolic manifolds.
RESUMEN: On compact Riemannian manifolds with boundary, the (anisotropic) Calderón’s problem asks to what extent the Dirichlet-to-Neumann map associated with the Laplace—Beltrami equation determines the metric (up to a natural obstruction). In this talk, I will discuss a similar problem, known as inverse scattering for asymptotically hyperbolic manifolds (i.e., manifolds that, outside a compact region, behave like the hyperbolic space): fixed an “energy level”, and given the analog of the Neumann data for solutions to certain 0-elliptic PDE depending on the fixed energy...
Read MoreFully Stochastic Reconstruction for Inverse Radiative Transport.
RESUMEN: The Radiative Transport Equation (RTE) arises in applications in tomography based on photon propagation. Whereas it has a direct solution for non-scattering media it is complicated to solve for cases involving significant scattering. In these cases, Monte Carlo (MC) methods are a widely applicable and accurate class of modelling techniques that converge to the deterministic solution in the limit of an infinite number simulated photons. Classical methods for solving the inverse problem that involve a non-linear optimisation approach can be combined with advances in stochastic...
Read MoreUn problema inverso de interfaz y su aplicación para el modelamiento de sismos de subducción.
RESUMEN: La costa del Pacífico es una zona con alta actividad sísmica. En los últimos 100 años, Chile ha sufrido 7 terremotos de magnitud 8.0 o superior, causando graves daños a diversas edificaciones, cambiando la geografía local y causando la muerte de miles de personas. De todos ellos, los más destructivos han sido sismos de subducción (Valdivia 1960, Constitución 2010). Un sismo de subducción puede ser modelado como la interacción de dos cuerpos donde uno se desliza con respecto al otro sobre una superficie, o bien, a partir de un único dominio dividido en dos subdominios con una...
Read MoreThe inverse elasticity problem, its extension to porous media and applications in biomedicine.
RESUMEN: The inverse elasticity problem can be simply stated as: given a deformed configuration and the forces that act on it, find an initial stress-free configuration such that when the given forces are applied to it, one recovers the given deformed configuration. Surprisingly, this problem can be framed as a (direct) elasticity one, whose mathematical properties are inherited from the original direct problem if the underlying material is sufficiently regular. In this seminar, I will review this problem and its main mathematical properties. After this brief introduction, I will show some...
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