Fecha: 3 y 4 de noviembre de 2016.
Hora: J-3 de noviembre de 10:30 a 13:00. V-4 de noviembre de 11:00 a 13:30.
Lugar: Aula de Seminarios de la ETSI Caminos (primera planta), UPM.
Título. Inverse scattering in random media
Conferenciante. Pedro Caro (Basque Center for Applied Mathematics)
Resumen. In inverse scattering theory the aim is to determine a
scattering potential from appropriate measurements. In many applications
the scatterer is non-smooth and vastly complicated. For such scatterers,
the inverse problem is not so much to recover the exact micro-structure
of an object but merely to determine the parameters or functions
describing the properties of the micro-structure. An example of such a
parameter is the local strength of the scatterer, which shows how
realizations oscillate around the mean. In mathematical terms, the
potential is assumed to be a Gaussian random function whose covariance
operator is a classical pseudo-differential operator. The local strength
is represented by the principal symbol of the covariance operator.
The goal of this mini-course will be to show that the backscattered
field, obtained from a single realization of the random potential,
determines uniquely its local strength.Throughout the course we will
discuss the notion of generalized random functions and the regularity of
Gaussian microlocally isotropic random fields. We will give an overview
of the forward scattering problem for this class of potentials.
Eventually, we show how we can reconstruct the local strength from some
average on the backscattering data.
The course will be based on a joint work with Tapio Helin and Matti Lassas.
Fecha: 3 y 4 de noviembre de 2016.
Hora: J-3 de noviembre de 10:30 a 13:00. V-4 de noviembre de 11:00 a
13:30.
Lugar: Aula de Seminarios de la ETSI Caminos (primera planta), UPM.
