Seminario del Departamento de Matemática e Informática Aplicadas
a las Ingenierías Civil y Naval
Inverse scattering in random media
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 10:30 a 13:00. V-4 de 11:00 a 13:30.
Lugar: Aula de Seminarios de la ETSI Caminos (primera planta), UPM.