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)

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.

3 y  4 de noviembre de 2016.
Hora:   J-3 de 10:30 a 13:00. V-4 de 11:00 a 13:30. 
Aula de Seminarios de la ETSI Caminos (primera planta), UPM.