Mathematics Seminar (Monday, 31 July)

[Math]

ICTP MATHEMATICS SEMINARS


Professor G. Doris Hinestroza
(Universidad del Valle, Cali, Colombia)


"General aspects of the inverse problems and their application to 
electrical capacitance tomography"

Monday, 31 July at 15:00 hrs

Venue: Seminar Room (1st floor, ICTP Main Building)

--------------------------------------------------

Abstract: In the last twenty years, the field of inverse problems has
undergone rapid development: The enormous increase in computing power 
and
the development of powerful numerical methods made it possible to 
simulate
real-world direct problems of growing complexity.
Inverse problems have been studied for nearly a century now. In these
kinds of problems we try to find where causes for a desired or an 
observed
effect are to be determined. An important key feature, both 
theoretically
and numerically, of inverse problems is ill-posedness, i.e., they do not
satisfy the Hadamard classical requirements of existence, uniqueness and
stability, under data perturbations.  Solutions of an inverse problem
might not exist for all, it might not be unique (which raises the
practically relevant question of identification coefficients) and it 
might
be unstable with respect to errors in the data. The last aspect is
especially important, since in real-world problems, measurements always
contain noise (another source of noise being errors in numerical
procedures), and approximation methods for solving inverse problems 
which
are as insensitive to noise as possible have to be constructed, 
so-called
regularization methods.
In this talk we consider the general aspects of the inverse problems and
in particular the application of this theory to the electrical 
capacitance
tomography.