SEMINARIO DI MATEMATICA
venerdì 12 aprile 2019
ore 11:00
Scuola Normale Superiore
Pisa
Aula Mancini
James Nagy
Terrà un seminario dal titolo:
“MATLAB Tools for Large-Scale Linear Inverse Problems”
Abstract:
Inverse problems arise
in a variety of applications: image processing, finance, mathematical
biology, and more. Mathematical models for these applications may involve integral equations, partial differential
equations, and dynamical systems, and solution
schemes are formulated by applying
algorithms that incorporate regularization techniques and/or statistical approaches. In most cases these solutions
schemes involve the need to solve a
large-scale ill-conditioned linear system that
is corrupted by noise and other errors. In this talk we describe
and demonstrate capabilities of a new MATLAB
software package that consists of
state-of-the-art iterative methods for solving such systems, which includes approaches that can
automatically estimate regularization
parameters, stopping iterations, etc., making them very simple to use. Thus, the package allows users to
easily incorporate
into their own applications (or simply
experiment with) different iterative
methods and regularization strategies with very little programming effort. On the other hand,
sophisticated users can also easily
access various options to tune the algorithms for certain applications. Moreover, the package includes
several test problems and examples to
illustrate how the iterative methods can be used on a variety of large-scale inverse problems.
The talk will begin with a brief introduction to
inverse problems, discuss considerations
that are needed to compute an approximate solution,
and describe some details about new efficient hybrid Krylov subspace methods that are implemented in our package.
These methods can guide users in
automatically choosing regularization parameters,
and can be used to enforce various
regularization schemes, such as sparsity.
We will use imaging examples that arise in medicine and astronomy to illustrate the performance of the
methods.
This is joint work with Silvia Gazzola
(University of Bath) and
Per Christian Hansen (Technical University of
Denmark).