Silvia Gazzola (Università di Pisa): Iterative regularization methods for solving inverse problems: classical and randomized algorithmic approaches | Joint Interdisciplinary Colloquium with the Institute for Mathematics

Iterative regularization methods for solving inverse problems: classical and randomized algorithmic approaches

Inverse problems broadly consist in recovering the causes of some observed and measured effects, and arise in many applications, such as imaging (e.g., computed tomography). Inverse problems are inherently ill-posed: even in a discrete linear setting (the one mainly adopted in this talk), regularization is pivotal in achieving meaningful solutions. This talk focuses on iterative regularization methods, mainly based on Krylov projection methods. Special emphasis is given on the so-called `hybrid projection' methods, i.e., regularization methods that combine projection onto suitable (Krylov) solution subspaces and variational regularization methods (such as Tikhonov). These solvers, when based on some standard Krylov methods, are well-established for regularizing linear inverse problems and allow adaptive choice of the regularization parameter(s). This talk will also present some novel randomized iterative solvers, which may provide (even) more efficient alternatives to their standard counterparts.

1 hour before the Gazzola's talk at 13:00h, Thomas Mach will bring everyone – PhD students, postdocs and professors alike – on the same page by providing an introduction to Krylov spaces in Bld 9, Room 1.22 reviving the What-is-…?-lectures series: What is … a Krylov subspace?

Afterwards we can socialize over some tea and coffee. 

Everyone is cordially invited!

If you want to join the institute's colloquium online, please ask Lisa Franz for the Zoom meeting details.