Inverse problems involve the reconstruction of hidden objects from possibly noisy indirect measurements and are ubiquitous in a variety of scientific and engineering applications. These kinds of problems have two main features that make them interesting yet challenging to solve. First, they tend to be ill-posed: the reconstruction is very sensitive to perturbations in the measurements. Second, real-world applications are often large-scale, resulting in computationally demanding tasks.
Suitable discretizations of linear inverse problems give rise to linear systems, allowing the use of powerful numerical linear algebra tools to solve them. In this talk, I will give a comprehensive overview of Krylov subspace methods for ill-posed problems, and I will discuss their regularization properties. Additionally, I will explore recent advancements that enhance their efficacy in tackling more complex optimization tasks. The presentation will feature results and examples drawn from various imaging applications, providing insights into the practical implications of these approaches.
Monday, February 12
For those joining remotely, email Malena Espanol for the Zoom link.
Malena Sabate Landman
Department of Mathematics