Abstract

Inverse problems involve the reconstruction of hidden objects from possibly noisy indirect measurements and are ubiquitous in a variety of scientific and engineering applications. This kind 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. This colloquium talk will center on discrete linear problems, offering a comprehensive overview of Krylov subspace methods for ill-posed problem —a well-established class of solvers— and delving into 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.