M5. Inverse Problems with Data-Driven Methods and Deep Learning

Data-driven and learning-based methods are nowadays among the leading research topics in the field of inverse problems. The growing interest in these techniques stems from their ability to extract prior information from the available training dataset and leverage this knowledge to address challenging applications. However, the ill-posed nature of inverse problems often prevents an application of learned methods as black boxes and requires a deeper mathematical understanding and analysis of the proposed techniques, incorporating insights from the underlying models, classical variational techniques, and the data itself. As a result, these approaches are frequently referred to as "hybrid models."

A common feature of these methods is their interdisciplinary nature, as they draw motivation, theoretical tools, and numerical insight from numerous areas of mathematics, including optimization, harmonic analysis, functional analysis, imaging, statistical inference, and more.

The goal of this mini-symposium is to provide an overview of recent advancements in data-driven and learning-based methods for inverse problems, bringing together experts from diverse backgrounds, as well as early-career researchers. Topics of interest include theoretical guarantees for learning-based techniques, explainability, the development of unsupervised or self-supervised approaches, and the application of modern machine learning tools, such as transformers and diffusion models.

Organizer:
Luca Ratti, University of Bologna, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.

Invited Speakers:
Sofia Agostoni, University of Genoa, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
(Deep) regularisation for multi-frame deconvolution under Poisson noise: the case of Image Scanning Microscopy

Paolo Angella, University of Genova, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Infinite-dimensional generative sensing

Duc-Lam Duong, University of Oulu, Finland, This email address is being protected from spambots. You need JavaScript enabled to view it.
Accelerating posterior sampling in Bayesian inverse problems with diffusion models

Markus Holzleitner, Johannes Kepler University, Austria,  This email address is being protected from spambots. You need JavaScript enabled to view it.
Regularized learning from functional data under covariate shift with applications to inverse problems

Alessandro Lanza, University of Bologna, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Data-driven approach for additive signal decomposition

Matti Lassas, University of Helsinki, Finland, This email address is being protected from spambots. You need JavaScript enabled to view it.
Mapping properties of neural networks and applications in inverse problems

Barbara Palumbo, Università di Genova, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Convergence Rates for Tikhonov Regularization on Compact Sets: Application to Neural Networks

Cordula Reisch, Roskilde University, Denmark, This email address is being protected from spambots. You need JavaScript enabled to view it.
An inverse problem perspective on model discovery with physics-informed neural networks

Amin Sabir, University of Bath, UK, This email address is being protected from spambots. You need JavaScript enabled to view it. 
Learned regularisation methods for light-sheet microscopy

Vu Thanh Trung (MSc), University of Cambridge, United Kingdom, This email address is being protected from spambots. You need JavaScript enabled to view it.
Plug-and-Play ADMM for Photocurrent Mapping: An Open-Source Implementation in LION