# Banach Bregman Mini

## Title
Bregman-based optimisation approaches for imaging inverse problems

## Abstract
Variational regularisation approaches for non-Hilbertian structures have in recent years become increasingly popular for imaging inverse problems. Bregman divergence is a natural notion of distance for many problem domains, and thus plays a crucial role algorithmic development and theoretical analysis. Moreover, Bregman divergence has been instrumental in optimisation, either as a regularisation tool or as inspiration for proximal-type algorithms. It has also found utility in enhancing the interpretability of certain neural networks. In this minisymposium, we emerging and senior experts working in this field and present some recent advances on this topic, showing their effectiveness and performance on a variety of image reconstruction problems.

In the field of imaging inverse problems, variational regularisation approaches tailored to non-Hilbertian structures have become extremely popular over the last years. Bregman divergences are a crucial analytical tool for these methods: they serve to quantify distances w.r.t. the underlying non-quadratic metric, allowing rigorous estimates and proofs also in Banach space scenarios. In the context of optimisation, Bregman divergences have shown to be a powerful regularisation tool and have also been employed to generalise proximal-like algorithms. Moreover, Bregman-like frameworks have recently been employed as an explainable tool for the analysis of neural networks.
In this minisymposium, we gather both experts and young researchers in this field and present some recent advances on this topic, showing their effectiveness and performance on a variety of image reconstruction problems.

## Invited speakers
- [x] kristian bredies
- [ ] bangti jin
- [ ] michael unser
- [x] ~~elena resmerita -- > Luca?~~
- [ ] Qinian Jin
- [ ] Jerome Bolte
- [ ] Tim Roith/Leon Bungert
- ~~[ ] Luca/Marta/Claudio~~ I am speaking elsewhere, Marta will have finished by then and Claudio can't make it
- [x] Martin Benning --> Luca?
- [x] ~~Emilie Chouzenoux~~
- [x] M'hamed Essafri --> Luca? (my PhD student and a CNRS researcher with whom I am working on Bregman relaxation of l_0 norm)
- [ ] Mirjeta Pasha - https://link.springer.com/article/10.1007/s11075-020-01004-6
- [ ] Alessandro Buccini https://scholar.google.com/citations?hl=en&user=lztFiJ0AAAAJ&view_op=list_works&sortby=pubdate
- [ ] Panos Patrinos
- [x] Tony
- [ ] Leclaire/Kamilov/Hurault/Papadakis

## Accepted
1. Martin Benning **Title** *Bregman-based inversion of second-order residual networks*
2. M'hamed Essafri **Title** *Generalized Relaxations of $\ell_0$-Regularized inverse problems with non-quadratic data terms*

## Invitation letter
Dear [NAME]

I hope you are doing well.
We are planning to organise a minisymposium entitled **Bregman-based optimisation approaches for imaging inverse problems**
at the in-person SIAM conference on Imaging Sciences (https://www.siam.org/conferences/cm/conference/is24), which will take place from May 28-31, 2024 in Atlanta, Georgia, USA.
Please find a tentative abstract at the end of this email.

Given your expertise and contributions in this field, we would be delighted if you could present a talk at our mini-symposium. Your work on [] would be particularly interesting and befitting, but please feel free to suggest a different topic.

Please note that we cannot cover any costs related to the participation in this conference. We hope you will be able to join us and would greatly appreaciate if you could provide a response soon (by 20 October).
If you are interested in participating, we kindly ask for a tentative title for your talk.
Alternatively, if you are unavailable but can recommend a researcher or colleague who would be a valuable addition to our minisymposium, please let us know.
Note that the conference allows **only one talk per speaker**.

Should you have any comments or questions please don’t hesitate to reach out to us.

Best
Luca Calatroni
Zeljko Kereta

Abstract