Speaker — Luca Calatroni (CMAP, École Polytechnique)
Abstract — The regularised formulation of a general ill-posed inverse problem in imaging typically combines an edge-preserving regularisation term (like the Total Variation semi-norm) and a data fitting function encoding noise statistics balanced against each other by a positive – possibly space-variant – weight. The optimal choice of such parameter is crucial to improve the image quality while avoiding overfitting, and it is a very challenging problem among the inverse problem community. When the noise level is known, classical approaches provide an estimate of such parameter based on discrepancy principles, but in many situations an accurate estimate of the noise intensity cannot be provided. In this talk we review the framework of bilevel optimisation as a powerful tool to estimate the optimal weighting where a training set of examples is provided and no prior assumption on the noise level is made.
For the design of efficient optimisation techniques we employ second-order large-scale and sampling techniques.
The applications will consider at first standard noise scenarios such as Gaussian, impulsive and Poisson distributions, which are very common in medical, microscopy and astronomy imaging. Finally, we will present more recent developments in the case of noise mixtures and of Cauchy and Rician noise settings, which are very typical, for instance, in SAR and MRI imaging problems.
Biography — Luca Calatroni is a Lecteur Hadamard research fellow at the CMAP of the École Polytechnique. He completed his PhD in November 2015 at the Cambridge Image Analysis (CIA) research group under the supervision of Carola-Bibiane Schönlieb in Cambridge, UK. After that, he has been an Experienced Researcher (ER) Marie Sklodowska-Curie fellow within the ITN Nano2fun for one year and started working at CMAP in October 2016. His research interests lie in the fields of mathematical image processing, variational modelling, non-smooth optimisation with applications to real-world applications (such as cultural heritage imaging or neuroscience). During his PhD he has been invited for a research collaboration with J. C. De Los Reyes at ModeMat (Quito, Ecuador) and more recently he has been invited at the University of Bologna for a collaboration and enrolled for teaching a PhD course in Spring 2019. He got the best paper award at the ICISP conference 2018. He has been and is currently involved in several research projects funded by EU (NoMADS EU RISE H2020 project), the CNRS (PEPS 2017 and JCJC 2018 project) and the IHP institute (RiP 2018).