Forum Numerica - Elena Morotti: A new framework for learning-based iterative minimization with applications to image processing

Inverse problem-based image processing is an active research field that has been recently revolutionized by the advent of convolutional neural networks, as deep learning-based schemes often yield superior results than classical optimization approaches. However, their ability to actually compute the inverse problem solution is still questionable and discussed in the literature, where unstable results have been reported both numerically and theoretically.
In this talk, I present a new hybrid scheme, called RISING, embedding deep learning tools in an optimization approach. Numerical results and theoretical aspects will be discussed, showing that RISING preserves the convergence properties of iterative solvers and, at the same time, it exploits the accuracy and flexibility of data-driven approaches.
As case study, tomographic image reconstruction from subsampled projection data will be mainly considered.

Elena Morotti is a junior assistant professor at the Department of Political and Social Sciences, since 2021. After the Master Degree in Mathematics at Bologna, she received her PhD in Applied Mathematics at the University of Padova in 2018 and she was a research fellow at the Department of Computer Science and Engineering in Bologna.
Her researches mainly concern the implementation and application of algorithms for medical image restoration and reconstruction, based on regularized inverse problem formulations with variational tools or neural networks.
In 2018-2020, she also developed projects with Virtual Reality technologies.
She is a founding member of the Learning and Optimization for Imaging in Bologna (LOIBO) research group and member of the Virtual and Augmented Reality Laboratory (VARLAB) and of the Computational Social Science Center (CssC).