Advanced Techniques in Optimization for Machine Learning and Imaging

In recent years, non-linear optimization has had a crucial role in the development of modern techniques at the interface of machine learning and imaging. The present book is a collection of recent contributions in the field of optimization, either revisiting consolidated ideas to provide formal theoretical guarantees or providing comparative numerical studies for challenging inverse problems in imaging. The work of these papers originated in the INdAM Workshop “Advanced Techniques in Optimization for Machine learning and Imaging” held in Roma, Italy, on June 20-24, 2022.

The covered topics include non-smooth optimisation techniques for model-driven variational regularization, fixed-point continuation algorithms and their theoretical analysis for selection strategies of the regularization parameter for linear inverse problems in imaging, different perspectives on Support Vector Machines trained via Majorization-Minimization methods, generalization of Bayesian statistical frameworks to imaging problems, and creation of benchmark datasets for testing new methods and algorithms.

1.STEMPO dynamic Xray tomography phantom.- 2.On a fixed point continuation method for a convex optimization problem.- 3.Majoration Minimization for Sparse SVMs.- 4.Bilevel learning of regularization models and their discretization for image deblurring and super resolution.- 5.Non Log Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms.- 6.On the inexact proximal Gauss-Newton methods for regularized nonlinear least squares problems.

Alessandro Benfenati is an Assistant Professor at the University of Milan, Italy. He earned his Ph.D. in 2015 in Mathematics at the University of Ferrara, Italy, and became a Post-doctoral researcher in the same university. He then moved to Paris in 2016, where he continued his research activity at University Paris Est-Marne-la-valle ´e and at ESIEE, as Post-Doctoral researcher. In 2019 he came back in Italy, at University of Milan. His research interests span several areas, from inverse problems in imaging framework, using variational techniques, to Deep Learning methods for data classification, semantic segmentation and data generation. Its most recent interest regards explainable artificial intelligence (XAI) research employing Geometric Deep Learning. 

Tatiana A. Bubba is an Assistant Professor in Applied Mathematics at the University of Bath, UK. After obtaining her PhD in 2016 from the University of Ferrara, Italy, she became a postdoctoral researcher at the University of Helsinki, Finland, where she was Academy Postdoc from 2020. In 2021 she relocated to UK, with a Royal Society Newton International Fellowship at the University of Cambridge, before taking her current post at the University of Bath in 2022. Her interest lies in computational inverse problems, especially tomographic imaging, and their interaction with regularisation theory and optimisation methods, multiscale representation system like shearlets, and deep learning strategies. 

Federica Porta is an Assistant Professor in Numerical Analysis at the University of Modena and Reggio Emilia, Italy. From the same university she obtained her PhD in 2015. After a postdoctoral research period at the University of Ferrara (Italy), she got her current position. Her research interest deals with the design and analysis of optimization methods for large-scale applications arising in image processing and machine learning. 

Marco Viola is an Assistant Professor in Applied and Computational Mathematics at the University College Dublin, Ireland. He earned a PhD in Operations Research at the Sapienza University of Rome (Italy) in 2019. Later, he moved to University of Campania “L. Vanvitelli” as a postdoc first and an assistant professor later, before joining UCD on February 2023. His research is mainly devoted to nonlinear optimization, with applications to machine learning, deep learning, and image processing.