The 2nd International Conference on Applied Mathematics, Informatics, and Computing Sciences (AMICS 2023)

Abstract: In recent years, the concept of sparsity has played a major role in various problems of applied mathematics and engineering sciences. We will review some of these developments from a personal point of view. The review will include wavelet denoising, sparsity-enforcing regularization for inverse problems, compressive sampling, as well as lasso and elastic net strategies for variable selection in statistics and learning theory, with applications in computer vision, genetics, economics and finance.
Theoretical progress in such matters would have been less significant if not going in parallel with the development of efficient numerical algorithms to compute the solutions. We will also review some of these algorithms for sparse recovery, with particular emphasis on the so-called iterative soft-thresholding algorithm and its descendants. We will also show how they can, in some cases, shed some light into the black box of neural networks.

Biography: Christine De Mol is a Professor at the `Université Libre de Bruxelles' (ULB) and a member of the Royal Academy of Science, Letters and Fine Arts of Belgium (`Académie royale de Belgique, classe des sciences’). She holds a Ph.D. in Physics (1979) and a habilitation degree in Mathematical Physics (1992) from ULB. Since 1975, she has held several research positions with the Belgian National Fund for Scientific Research (FNRS). She left the FNRS in 1998 as an Honorary Research Director to become a full-time Professor at ULB, where she is affiliated with both the Mathematics Department and the European Centre for Advanced Research in Economics and Statistics (ECARES). She has also held several visiting positions at the Universities of London, Rome, Montpellier, Paris-Sud, Genoa, Bonn and St. Gallen. In 2012 and 2013, she served as the elected Chair of the SIAM Activity Group on Imaging Science. She is an Associate Editor of the `SIAM Journal on Imaging Sciences’ and a member of the Editorial Board of the journal `Numerical Functional Analysis and Optimization’. She is the author or co-author of more than eighty publications (see her Google Scholar profile) and a co-author with M. Bertero and P. Boccacci of the textbook `Introduction to Inverse Problems in Imaging’. Her research interests in applied mathematics include inverse problems, sparsity-enforcing regularization theory, wavelets and applications, learning theory, portfolio theory in finance, as well as the analysis and forecasting of high-dimensional time series.