Description
The 9th Seminar:
Date and Time: March 2nd 6:00pm – 7:00pm(JST) 10:00am-11:00pm(CET)
Venue: Zoom webinar
Language: English
Speaker: Michael Unser, Biomedical Imaging Group, EPFL-CIS, Switzerland.
Title: New representer theorems for inverse problems and machine learning
Abstract:
Image reconstruction from a finite number of measurements and supervised learning share a common feature: they both are fundamentally ill-posed. In practice, this indetermination is dealt with by imposing constraints on the solution; these are either implicit, as in neural networks, or explicit via the use of a regularization functional. In this talk, I present a unifying perspective that revolves around a new representer theorem that characterizes the solution of a broad class of functional optimization problems. I then use this theorem to derive the most prominent classical algorithms — e.g., kernel-based techniques and smoothing splines — as well as their “sparse” counterparts. This leads to the identification of sparse adaptive splines, which have some remarkable properties.
I then show how these results can guide the design of deep, as well as not-so-deep, spline-based neural architectures that extend the classical ReLU nets.
Bio:
Michael Unser is Full Professor at the EPFL and the academic director of EPFL’s Center for Imaging, Lausanne, Switzerland. His primary areas of investigation are biomedical imaging and applied functional analysis. He is internationally recognized for his research contributions to sampling theory, wavelets, the use of splines for image processing, stochastic processes, and computational bioimaging. He has published over 400 journal papers on those topics. He is the author with P. Tafti of the book “An introduction to sparse stochastic processes”, Cambridge University Press 2014. From 1985 to 1997, he was with the Biomedical Engineering and Instrumentation Program, National Institutes of Health, Bethesda USA, conducting research on bioimaging. Dr. Unser has served on the editorial board of most of the primary journals in his field including the IEEE Transactions on Medical Imaging (associate Editor-in-Chief 2003-2005), IEEE Trans. Image Processing, Proc. of IEEE, and SIAM J. of Imaging Sciences. He is the founding chair of the technical committee on Bio Imaging and Signal Processing (BISP) of the IEEE Signal Processing Society. Prof. Unser is a fellow of the IEEE (1999), an EURASIP fellow (2009), and a member of the Swiss Academy of Engineering Sciences. He is the recipient of several international prizes including five IEEE-SPS Best Paper Awards, two Technical Achievement Awards from the IEEE (2008 SPS and EMBS 2010), the Technical Achievement Award from EURASIP (2018), and a recent Career Achievement Award (IEEE EMBS 2020). He was awarded three ERC AdG grants: FUNSP (2011-2016), GlobalBioIm (2016-2021), and FunLearn (2021-2026).
