Guest Speakers

Yann Traonmilin (IMB, Bordeaux, France)

Title: A framework for non-convex recovery of low dimensional models in infinite dimension

Abstract: Non-convex methods for linear inverse imaging problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. This framework recovers existing results about low-rank matrix factorization and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements.

(Joint work with Jean-François Aujol and Arthur Leclaire)

Biography: After his masters degree from Telecom Paristech in 2006, Y. Traonmilin was a researcher in geophysical signal processing (CGGVeritas) where he conceived denoising methods and structural analysis tools until 2011. From 2011 to 2014, he completed a PhD where he studied mathematical foundations of the multi-image super-resolution problem (Telecom Paristech). After a 3 years post-doc at INRIA Rennes, where he studied performance guarantees for general inverse problems with low dimensional models, he joined CNRS at Institut de mathématiques de Bordeaux in 2017. Since then, he is studying mathematical foundations of inverse problems in data science with a focus on theoretical performance guarantees of convex and non-convex estimation methods for the recovery of low-dimensional models.

Martin Genzel (U. Utrecht, The Netherlands)

Title: Solving Inverse Problems With Deep Neural Networks: Robustness (and Accuracy) Included?

Abstract: In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In analogy to adversarial attacks in classification, it was shown that slight distortions in the input domain may cause severe artifacts. In this talk, we will shed new light on this concern and deal with an extensive empirical study of the robustness of deep-learning-based algorithms for solving underdetermined inverse problems. This covers compressed sensing with Gaussian measurements as well as image recovery from Fourier and Radon measurements, including a real-world scenario for magnetic resonance imaging (using the NYU-fastMRI dataset). Our main focus is on computing adversarial perturbations of the measurements that maximize the reconstruction error. In contrast to previous findings, our results reveal that standard end-to-end network architectures are not only surprisingly resilient against statistical noise, but also against adversarial perturbations. Remarkably, all considered networks are trained by common deep learning techniques, without sophisticated defense strategies. If time permits, we will also relate our results to the aspect of accuracy, which is discussed in the context of the recent AAPM Sparse-View CT Challenge.

This is joint work with Maximilian März and Jan Macdonald (both TU Berlin).

Biography: Martin Genzel received his B.S. and M.S. in Mathematics in 2013 and 2015, respectively, from the Technical University Berlin (Germany). There he also received his Ph.D. degree in 2019, based at the Applied Functional Analysis Group. He is now a postdoctoral researcher with Sjoerd Dirksen at the Mathematical Institute of Utrecht University. His research is focusing on topics at the interface of applied mathematics, signal processing, and machine learning, in particular, inverse problems, compressed sensing, high-dimensional statistics, and deep learning.