Abstract: Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Recent advances in machine learning and image processing have illustrated that it is often possible to learn inverse problem solvers from training data that can outperform more traditional approaches by large margins. These promising initial results lead to a myriad of mathematical and computational challenges and opportunities at the intersection of optimization theory, signal processing, and inverse problem theory.

In this talk, we will explore several of these challenges and the foundational tradeoffs that underlie them. First, we will examine how knowledge of the forward model can be incorporated into learned solvers and its impact on the amount of training data necessary for accurate solutions. Second, we will see how the convergence properties of many common approaches can be improved, leading to substantial empirical improvements in reconstruction accuracy. Finally, we will consider mechanisms that leverage learned solvers for one inverse problem to develop improved solvers for related inverse problems.

This is joint work with Davis Gilton and Greg Ongie.

Bio: Rebecca Willett is a Professor of Statistics and Computer Science at the University of Chicago. Her research is focused on machine learning, signal processing, and large-scale data science. Willett received the National Science Foundation CAREER Award in 2007, was a member of the DARPA Computer Science Study Group, received an Air Force Office of Scientific Research Young Investigator Program award in 2010, and was named a Fellow of the Society of Industrial and Applied Mathematics in 2021. She is a co-principal investigator and member of the Executive Committee for the Institute for the Foundations of Data Science, helps direct the Air Force Research Lab University Center of Excellence on Machine Learning, and currently leads the University of Chicago’s AI+Science Initiative. She serves on advisory committees for the National Science Foundation’s Institute for Mathematical and Statistical Innovation, the AI for Science Committee for the US Department of Energy’s Advanced Scientific Computing Research program, the Sandia National Laboratories Computing and Information Sciences Program, and the University of Tokyo Institute for AI and Beyond. She completed her PhD in Electrical and Computer Engineering at Rice University in 2005 and was an Assistant then tenured Associate Professor of Electrical and Computer Engineering at Duke University from 2005 to 2013. She was an Associate Professor of Electrical and Computer Engineering, Harvey D. Spangler Faculty Scholar, and Fellow of the Wisconsin Institutes for Discovery at the University of Wisconsin-Madison from 2013 to 2018.