Research Staff Scientist, CIBM SP EPFL Mathematical Imaging Section.
Abstract
Algorithms to solve inverse problems are at the core of imaging, where they are known as image reconstruction methods. These methods recover the desired images from the indirect measurements provided by physical measurement devices such as PET, MRI, or EEG systems. Medical imaging critically depends on the guarantees these methods provide to inform diagnostic and treatment decisions. Of specific relevance is how stable they are–how much the recovered image changes when the measurements change slightly. In this talk, I will first briefly present a unified understanding of the history of image reconstruction. Then, I will clearly lay out the stability guarantees provided by different modern image reconstruction methods, focusing on our own work on the stability of Lp-regularization strategies.