Compressed Sensing and Deep Learning - Investigation of stability properties for linear inverse problems

Abstract

Deep Learning (DL) has already begun to find its way into the computational scientist's toolkit, yet the amount of material on numerical analysis of these techniques is somewhat lacking. In recent years, an instability phenomenon has been discovered when DL is used to solve certain problems in computational science, namely, in inverse problems in imaging. In this thesis, we give a brief introduction to compressed sensing and neural networks, take a closer look at the instability phenomenon in Neural Networks (NN) used for inverse problems through the eyes of numerical stability, and compare DL methods to the more well-established scientific techniques in image reconstruction, namely, Compressed Sensing (CS).