Compressed sensing (CS) and its relation to neural networks and deep learning

CS transformed medical imaging through the 2017 approval by the US Food and Drug Administration (FDA) of CS techniques in Magnetic Resonance Imaging (MRI), resulting in widespread use (scanners at the UiO hospitals are now run with CS). However, the success of deep learning (DL) has sparked a vast interest in the question: can DL can outperform CS in image reconstruction? Indeed, in 2018 Nature published the paper "Image reconstruction by domain transform manifold learning" representing the tip of the iceberg of DL methods promising improved performance and "... observed superior immunity to noise…" Despite the promise, DL becomes, as in the classification problem, completely unstable also for image reconstruction (however, for completely different reasons). The phenomenon can be understood by linking CS and DL. In fact, CS may be viewed as a constructive way, without any learning, to build stable neural networks for image reconstruction. The question then becomes: why do trained neural networks based on DL become unstable yet the constructed (untrained) networks based on CS remain stable?

The lecture will be given by Dr. Anders Hansen. Dr. Anders Hansen is head of the group in Applied Functional and Harmonic Analysis within the Cambridge Centre of Analysis at DAMTP. He is also Prof. II at the Institute of Mathematics, UiO.