In it, we show that current deep learning approaches for image reconstruction are unstable: namely, small perturbations in the measurements lead to a myriad of artefacts in the recovered images. This has potentially serious consequences for the safe and secure deployment of machine learning techniques in imaging applications.
My MSc student Qinghong (Jackie) Xu successfully defended her Master’s thesis. Congratulations!
Jackies thesis is titled “Compressive Imaging with Total Variation Regularization and Application to Auto-calibration of Parallel Magnetic Resonance Imaging”. It contains a novel (and technical) theoretical analysis of TV regularization in compressed sensing, and a new method for auto-calibration in parallel MRI. Stand by for the paper later this year!
When approximating a multivariate function defined on an irregular domain, a good choice of sampling points is critical. In this paper, my PhD student Juan and I develop new, practical sampling strategies for which the sample complexity is near-optimal: specifically, it is linear (up to a log factor) in the degree of the approximation. This improves previous approaches which were at best quadratic in the degree. Here’s the paper: