TopMath Talk with Stefan Bamberger
"The Role of Fourier Transforms in Signal Reconstruction"
TopMath Talk Abstract
The field of compressed sensing deals with the reconstruction of signals from a minimal number of measurements. For measurements acquired by completely randomized linear transforms, provably optimal recovery guarantees can be shown, surpassing all known deterministic constructions by far. For structured matrices generated by a small number of random parameters, such as randomized Fourier transforms, still many problems are unsolved and their analysis is significantly more involved and leads to surprising connections to other mathematical fields.