A03 Group actions and t-designs in sparse and low rank matrix recovery

The aim of this project is to systematically employ group theoretic methods for the construction of measurement schemes for sparse and low rank matrix recovery, as well as phase retrieval. We intend to provide explicit constructions of measurement schemes arising from single or finitely many group orbits, to numerically test their potential for signal and low rank matrix recovery, and to formulate and prove theoretical recovery guarantees. We will consider measurement schemes obtained as randomly sampled points in designs, as well as measurements arising from the actions of finite Weyl-Heisenberg and affine groups.