Phase Retrieval and System Identification in Dynamical Sampling

16.01.2023 15:00 - 16:30

Marzieh Hasannasab (Universität zu Lübeck)

Considering finite-dimensional signals evolving in time under the action of a matrix, our aim is to recover the signal up to a global phase from the absolute value of certain space-time measurements.  The loss of the phase turns the well-posed dynamical sampling into a severe  ill-posed inverse problem. Here, we combine phase retrieval in dynamical sampling with the identification of the system in case that the evolving matrix is unknown.  Using Prony's method, we establish several recovery guarantees for signal and system. The proofs are constructive, yield analytic recovery methods and the required assumptions are satisfied by almost all signals, operators, and sampling vectors.

L. Liehr and I. Shafkulovska