Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Vector recovery from saturated frame coefficients

Vortrag von Prof. Dr. Daniel Freeman

**Datum:** 29.11.23 **Zeit:** 16.30 - 17.30 **Raum:** ETH HG E 1.2

'A frame (x_j) for a Hilbert space H allows for a linear and stable reconstruction of any vector x in H from the linear measurements (). However, there are many situations where some information of the frame coefficients is lost. In applications such as signal processing, electrical engineering, and digital photography one often uses sensors with an effective range and any measurement above that range is registered as the maximum. Depending on the context, recovering a vector from such measurements is called either declipping or saturation recovery. We will discuss a frame theoretic approach to this problem in a similar way to what Balan, Casazza, and Edidin did for phase retrieval. This perspective motivates many interesting open problems. The talk is based on joint work with W. Alharbi, D. Ghoreishi, B. Johnson, and N. Randrianarivony.'