13. November 2018
Seminar Room, Wohllebengasse 12-14 / Ground Floor
Stability analysis for phase retrieval - Rima Alaifari
Abstract: Stability analysis for phase retrieval
Rima Alaifari, Department of Mathematics, ETH Zürich
In phase retrieval problems, a signal is sought to be reconstructed from only the magnitudes of a set of complex measurements. The missing information of the phase of the measurements severely obstructs the signal reconstruction.We study this problem in the setting where the signal belongs to an infinite-dimensional Hilbert space. This problem is inherently unstable, i.e. highly sensitive to noise in the measurements. We show that in some sense this property is independent of the redundancy of the measurements. However, the instabilities observed in practice are all of a certain type. Motivated by this observation, we introduce a new paradigm for stable phase retrieval.We demonstrate that in audio processing applications this new notion of stability is natural and meaningful and that in this new setting stability holds for certain measurement systems. This is joint work with I. Daubechies (Duke University), P. Grohs (University of Vienna) and R. Yin (Duke University).