The Taub Faculty of Computer Science Events and Talks
Boaz Nadler (Weizmann Institute of Science)
Tuesday, 26.11.2013, 11:30
Phase retrieval - namely the recovery of a signal from its absolute Fourier
transform is a problem of fundamental importance in many fields.
In 1-D Phase retrieval is ill-posed, admitting multiple solutions.
In 2-D it often admits a unique solution, but finding it is challenging.
Current iterative algorithms are computationally intensive and in general have no
theoretical guarantees on the properties of their obtained solution.
In this talk I'll present a novel framework, denoted vectorial phase retrieval.
The key underlying idea is that in many physical scenarios one can measure
not only one signal, but also another independent one, and their interference.
From a mathematical perspective, We show that this novel framework leads to
uniqueness already in the 1-D case. We next derive
computationally efficient and robust to noise algorithms
for recovery of the phases under several 1-D and 2-D settings
of practical physical interest.
We illustrate the reconstruction performance of our
algorithms both with simulated signals, as well as on actual experimental 2-d data.
We conclude with some yet unresolved challenges - mathematical, statistical and computational.