Pixel Club: Vectorial Phase Retrieval for 1-d Signals and 2-d Images

Boaz Nadler (Weizmann Institute of Science)
Tuesday, 26.11.2013, 11:30
Room 337 Taub Bld.

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.

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