Codes and Expansions (CodEx) Seminar

Dylan Domel-White (Vanderbilt University):
Algorithms and Guarantees for One-bit Phase Retrieval

Phase retrieval is the task of reconstructing a signal in a Hilbert space from magnitudes of linear maps applied to it. Recently, there has been some interest in "one-bit phase retrieval", i.e. performing phase retrieval after coarse quantization of the magnitude measurements. We present two algorithms for one-bit phase retrieval along with error bounds for each. The first, Principal Eigenspace Programming (PEP), allows accurate recovery from a collection of one-bit magnitude measurements in a non-adaptive way and we present both pointwise and uniform error bounds for its performance. The second, Iteratively Consistent Quantized Phase Retrieval (ICQPhase), uses the measurements in a streaming way to iteratively update the current estimate for the measure signal.