Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)
Fariborz Salehi, Ehsan Abbasi, Babak Hassibi
The problem of estimating an unknown signal, x0∈Rn, from a vector y∈Rm consisting of m magnitude-only measurements of the form yi=|aix0|, where ai's are the rows of a known measurement matrix A is a classical problem known as phase retrieval. This problem arises when measuring the phase is costly or altogether infeasible. In many applications in machine learning, signal processing, statistics, etc., the underlying signal has certain structure (sparse, low-rank, finite alphabet, etc.), opening of up the possibility of recovering x0 from a number of measurements smaller than the ambient dimension, i.e., $m