Phaseless super-resolution is the problem of reconstructing a signal from low-frequency (super-resolution) Fourier magnitude (phaseless) measurements, and is the combination of two classical signal processing problems. We consider the setting in which the signal to be recovered is sparse, and the measurements consist of the magnitudes of the low-frequency Fourier coefficients of certain masked versions of the signal. We develop a single convex optimisation problem for phaseless super-resolution that, in the noise-free setting, recovers sparse signals (satisfying a minimum separation condition) from a near-optimal number of phaseless masked measurements. We also establish stability guarantees for approximate recovery in the presence of measurement noise.
Joint work with: Kishore Jaganathan (Illumina), Maryam Fazel (University of Washington), Yonina Eldar (Technion), Babak Hassibi (Caltech)