Phase retrieval^__the recovery of a signal from the magnitude of its linear measurements^__is motivated by the fact that most of the optical devices can easily measure the intensity, rather than the phase, of the incoming light. To recover the unknown signal form only intensity measurements is a challenging task and is indeed a nonconvex quadratic inverse problem.

We present low-complexity algorithms for the phase retrieval problem based on the majorization-minimization algorithmic framework. We develop three algorithms for the oversampled phase retrieval problem and two algorithms for the undersampled phase retrieval problem. The proposed algorithms monotonically decrease their objective function value by solving a sequence of simple surrogate problems instead of the original non...[ Read more ]

Phase retrieval^__the recovery of a signal from the magnitude of its linear measurements^__is motivated by the fact that most of the optical devices can easily measure the intensity, rather than the phase, of the incoming light. To recover the unknown signal form only intensity measurements is a challenging task and is indeed a nonconvex quadratic inverse problem.

We present low-complexity algorithms for the phase retrieval problem based on the majorization-minimization algorithmic framework. We develop three algorithms for the oversampled phase retrieval problem and two algorithms for the undersampled phase retrieval problem. The proposed algorithms monotonically decrease their objective function value by solving a sequence of simple surrogate problems instead of the original nonconvex problem. We complement our analysis with extensive empirical experiments under various settings.

We also leverage phase retrieval ideas together with time-varying beamforming and phase modulation to track a multiple-input single-output channel from received signal strength feedback alone. We derive three efficient algorithms from two different channel models, namely a general slowly time-varying channel model and a specic auto-regressive channel model. Interestingly, this is the first application of phase retrieval where assuming independent and identically distributed Gaussian measurement vectors can be practically justified.