Phase Retrieval: Stability and Recovery Guarantees

Understand

We consider stability and uniqueness in real phase retrieval problems over general input sets.

• Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study conditions under which x can be stably recovered from the measurements.
• In the noise-free setting we derive a general expression on the number of measurements needed to ensure that a unique solution can be found in a stable way, that depends on the set T through a natural complexity parameter.
• This parameter can be computed explicitly for many sets T of interest.