Phase retrieval from very few measurements

Understand

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available.

• To reconstruct the signal, one must perform a process known as phase retrieval.
• This paper focuses on completely determining signals with as few intensity measurements as possible, and on efficient phase retrieval algorithms from such measurements.
• For the case of complex M-dimensional signals, we construct a measurement ensemble of size 4M-4 which yields injective intensity measurements; this is conjectured to be the smallest such ensemble.