Almost Phase Retrieval with Few Intensity Measurements

Abstract EN

In signal processing, the phases of the measurements are often unknown.

To recover a signal of length N, Balan, Casazza, and Edidin showed that it suffices to know at least 2N-1 intensity measurements.

We give another characterization of frames which give phase retrieval for almost all signals with only N+1 intensity measurements.

We provide a method to test if a frame has this property or not.

With our method, we can construct tight frames or modify any frames such that they give almost phase retrieval.

Numerical results show that frames with this property can recover signals with high probability.