Phase Retrieval on Real Hilbert Spaces by the Area of Parallelogram

Phase retrieval is the problem of recovering a signal from the absolute values of linear measurement coefficients, which has turned into a very active area of research. We introduce a new concept we call standard 2-norm phase retrieval on real Hilbert space via the area of parallelograms spanned by any two vectors. We will discuss what are the necessary and sufficient conditions and what is the minimal number of vectors required to allow standard 2-norm phase retrieval. We also study the relationship between the standard 2-norm phase retrieval and the phase retrieval by projections.